Journal of Sound and Vibration (10958568)570
Non-uniformity and damage are the two primary subjects in studying the vibrations of the beam-type elements. An exact closed-form explicit solution for the transverse displacement of a non-uniform multi-cracked beam with any type of boundary conditions is introduced. The generalized functions and the distributional derivative concepts are adopted. Four fundamental functions are introduced. These functions make the boundary conditions' process and compute the frequency equation more convenient. By introducing the non-dimensional parameters, the non-dimensional motion equation of the damaged beam with an arbitrary count of cracks is derived, and its exact closed-form explicit solution is obtained based on the four introduced fundamental functions. The standard method of computing these functions is presented, and the closed-form of these functions is determined for eight cases like uniform and conical beams. The closed-form of the frequency equation and mode shapes of the non-uniform multi-cracked beam are derived for several boundary conditions. The influence of the count of cracks, their location and intensity, and the boundary conditions on the natural frequency and mode shape are assessed by running a numerical study. The first and second frequencies of a conical beam are computed to verify the obtained results by applying this newly presented closed-form solution and the Differential Quadrature Element Method. A good agreement is evident when the obtained results are compared. © 2023
Structural Engineering and Mechanics (12254568)91(1)pp. 87-102
In recent years, the focus on vibration analysis of multilayer smart structures has attracted considerable attention in many engineering applications. In this work, vibration analysis of a three-layer microporous beam with a core amplified by a composite material reinforced with graphene platelets and two piezoelectric thin films is discussed. It is assumed that piezoelectric layers with a thickness of 0.01 core are very thin and the properties of the matrix and reinforcement vary in the thickness directions. The governing equations of motion are obtained using an energy approach and the method of numerical differential quadrature to solve them. The results of this work are compared to other research and there is good agreement between them. The influences of the volumetric weight fraction of graphene wafers, different graphene platelets distributions, porosity distribution, mass scale parameters and thin ratio of graphene platelets take into account the natural dimensionless frequencies of the micro-beam. The results of this study show that the symmetric distribution of graphene platelets based on the symmetric porosity distribution has a great influence on the natural frequencies without basic dimension of the micro-beam, while the shape ratios of graphene platelets do not have a significant influence on natural frequency changes. Copyright © 2024 Techno-Press, Ltd.
Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering (09544100)238(9)pp. 856-873
The aim of this work is to investigate the flutter characteristics of nanocomposite cantilever trapezoidal plates with non-uniform thickness enriched with either carbon nanotubes (CNTs), graphene nanoplatelets (GNPs), or graphene oxide powders (GOPs) which are distributed functionally graded (FG) in the axial direction. It is assumed that the thickness of the plate and the volume fraction of the nanofillers vary in one direction from the wider clamped edge of the plate to the outer narrower free one. The modeling of the plate is done using the first-order shear deformation theory (FSDT) and the aerodynamic pressure generated by the aerodynamic pressure is modeled using the linear approximation of the piston theory. The material properties of the plate are calculated using the mixing rule (ROM) and the Halpin–Tsai model. The governing equations and boundary conditions at the clamped and free edges of the plate are derived via Hamilton’s principle. An approximate solution is applied using the differential quadrature method (DQM) to calculate the natural frequencies and the damping ratios of the plate. Numerical examples show that it is possible to find an optimal thickness variation profile that provides the greatest aeroelastic stability. It is concluded that by considering the same value for the mass fractions of the nanofillers, the highest aeroelastic stability can be attained by utilizing the GNPs as the reinforcers. It is found that to attain further improvement in aeroelastic stability, most nanofillers should be distributed near the clamped edge and away from the outer free edge. © IMechE 2024.
Sharifi d., D.,
Torabi, K.,
Rahaghi, M.I.,
Shahbazi, H. Journal Of The Brazilian Society Of Mechanical Sciences And Engineering (16785878)45(3)
Most of the researches conducted in the multirotors field can be divided in two parts of structure and layout of the new flying propellers and designing controllers fit for the desired performance. One of the issues stated in this study is the limitation of independent control of 6 DoF for the aerial vehicle with conventional structure such as octarotors. Conventional aerial vehicles are only capable of controlling in 4 DoF. This is because all rotors are placed in one plane and the resulting thrust force is parallel. The presented paper aims to create a novel structure in the configuration of the rotors of an octarotor to realize the capability of controlling the position and angle of the octarotor independently and going through a predetermined path and being in specific directions. The proposed model offers the capability of changing the octarotor speed and angle of the four arms for controlling purposes. Also, to optimally provide the maneuverability of the aerial vehicle a robust controller using neural networks and reinforcement learning is proposed to determine these velocities and angles. Therefore, the ability to control the octarotor with 6 DoF independently, ability to track path and statues of the octarotor, and also, robustness against external forces, variation in payload weight, and possible disturbances in motor performance are the results of this study. Finally, simulation results for the mentioned abilities are presented and examined. © 2023, The Author(s), under exclusive licence to The Brazilian Society of Mechanical Sciences and Engineering.
In this research, the problem of controlling a one-link robot with joint flexibility by the non-linear model predictive control method (NMPC) is considered. The issue concerning the input-to-state stability (ISS) of the NMPC has been considered. Through using the cost function of the NMPC problem in order to play the role of the Lyapunov function, the ISS stability of the system in the presence of disturbances and uncertainties, such as robot joint flexibility, is reached. Two modeling examples for a single-link robot have been investigated, which include unmeasurable variables as a portion of the system state variables. These unmeasured states are representative of the unmodeled dynamics, standing for either the flexibility at the joint or the link itself. In the first example, the control input is the actuation torque, and in the second one, the voltage to the motor. Simulation results demonstrate the effectiveness and stability of the proposed approach in the presence of disturbances and system uncertainties. © 2023 IEEE.
Journal of Sandwich Structures and Materials (15307972)24(2)pp. 1313-1339
A novel angle graded auxetic honeycomb (AGAH) core is designed for sandwich structures in the present study. The angle of the cells is varied through the thickness of the AGAH core using linear functions. Therefore, the thickness of the cell walls is kept constant along the gradation of the cell angle, and the length of the cell walls is changed through the core thickness as the result of angle variation. New analytical relations are proposed to predict the equivalent elastic properties of the AGAH core. The performance of the new proposed core is analytically assessed for the vibrational behavior of a sandwich plate. The governing equations are deduced adopting Hamilton’s principle under the assumption of quasi-3D exponential plate theory. Three-dimensional finite element (3D-FE) simulation is accomplished to verify the analytical results of the vibrational response of the sandwich structure. The influence of variation of the cell wall, the cell angle and cell aspect ratio of AGAH core, and geometric parameters of the sandwich structure are investigated on the vibration response of the sandwich panel. The present graded design of the auxetic honeycomb enhances the specific stiffness (i.e., stiffness to density ratio) and consequently increases the natural frequencies of sandwich structures with this type of core. © The Author(s) 2021.
