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Mechanics Based Design of Structures and Machines (15397742)53(8)pp. 5762-5794
This paper discusses vibrational energy harvesting, a technology that captures energy from ambient sources and transduces it into electric energy. The primary challenge in designing Vibration energy harvesters is that both power output and frequency bandwidth may not be simultaneously enhanced. Numerous studies have ventured into methodologies to augment power output and broaden the bandwidth for effective energy harvesting. However, these often hinge on beam structures, leading to intricate geometries that require substantial space. The research highlighted in this paper suggests innovative ideas based on multimodal energy harvesting techniques, devoid of the complexities inherent in previous designs. A semi-analytical electroelastic model for piezoelectric multi-plate energy harvesters, grounded in the principles of classical plate theory is proposed in this research. The mode shapes of the plate are numerically obtained using the differential quadrature method (DQM) under the clamped-free-clamped-free (CFCF) boundary conditions. Subsequently, modal analysis is employed to extract the output voltage of the system. The results are validated against pioneering research and various case studies are examined to explore the effect of diverse parameters on the magnitude and bandwidth of output voltage. The findings demonstrate that by fine-tuning the material properties of the harvester’s components, an optimal design can be realized. © 2025 Taylor & Francis Group, LLC.
International Journal of Systems Science (00207721)
This research proposes a novel hybrid force/position control (RL-HC) approach for robotic systems, utilising reinforcement learning. The proposed controller demonstrates superior robustness and performance, particularly in tracking the end-effector's position and contact force, compared to the hybrid sliding mode force/position control (HSMC) method, even in the presence of structural and non-structural uncertainties. The RL-HC controller is designed around a fixed-time sliding mode model, integrating force and position control components. The stability of