Mechanics Based Design of Structures and Machines (15397742)50(3)pp. 969-992
In this paper, an exact solution is presented for whirling analysis of rotors carrying concentrated masses. Effect of various parameters on the forward and backward frequencies are investigated including velocity of spin and quantity, translational inertia and position of the concentrated masses. It is shown that vibration characteristics of rotors can be affected by concentrated elements depended on the position of point masses and value of their translational inertia. The most advantage of the presented solution is that for rotors with any number of concentrated masses, all natural frequencies can be obtained through solution of a determinant of order 2. © 2020 Taylor & Francis Group, LLC.
Composite Structures (02638223)286
The present paper proposed an auxetic honeycomb for sandwich structure with a novel graded design. The auxetic graded design is achieved by a variation of honeycomb cell angle through the core thickness. This variation affects the other geometric parameters and the mechanical properties. The enhanced specific bending properties of the sandwich structure are obtained by using Taguchi design of experiments (DOEs) by optimizing the cell wall thickness, cell aspect ratio, and cell angle gradation. The specimens of the DOEs are fabricated using fused deposition modeling (FDM) 3D printer. The strain fields in the core and the damage evolution under real-time flexural loading conditions are assessed by performing digital image correlation (DIC) analysis. The experimental and DIC analysis results are validated by the three-dimensional finite element analysis with consideration of elastoplastic behavior and crack growth possibility. The results indicate that the reduction of the cell wall thickness to length ratio increases the bending failure stress and specific absorbed energy by 35% and 45.8%, respectively, and the optimum cell angle gradation improves the flexural modulus to density ratio with an increase of 18.9%. © 2022 Elsevier Ltd
International Journal for Computational Methods in Engineering Science and Mechanics (15502295)22(4)pp. 333-343
Vibrational characteristic in structures that can be modeled as several concentrated masses on the beam are of great interest. In this article, variational iteration method (VIM) is used to find a semi-analytical solution for the transverse vibration of an Euler–Bernoulli beam carrying concentrated masses and also to close the condition of the problem into real boundary conditions wherein the cross-sectional changes are applied at points where there is concentrated mass. In order to achieve the Lagrange multiplier, in addition to using variational theory and stationary conditions, a simple polynomial is considered for the initial approximation. © 2021 Taylor & Francis Group, LLC.
Ceramics International (02728842)47(3)pp. 3279-3291
A nonlinear developed model for various PZT wind energy harvesters with arbitrary dimensions and location of electroceramics has been prepared. This model can describe unimorph and bimorph harvesters with different cantilever cross-sections attached to a tip body with different shapes. The system model has been validated with results reported in the literature. A set of parametric studies has been conducted to examine the influences of the cantilever shape in addition to the shape of the tip body. Furthermore, the impacts of load resistance and wind speed on the output power have been analyzed. The effects of number, position, and dimensions of piezoceramics on the harvester performance have also been investigated. It is found that by increasing the total area of electroceramics (including the length, width, or the number of PZT patches), the peak of the wind critical speed and the middle resistance range where the instability speed is very sensitive to the electrical load shifts toward the lower resistances. Moreover, several instrumental points to design efficient and affordable vibrating wind harvesters at low and high flows have been obtained. © 2020 Elsevier Ltd and Techna Group S.r.l.
Journal Of The Brazilian Society Of Mechanical Sciences And Engineering (16785878)42(5)
In this article, the nonlinear transverse vibration of an elastically connected double microbeam system carrying a moving particle is assessed based on the modified couple stress and non-classical Timoshenko beam theories. Hamilton’s principle is applied to develop the motion equations and corresponding boundary conditions, and the Galerkin method is used to solve these equations. The numerical study reveals that the nonlinear and modified couple stress theories predict a stiffer system than the linear and classical theories do. A parametric study is run to determine the different parameters’ influence like the aspect ratio, the stiffness modulus of the elastic layer and the velocity of the moving particle, on the dynamic response of the system. The results show that the aspect ratio has a significant effect on the dynamic response of the system, indicating that the classical theory cannot predict the dynamic behavior of micro-size beam systems. The elastic layer stiffness modulus and the velocity of the moving particle have considerable effects on the dynamic deflections of the double-microbeam system. © 2020, The Brazilian Society of Mechanical Sciences and Engineering.
Mirsafai s., S.,
Torabi, K.,
Ashrafi m., M.,
Hamadanian m., M. Bulletin of Materials Science (02504707)43(1)
This paper reports the development of nitrile butadiene rubber (NBR) nanocomposite toughened by the combination of polyvinyl chloride (PVC) and CuFe 2O 4 nanoparticles (NPs). CuFe 2O 4 NPs synthesized by sol–gel auto-combustion route. Response surface methodology was applied for optimization and modelling of the tensile strength and elongation of NBR/PVC/CuFe 2O 4 nanocomposite. By using XRD, SEM, EDX and VSM, we characterized CuFe 2O 4 NPs and the optimized NBR/PVC/CuFe 2O 4 nanocomposite, and investigated the mechanical properties of NBR/PVC/CuFe 2O 4 nanocomposite. Results showed that the surface cracking of NBR decreased as the PVC and CuFe 2O 4 content increased, which leads to better mechanical properties of NBR. © 2020, Indian Academy of Sciences.
Composite Structures (02638223)212pp. 129-147
In this paper, some methods to determine the absolute frequencies of traveling waves in a rotating cross-ply laminated cylindrical shell with elastic supports are investigated. Based on the Sanders’ shell theory and by taking into account the Hamilton principle, the governing equations of motion are derived in the rotating coordinate system, which considers the effects of initial hoop tension, the centrifugal and the Coriolis forces due to the rotation as well. The constraint equations of elastic supports are modelled by using artificial distributed elastic springs in the possible directions. By substitution of mode shape profile functions into equations and using the differential quadrature method, the eigenvalue equations of the rotaing shell are derived in both rotating and fixed systems. To make more comparison, the eigenvalue equation of synchronous critical speeds is also derived. Convergence and comparison of the proposed method is investigated through comparing its results with available literature. The comparison results shows that the direction of the corresponding traveling waves and the graphical determination of critical speeds are determined by a more convenient criteria with easier physical interpretation in the fixed system, specially by using the direct method which is more efficient in computation than the converting method. © 2019
SN Applied Sciences (25233971)1(9)
This paper deals with the free transverse vibration characteristics of a rotating non-uniform nanocantilever with multiple open cracks. Employing Eringen’s nonlocal elasticity and the Timoshenko beam theory, the non-dimensional governing differential equations for the above-mentioned problem are derived. The cracked beam is divided into intact sub-beams between two subsequent cracks connected by linear and rotational springs. Differential quadrature element method is utilized to solve the established governing equations of motion of each segment, along with the corresponding boundary conditions and compatibility conditions at the cracked sections. The frequency parameters and vibration modes of the rotating cracked beam for different crack positions and severities under various nonlocal, geometric and dynamic conditions are studied, and the relevant graphs are plotted. Since rotating nanocantilevers are found mostly as blades of rotating nanodevices, the results can provide useful guidance for the study and design of the next generations of nanoturbines, nanogears etc. © 2019, Springer Nature Switzerland AG.
Mohammadimehr, M.,
Afshari, H.,
Salemi m., ,
Torabi, K.,
Mehrabi, M. Structural Engineering and Mechanics (12254568)71(5)pp. 525-544
In the present study, buckling and free vibration analyses of annular thin sector plate made of functionally graded materials (FGMs) resting on visco-elastic Pasternak foundation, subjected to external radial, circumferential and shear in-plane loads is investigated. Material properties are assumed to vary along the thickness according to an power law with Poisson’s ratio held constant. First, based on the classical plate theory (CPT), the governing equation of motion is derived using Hamilton’s principle and then is solved using the generalized differential quadrature method (GDQM). Numerical results are compared to those available in the literature to validate the convergence and accuracy of the present approach. Finally, the effects of power-law exponent, ratio of radii, thickness of the plate, sector angle, and coefficients of foundation on the fundamental and higher natural frequencies of transverse vibration and critical buckling loads are considered for various boundary conditions. Also, vibration and buckling mode shapes of functionally graded (FG) sector plate have been shown in this research. One of the important obtained results from this work show that ratio of the frequency of FG annular sector plate to the corresponding values of homogeneous plate are independent from boundary conditions and frequency number. Copyright © 2019 Techno-Press, Ltd.
Ashrafi m., M.,
Hamadanian m., M.,
Mirsafai s., S.,
Torabi, K. Fibers and Polymers (12299197)20(11)pp. 2247-2253
In this study, nitrile-butadiene rubber (NBR) based nanocomposites reinforced with PVC as a polymeric filler and NiFe2O4 as nanofllers with different weight fractions (wt%) were prepared and characterized. The experiments were developed according to response surface methodology (RSM) combined with central composite design (CCD) to optimize the effects of two variable parameters (PVC and NiFe2O4) on the mechanical properties. The NiFe2O4 nanoparticles (NPs) were synthesized by sol-gel auto-combustion method and, the NBR/PVC/NiFe2O4 nanocomposites were prepared by two-roll mill method. The elongation and tensile strength of the optimized nanocomposite were obtained to be 300 % and 18 MPa, respectively. The surface SEM images showed that the NiFe2O4 NPs were well distributed in the NBR matrix. Furthermore, cross-sectional SEM images showed that the cracks on the nanocomposite matrix decreased compared to pure NBR. Also, NBR/PVC/NiFe2O4 nanocomposite shows weak ferromagnetic behavior at room temperature than NiFe2O4NPs. The NiFe2O4 NPs and optimal sample of NBR/PVC/NiFe2O4 nanocomposites were investigated by X-ray diffraction (XRD), scanning electron microscopy (SEM), energy dispersive X-ray (EDX), vibrating sample magnetometer (VSM). © 2019, The Korean Fiber Society.
Journal of Sandwich Structures and Materials (15307972)21(2)pp. 503-531
As a useful tool for designing wings and tail fins of aircrafts, this paper presents an optimization for flutter characteristics of cantilevered functionally graded sandwich plates. The plate is composed of an isotropic homogeneous core and two functionally graded face sheets. The plate is modeled based on the first-order shear deformation theory. The aerodynamic pressure is estimated using supersonic piston theory and using Hamilton's principle, the set of governing equations and boundary conditions are then derived. Applying a transformation of coordinates, governing equations and boundary conditions are converted and solved numerically by differential quadrature method. Natural frequencies, damping ratio, corresponding mode shapes, critical aerodynamic pressure, and flutter frequency are calculated. In order to achieve an optimum design, particle swarm optimization is employed to find the best values of aspect ratio, thickness of the plate, thickness of the core, power law index, and angles of the plate which increase critical aerodynamic pressure. Some constrains on the angles of the plate and its mass and area (lift force) are also considered. © The Author(s) 2017.
Torabi, K.,
Sharifi d., D.,
Ghassabi, M.,
Mohebbi a., Iranian Journal Of Science And Technology, Transactions Of Mechanical Engineering (22286187)43pp. 425-440
In this article, linear and nonlinear transverse vibration of Euler–Bernoulli beams with multiple concentrated masses have been investigated using variational iteration method (VIM), and the effects of concentrated mass on natural frequencies and mode shapes have been taken into account as well. VIM is a powerful method with high convergence which gives analytical solution to linear problems and is capable of being extended to present semi-analytical solutions to nonlinear ones. The proper choice of Lagrange’s multiplier and Initial Function can increase the convergence speed. In this study, along with presenting the suitable trend for determining these two functions, the obtained frequencies in linear and nonlinear states are compared with those calculated from other methods, and the accuracy and convergence speed of this procedure are examined. It is concluded that with increasing the intensity of concentrated mass, linear natural frequency and the ratio of nonlinear frequency to linear one will decline. © 2018, Shiraz University.
Journal of Sandwich Structures and Materials (15307972)21(8)pp. 2887-2920
In this article, free flexural vibration and supersonic flutter analyses are studied for cantilevered trapezoidal plates composed of two homogeneous isotropic face sheets and an orthotropic honeycomb core. The plate is modeled based on the first-order shear deformation theory, and aerodynamic pressure of external flow with desired flow angle is estimated via the piston theory. For this goal, first applying the Hamilton's principle, the set of governing equations and boundary conditions are derived. Then, using a transformation of coordinates, the governing equations and boundary conditions are converted from the original coordinates into new computational ones. Finally, the differential quadrature method is employed and natural frequencies, corresponding mode shapes, and critical speed are numerically achieved. Accuracy of the proposed solution is confirmed by the finite element simulations and published experimental results. After the validation, effect of various parameters on the vibration and flutter characteristics of the plate are investigated. It is concluded that geometry of hexagonal cells in the honeycomb core has a weak effect on the natural frequencies and critical speed of the sandwich plate, whereas thickness of the honeycomb core has main influence on the natural frequencies and the critical speed. Besides, it is shown that the honeycomb core thickness has optimum values that lead to the most growth in the natural frequencies or critical speed. These optimum magnitudes can be taken into account by designers to increase the natural frequencies or expand flutter boundaries and make aircrafts safer in supersonic flights. It is also concluded that geometrical parameters of the hexagonal cells and thickness of the honeycomb core have no significant effect on the value of the critical flow angle. © The Author(s) 2017.
Mohandes, M.,
Ghasemi, A.R.,
Irani-rahagi, M.,
Torabi, K.,
Taheri-behrooz, F. JVC/Journal of Vibration and Control (10775463)24(14)pp. 3026-3035
The free vibration of fiber–metal laminate (FML) thin circular cylindrical shells with different boundary conditions has been studied in this research. Strain–displacement relations have been obtained according to Love’s first approximation shell theory. To satisfy the governing equations of motion, a beam modal function model has been used. The effects of different FML parameters such as material properties lay-up, volume fraction of metal, fiber orientation, and axial and circumferential wavenumbers on the vibration of the shell have been studied. The frequencies of shells have been calculated for carbon/epoxy and glass/epoxy as composites and for aluminum as metal. The results demonstrate that the influences of FML lay-up and volume fraction of composite on the frequencies of the shell are remarkable. © The Author(s) 2017.
Torabi, K.,
Jafarzadeh jazi, A.,
Shahriari B.,
Torabi, K. International Journal of Mechanical Sciences (00207403)131pp. 728-743
Concentrated masses mounted on a Nanobeam have important effects on its transverse vibrations. In this paper the effects of concentrated masses on lateral vibration of a Nanobeam is investigated by utilizing two different points of view about shear force in the beam. The investigation is conducted with and without considering small scale effect on shear force. Timoshenko beam and nonlocal theories have been used in Newton's second law to model transverse dynamic behavior of a Nanobeam; then the mathematical model of concentrated masses is imposed into the equations of motion by using Dirac's delta function. After obtaining exact closed form solution, basic functions are used to simplify calculations. Different parameters of the Nanobeam are used to study transverse vibration of Nanobeam carrying concentrated masses. These parameters include number, mass and location of concentrated masses and length, cross section area and small scale factor of Nanobeam. Finally, the effects of these parameters are presented in diagrams for two points of view. The diagrams show significant difference between consideration and disregarding of small scale factor in shear force in higher natural frequencies of Nanobeam. (C) 2017 Elsevier Ltd. All rights reserved.
Torabi, K.,
Afshari, H.,
Sadeghi m., M.H.,
Toghian h., Journal of Solid Mechanics (discontinued) (20087683)9(4)pp. 760-782
In this paper, an exact closed-form solution is presented for free vibration analysis of Euler-Bernoulli conical and tapered beams carrying any desired number of attached masses. The concentrated masses are modeled by Dirac's delta functions which creates no need for implementation of compatibility conditions. The proposed technique explicitly provides frequency equation and corresponding mode as functions with only two integration constants which leads to solution of a two by two eigenvalue problem for any number of attached masses. Using Basic functions which are made of the appropriate linear composition of Bessel functions leads to make implementation of boundary conditions much easier. The proposed technique is employed to study effect of quantity, position and translational inertia of the concentrated masses on the natural frequencies and corresponding modes of conical and tapered beams for all standard boundary conditions. Unlike many of previous exact approaches, presented solution has no limitation in number of concentrated masses. In other words, by increase in number of attached masses, there is no considerable increase in computational effort. © 2017 IAU, Arak Branch.
Journal of Reinforced Plastics and Composites (07316844)36(15)pp. 1116-1128
A new practical procedure is presented for delamination detection in beam-like composite structures. This technique identifies the delamination axial location and its length accurately based on the only first natural frequency. An additional simply support condition besides the boundary conditions is defined and it is moved along the beam length. When this support is located on delamination, especially its tips, the frequency reduction will be noticeable. Simulating this idea in ABAQUS finite element software shows that the location and size of delamination can be detected accurately. To verify the numerical results, some experiments are conducted and a new fixture is designed and manufactured for simulating the additional moving support along the length of the beam. Both finite element and experimental results show the ability of the proposed method in delamination detection for different boundary conditions. Also, this new simple and applicable technique can be used even for small delamination lengths by monitoring only the first natural frequency, unlike the available methods in the literature. © SAGE Publications.
Journal Of The Brazilian Society Of Mechanical Sciences And Engineering (16785878)39(12)pp. 4887-4894
Complicated structures used in a wide variety of engineering fields consist of simple structural elements like beams which in some cases include one discontinuity such as a crack or mass and are more likely to vibrate with larger amplitude. In this article, considering shear deformation and rotatory inertia, transverse vibration of nonlinear Timoshenko beam carrying a concentrated mass oscillating with large amplitude is investigated using VIM. This method is a very powerful method with suitable convergence speed in which by choosing the proper Lagrange’s multiplier and Initial Function, the convergence speed could increase even more. This method would be able to present analytical solutions for linear equations and semi-analytical solutions for non-linear ones. One of the greatest advantages of this method is that its calculations are not dependent on the number of masses located on the beam. In this paper, along with presenting the suitable trend for determining the Lagrange’s multiplier, the effects of concentrated mass on natural frequencies in linear and non-linear states are taken into account. The obtained results, moreover, are compared with the results gained through other procedures and the accuracy and speed convergence are studied as well. © 2017, The Brazilian Society of Mechanical Sciences and Engineering.
Journal Of The Brazilian Society Of Mechanical Sciences And Engineering (16785878)39(5)pp. 1545-1561
In this paper, based on the first-order shear deformation theory for modeling the structure and the supersonic Piston theory to estimate the aerodynamic pressure, the set of governing equations and boundary conditions for flutter analysis of a trapezoidal thick plate with variable thickness are derived. Using a transformation of coordinates, governing equations and boundary conditions are converted from the original coordinates into a new computational one. Using differential quadrature method, natural frequencies, damping ratio, and corresponding mode shapes are derived, and critical aerodynamic pressure and flutter frequency are determined. Critical aerodynamic pressure of the plate is considered as an objective function to increase and using particle swarm optimization, optimum values of aspect ratio, thickness, variation of thickness, and angles of the plate are found. Meanwhile, some constrains on the volume (weight) and area (lift force) of the plate are considered. This constrained optimization can be considered as a useful tool for design wing and tail fin of aircrafts. © 2016, The Brazilian Society of Mechanical Sciences and Engineering.
Mechanics of Advanced Materials and Structures (15210596)24(9)pp. 725-736
In the present study, transverse vibrations of nanobeams with manifold concentrated masses, resting on Winkler elastic foundations, are investigated. The model is based on the theory of nonlocal elasticity in the presence of concentrated masses applied to Euler–Bernoulli beams. A closed-form expression for the transverse vibration modes of Euler–Bernoulli beams is presented. The proposed expressions are provided explicitly as the function of two integrated constants, which are determined by the standard boundary conditions. The utilization of the boundary conditions leads to definite terms of natural frequency equations. The natural frequencies and vibration modes of the concerned nanobeams with different numbers of concentrated masses in different positions under some typical boundary conditions (simply supported, cantilevered, and clamped–clamped) have been analyzed by means of the proposed closed–form expressions in order to show their efficiency. It is worth mentioning that the effect of various nonlocal length parameters and Winkler modulus on natural frequencies and vibration modes are also discussed. Finally, the results are compared with those corresponding to a classical local model. © 2017 Taylor & Francis Group, LLC.
Torabi, K.,
Ghassabi, M.,
Heidari-rarani, M.,
Sharifi d., D. International Journal of Engineering, Transactions A: Basics (17281431)30(10)pp. 1565-1572
In this paper, a relatively new method, namely variational iteration method (VIM), is developed for free vibration analysis of a Timoshenko beam with different boundary conditions. In the VIM, an appropriate Lagrange multiplier is first chosen according to order of the governing differential equation of the boundary value problem, and then an iteration process is used till the desired accuracy is achieved. Solution of VIM for natural frequencies and mode shapes of a Timoshenko beam is compared to the available exact closed-form solution and numerical results of differential quadrature method (DQM). The accuracy of VIM is approximately the same as exact solution and much better than the DQM for solving the free vibration of a Timoshenko beam. Also, convergence speed and simplicity of this method is more than the other two methods because it works with polynomial at the first iteration. Thus, VIM can be used for solving the complicate engineering problems which do not have analytical solution.
Engineering Solid Mechanics (22918752)5(1)pp. 71-92
This paper presents a numerical solution for vibration analysis of cantilevered non-uniform trapezoidal thick plates. Based on the first shear deformation theory, kinetic and strain energies of the plate are derived and using Hamilton's principle, governing equations and boundary conditions are derived. A transformation of coordinates is used to convert the equations and boundary conditions from the original coordinates into a new computational coordinates. Using Differential quadrature method (DQM), natural frequencies and corresponding modes are derived numerically. Convergence and accuracy of the proposed solution are confirmed using results presented by other authors and also results obtained based on the finite element method using ANSYS software. Finally, as the case studies, two cases for variation of thickness are considered and the effects of angles, aspect ratio and thickness of the plate on the natural frequencies are studied. It is concluded that two angles of the trapezoid have opposite effect on the natural frequencies. Also, it is shown that all frequencies rise as value of thickness increases or value of the aspect ratio of the plate decreases. The most advantage of the proposed solution is its applicability for plates with variable thickness. © 2017 Growing Science Ltd. All rights reserved.
Journal of Solid Mechanics (discontinued) (20087683)9(1)pp. 138-156
In this paper, exact solution for two-plane transverse vibration analysis of axial-loaded multi-step Timoshenko rotor carrying concentrated masses is presented. Each attached element is considered to have both translational and rotational inertia. Forward and backward frequencies and corresponding modes are obtained using transfer matrix method (TMM). The effect of the angular velocity of spin, value of the translational and rotational inertia, position of the attached elements and applied axial force on the natural frequencies are investigated for various boundary conditions. © 2017 IAU, Arak Branch. All rights reserved.
Moghadam, A.A.A.,
Torabi, K.,
Kaynak, A.,
Zainal alam, M.N.H.,
Kouzani, A.Z.,
Mosadegh, B. Soft Robotics (21695172)3(2)pp. 82-97
This article describes an efficient control-oriented model of a soft robot made of electroactive polymers. The proposed soft robot is constructed from two flexible links and has a multiphysics dynamic model consisting of both an electrochemical and electromechanical model. The electrochemical model is based on a distributed RC line approach, and the electromechanical model, considering the continuum vibration of the robot, is derived based on Hamilton's principle. The governing equation of the soft robot is solved by means of the Rayleigh-Ritz-Meirovitch substructure synthesis method, and the Laplace operator is used to obtain the transfer function of the soft robot as a 2 by 2 multiple-input multiple-output system. © Mary Ann Liebert, Inc. 2016.
Engineering Solid Mechanics (22918752)4(2)pp. 97-108
In this paper, an analytical solution for whirling analysis of axial-loaded Timoshenko rotor is presented and corresponding basic functions are derived. The set of governing equations for whirling analysis of the rotor consists of four coupled partial differential equations; using complex displacements, these equations can be reduced to two coupled partial differential equations. The versatility of the proposed solution is confirmed using published results and the effect of angular velocity of spin, axial load, slenderness and Poisson's ratio on the natural frequencies of the rotor are investigated. © 2016 Growing Science Ltd. All rights reserved.
International Journal of Mechanical Sciences (00207403)115pp. 1-11
Delamination is a major damage mode in laminated composite structures which causes reduction in stiffness and strength and affects their vibration characteristics. This paper deals with the effects of delamination size and its thickness-wise and lengthwise location on the vibration characteristics of cross-ply laminated composite beams. Free and constrained mode models are introduced and compared in the analytical and finite element methods for the first three modes and a comprehensive discussion among these results is done. To verify the results, modal tests were carried out on the delaminated specimens. Unlike the available experimental research, the proportion of delamination size to the beam length (a/L) is relatively small (i.e., a/L=0.20, 0.10 and 0.05). Moreover, these experiments are focused on the effect of the axial location of delamination on the first three natural frequencies. All results are considered under both the clamped-free and clamped-clamped boundary conditions. Finally, some interesting relationships are presented between the frequencies reduction and their corresponding mode shapes, which can be useful for delamination detection. © 2016 Published by Elsevier Ltd.
Journal of Solid Mechanics (discontinued) (20087683)8(1)pp. 184-203
This paper presents a numerical solution for vibration analysis of a cantilever trapezoidal thick plate. The material of the plate is considered to be graded through the thickness from a metal surface to a ceramic one according to a power law function. Kinetic and strain energies are derived based on the Reissner-Mindlin theory for thick plates and using Hamilton's principle, the governing equations and boundary conditions are derived in the Cartesian coordinates. A transformation of coordinates is used to convert the equations and boundary conditions from the original coordinate into a new computational coordinates. Generalized differential quadrature method (GDQM) is selected as a strong method and natural frequencies and corresponding modes are derived. The accuracy and convergence of the proposed solution are confirmed using results presented by other authors. Finally, the effect of the power law index, angles and thickness of the plate on the natural frequencies are investigated. © 2016 IAU, Arak Branch. All rights reserved.
Moghadam, A.A.A.,
Kouzani, A.Z.,
Torabi, K.,
Kaynak, A.,
Shahinpoor, M. Smart Materials and Structures (09641726)24(3)
This paper presents the design, analysis and fabrication of a novel low-cost soft parallel robot for biomedical applications, including bio-micromanipulation devices. The robot consists of two active flexible polymer actuator-based links, which are connected to two rigid links by means of flexible joints. A mathematical model is established between the input voltage to the polymer actuators and the robot's end effector position. The robot has two degrees-of-freedom, making it suitable for handling planar micromanipulation tasks. Moreover, a number of robots can be configured to operate in a cooperative manner for increasing micromanipulation dexterity. Finally, the experimental results demonstrate two main motion modes of the robot. © 2015 IOP Publishing Ltd.
Computers and Mathematics with Applications (08981221)67(3)pp. 527-541
In this paper, a differential quadrature element method (DQEM) for free transverse vibration analysis of multiple cracked non-uniform Timoshenko beams with general boundary conditions is proposed. Governing equations, the compatibility conditions at the damaged cross-sections and implementation of the external boundary conditions are derived and formulated by the differential quadrature analogue. The accuracy, convergence, and versatility of the proposed method are confirmed by the exact solution of the uniform beam which has been presented by other authors, and 2D finite element method (FEM) numerical results for non-uniform beam. After the validation of the presented method, the effect of quantity, depth and location of the cracks on the frequency values of vibrations are investigated. The achieved results show that the existence of the crack leads to a decrease in the frequencies of the vibrations through decrease in the stiffness of the beam. Meanwhile, the compatibility conditions at the damaged section is considered as a discontinuity in slope and vertical displacement where the effect of the discontinuity in the slope is more considerable as many authors have neglected the discontinuity in the vertical displacement. As it will be shown, consideration of the discontinuity in the vertical displacement causes more decrease in the frequencies. © 2013 Elsevier Ltd. All rights reserved.
Journal of Solid Mechanics (discontinued) (20087683)6(2)pp. 135-149
In this study, the analysis of transverse vibrations of rectangular plate with circular central hole with different boundary conditions is studied and the natural frequencies and natural modes of a rectangular plate with circular hole have been obtained. To solve the problem, it is necessary to use both Cartesian and polar coordinate system. The complexity of the method is to apply an appropriate model, which can solve the problem of transverse vibrations of a plate. So, it has been tried that the functions of the deflection of plate, in the form of polynomial functions proportionate with finite degrees, to be replaced by Bessel function, which is used in the analysis of the vibrations of a circular plate. Then with the help of a semi-analytical method and orthogonality properties of the eliminated position angle, without any need to analyze so many points on the edges of the rectangular plate, we can prevent the coefficients matrix from becoming so much large as well as the equations from becoming complicated. The above mentioned functions will lead to reducing the calculation time and simplifying the equations as well as speeding up the convergence. © 2014 IAU, Arak Branch.
Applied Mathematics and Computation (18735649)238pp. 342-357
Concentrated masses on the beams have many industrial applications such as gears on a gearbox shafts, blades and disks on gas and steam turbine shafts, and mounting engines and motors on structures. Transverse vibration of the beam carrying a point mass was studied in many cases by both Euler-Bernoulli and Timoshenko beam theory for a limited number of concentrated masses mounted on a specific place on the beam. This was also investigated for a beam carrying multiple concentrated masses, yet they were solved by numerical methods such as Differential Quadrature (DQ) method. The present study investigated an exact solution for free transverse vibrations of a Timoshenko beam carrying multiple arbitrary concentrated masses anywhere on the beam with various boundary conditions. Using Dirac's delta in governing equations, the effects of concentrated masses were imposed. After extracting a closed form solution, basic functions were used to reduce the amount of computations. Standard symmetric and asymmetric boundary conditions were enforced for beam; in addition, the effects of value, position, and number of concentrated masses were examined. Generally, while the existence of concentrated masses reduces the natural frequencies, the reduction depends on the parameters of concentrated masses. Finally, there were acquired mode shapes for different boundary conditions and different value, position, and number of concentrated masses. © 2014 Elsevier Inc. All rights reserved.
Engineering Solid Mechanics (22918752)2(4)pp. 313-320
In this paper, an analytical method is proposed for calculation of natural frequencies of a delaminated composite beam from both free and constrained mode frequencies. In previous studies, the frequencies of a delaminated composite beam were computed with assumption of occurring open or close delamination during the vibration. According to this assumption, two separated modes, i.e., “free mode” and “constrained mode”, are occurred in vibration of the delaminated beam. In fact, a delamination may breathe (open and close) during the vibration and the assumptions of the free or constrained mode models are not completely correct in the whole of the vibration period. For this reason, a new formulation is proposed for calculation of natural frequencies based on the breathing of delamination. The obtained results are compared with various theoretical and experimental results available in the literature. Thus, the effects of location and size of delamination can be investigated on the natural frequencies of delaminated beams. © 2014 Growing Science Ltd. All rights reserved.
Journal of Solid Mechanics (discontinued) (20087683)6(1)pp. 28-42
In this paper, the transverse vibrations of rectangular plate with circular central hole have been investigated and the natural frequencies of the mentioned plate with point supported by Rayleigh-Ritz Method have been obtained. In this research, the effect of the hole is taken into account by subtracting the energies of the hole domain from the total energies of the whole plate. To determine the kinetic and potential energies of plate, admissible functions for rectangular plate are considered as beam functions and it has been tried that the functions of the deflection of plate, in the form of polynomial functions proportionate with finite degrees, to be replaced by Bessel function, which is used in the analysis of the vibrations of a circular plate. Consideration for a variety of edge conditions is given through a combination of simply supported, clamped and free boundary conditions. In this study, the effects of increasing the diameter of the hole and the effects of number of point supported on the natural frequencies were investigated and the optimum radius of the circular hole for different boundary conditions are obtained. The method has been verified with many known solutions. Furthermore, the convergence is very fast with any desirable accuracy to exact known natural frequencies. © 2014 IAU, Arak Branch.
Moghadam, A.A.A.,
Torabi, K.,
Moavenian, M.,
Davoodi, R. Journal of Intelligent Material Systems and Structures (15308138)24(4)pp. 484-498
In this article, analytical dynamic model derivation and robust position control of a microrobot based on fast trilayer polypyrrole-bending actuators employing quantitative feedback theory is presented. The conjugated polymer actuators based on polypyrrole can be employed to achieve microscale precision positioning, having a wide range of application including biomimetic robots and biomedical devices. There has been extensive research on modeling the electrochemical dynamics of polypyrrole bending actuators. However, the mechanical dynamics modeling of actuator remains to be unexplored. In this article, we first develop a proper mechanical dynamics model for the fast-conducting polymer actuators that matches well with the existing experimental results and then extend it to a microrobot. In the controlling part, the robust control quantitative feedback theory will be used to control the microrobot with variable tip loading. The numerical simulation results show that the quantitative feedback theory controller has consistent and robust-tracking performance. © The Author(s) 2012.
Engineering Solid Mechanics (22918752)1(1)pp. 9-20
In this paper, a differential quadrature element method (DQEM) is developed for free transverse vibration analysis of a non-uniform cantilever Timoshenko beam with multiple concentrated masses. Governing equations, compatibility and boundary conditions are formulated according to the differential quadrature rules. The compatibility conditions at the position of each concentrated mass are assumed as the continuity in the vertical displacement, rotation and bending moment and discontinuity in the transverse force due to acceleration of the concentrated mass. The effects of number, magnitude and position of the masses on the value of the natural frequencies are investigated. The accuracy, convergence and efficiency of the proposed method are confirmed by comparing the obtained numerical results with the analytical solutions of other researchers. The two main advantages of the proposed method in comparison with the exact solutions available in the literature are: 1) it is less time-consuming and subsequently moreefficient; 2) it is able to analyze the free vibration of the beams whose section varies as an arbitrary function which is difficult or sometimes impossible to solve with analytical methods. © 2013 Growing Science Ltd. All rights reserved.
Journal of Solid Mechanics (discontinued) (20087683)5(4)pp. 336-349
In this paper, vibration analysis of multiple-stepped Bernoulli-Euler and Timoshenko beams carrying point masses is presented analytically for various boundary conditions. Each attached element is considered to have both translational and rotational inertias. The method of solution is "transfer matrix method" which is based on the changes in the vibration modes at the vicinity of any discontinuity in geometrical and natural parameters; these changes are shown by transfer matrices depended on the geometry of each step or value of the translational and rotational inertias of each attached element. First, natural frequencies and corresponding normal mode shapes are obtained by implementation of the compatibility conditions and external boundary conditions; Then, the precision of the proposed method is checked by comparison of the results with other exact solutions; Finally, the effect of the translational and rotational inertias and position of the attached elements on the natural frequencies of multi-stepped beams are investigated for various boundary conditions. © 2013 IAU, Arak Branch.
Thin Solid Films (00406090)520(21)pp. 6595-6602
This paper is concerned with the free transverse vibration of cracked nanobeams modeled after Eringen's nonlocal elasticity theory and Timoshenko beam theory. The cracked beam is modeled as two segments connected by a rotational spring located at the cracked section. This model promotes discontinuities in rotational displacement due to bending which is proportional to bending moment transmitted by the cracked section. The governing equations of cracked nanobeams with two symmetric and asymmetric boundary conditions are derived; then these equations are solved analytically based on concerning basic standard trigonometric and hyperbolic functions. Besides, the frequency parameters and the vibration modes of cracked nanobeams for variant crack positions, crack ratio, and small scale effect parameters are calculated. The vibration solutions obtained provide a better representation of the vibration behavior of short, stubby, micro/nanobeams where the effects of small scale, transverse shear deformation and rotary inertia are significant. © 2012 Elsevier B.V. All rights reserved.
Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering (09596518)226(1)pp. 70-81
Recent advances in micro-electromechanical systems (MEMS) have led to the creation of small low-cost gyroscopes that have low power consumption levels. This paper presents a novel design methodology for a robust controller that can improve the performance of a vibratory MEMS gyroscopes despite the existence of coupling between vibratory gyroscope modes and inherent model uncertainties. The drive-mode of the gyroscope is able to track a desired sinusoidal trajectory while the sensing mode is bounded against uncertainties. In other words, while the sensing mode of the gyroscope operates under a bounded unknown disturbance and measurement noise, the multivariable robust quantitative feedback theory (QFT)-based controller compensates undesirable mechanical spring coupling between two vibrating directions, regulates both modes, and most significantly compels the output of the sensing mode to be bounded and the output of the drive mode to track a desired sinusoidal reference signal at a given amplitude and frequency. The robust performance of the closed-loop system is verified through a series of frequency-domain analyses. Finally, the effectiveness of the proposed QFT-based controller is demonstrated through simulations. © Author 2011.
Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering (09596518)226(6)pp. 806-822
Conjugated polymers are emerging materials which have a wide range of applications including biomimetic robots and biomedical devices. These novel materials attract considerable attention owing to their interesting sensing and actuating behavior. However, complicated electro-chemo-mechanical dynamics is a drawback for their application in functional devices. Although extensive research has been conducted on static modeling of conductive polymers, the dynamic modeling is not well understood. In this paper we focus on dynamic modeling and robust control of a fast trilayer polypyrrole actuator as a distributed parameter system. The Euler-Bernoulli beam model with inclusion of Kelvin-Voigt damping and tip loading is utilized for vibration analysis of the smart actuator. Considering the spatio-temporal dynamics of the actuator, a one-point feedback controller based on quantitative feedback theory is designed that can suppress arbitrary external disturbances and consistently track desired inputs. © IMechE 2012.
Applied Mechanics and Materials (discontinued) (16627482)110pp. 4532-4536
In this paper, free vibration differential equations of cracked beam are solved by using differential transform method (DTM) that is one of the numerical methods for ordinary and partial differential equations. The Euler-Bernoulli beam model is proposed to study the frequency factors for bending vibration of cracked beam with ant symmetric boundary conditions (as one end is clamped and the other is simply supported). The beam is modeled as two segments connected by a rotational spring located at the cracked section. This model promotes discontinuities in both vertical displacement and rotational due to bending. The differential equations for the free bending vibrations are established and then solved individually for each segment with the corresponding boundary conditions and the appropriated compatibility conditions at the cracked section by using DTM and analytical solution. The results show that DTM provides simple method for solving equations and the results obtained by DTM converge to the analytical solution with much more accurate for both shallow and deep cracks. This study demonstrates that the differential transform is a feasible tool for obtaining the analytical form solution of free vibration differential equation of cracked beam with simple expression. © (2012) Trans Tech Publications, Switzerland.
Applied Mechanics and Materials (discontinued) (16627482)110pp. 2400-2405
Analysis of transverse vibration of beams is presented in this paper. Unfortunately, complexities which appear in solving differential equation of transverse vibration of non-uniform beams, limit analytical solution to some special cases, so that the numerical method is presented. DTM is a numerical method for solving linear and some non-linear, ordinary and partial differential equations. In this paper, this technique has been applied for solving differential equation of transverse vibration of conical Euler-Bernoulli beam. Natural circular frequencies and mode shapes have been calculated. Comparing results with the cases which exact solution have been presented, shows that DTM is a strong method especially for solving quasi-linear differential equations. © (2012) Trans Tech Publications, Switzerland.
Moghadam, A.A.A.,
Moavenian, M.,
Torabi, K.,
Tahani, M. Smart Materials and Structures (09641726)20(11)
Analytical modeling of conjugated polymer actuators with complicated electro-chemo-mechanical dynamics is an interesting area for research, due to the wide range of applications including biomimetic robots and biomedical devices. Although there have been extensive reports on modeling the electrochemical dynamics of polypyrrole (PPy) bending actuators, mechanical dynamics modeling of the actuators remains unexplored. PPy actuators can operate with low voltage while producing large displacement in comparison to robotic joints, they do not have friction or backlash, but they suffer from some disadvantages such as creep and hysteresis. In this paper, a complete analytical dynamic model for fast trilayer polypyrrole bending actuators has been proposed and named the analytical multi-domain dynamic actuator (AMDDA) model. First an electrical admittance model of the actuator will be obtained based on a distributed RC line; subsequently a proper mechanical dynamic model will be derived, based on Hamilton's principle. The purposed modeling approach will be validated based on recently published experimental results. © 2011 IOP Publishing Ltd.
International Journal of Applied Electromagnetics and Mechanics (13835416)35(4)pp. 281-305
Conjugated polymer actuators can be employed to achieve micro scale precision positioning, having a wide range of application including biomimetic robots, and biomedical devices. They can operate with low voltage while producing large displacement, in comparison to robotic joints, they do not have friction or backlash, but on the other hand, they have complicated electro-chemo-mechanical dynamics, which makes accurate and robust control of the actuator difficult. There has been extensive research on modeling the electrochemical dynamics of polypyrrole bending actuators. However the mechanical dynamics modeling of actuator remains to be unexplored. In this paper finite element modeling and robust control of fast trilayer polypyrrole bending actuators is proposed. In the modeling part the infinite-dimensional admittance model of actuator will be replaced with a family of linear uncertain transfer functions based on Golubev Method. Further model development will take into account the proper mechanical dynamics, which is essential, when using fast conducting polymer actuators. The purposed modeling approach will be validated based on the existing experimental data. In the controlling part the robust control QFT will be applied to control the highly uncertain dynamics of the conjugated polymer actuators while the actuator carrying variable tip loadings. Finally the analysis of design shows that QFT controller has consistent and robust tracking performance. © 2011 - IOS Press and the authors. All rights reserved.
IEEE Transactions on Nuclear Science (15581578)58(1 PART 2)pp. 258-266
In this paper, a robust power control system for the nuclear reactor using the Quantitative Feedback Theory method (QFT) is presented. A nonlinear uncertain dynamic system with different working condition has been considered for the nuclear reactor. To design a robust control system for the nuclear reactor, two different controls oriented linear models have been identified. The nonlinearity and uncertainty of the system are modeled as uncertainty for a nominal LTI system. The QFT controller has been designed and simulated to control the reactor power. The proposed control system has a favorable performance over the wide range of reactor operating conditions and can easily be implemented. © 2011 IEEE.
In recent years, interests have emerged for application of MEMS for optical switching in telecommunications industry. Real time robust control of a nonlinear MEMS optical switch using quantitative feedback theory (QFT) method in switching operation is considered in the present work. Nonlinear system rendered into linear configuration by employing system identification techniques to exploit applications of QFT to envisage robust stabilization, tracking specification and perturbation attenuation. Simulation studies are conducted to show the efficiency of the proposed robust scheme as well. ©2010 IEEE.
Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering (09596518)224(1)pp. 41-51
Conducting polymer actuators are used in a diverse range of applications including biomimetic robots and biomedical devices. In comparison to robotic joints, they do not have friction or backlash, but on the other hand, they have complicated electro-chemo-mechanical dynamics which makes modelling and control of the actuator really difficult. In addition they also have the disadvantages of creep, hysteresis, and highly uncertain and time-varying dynamics. In this paper a Takagi-Sugeno (T-S) fuzzy model is used to represent the uncertain dynamics of the actuator, and the resulted fuzzy model is validated using experimental data. A system that consists of fuzzy state feedback to a PI controller is designed on the basis of the obtained T-S fuzzy model using the parallel distributed compensation scheme. The sufficient conditions for the existence of such a controller are derived in terms of linear matrix inequalities. The obtained results show that the designed controller can achieve a good control performance despite the existence of uncertain actuator dynamics.
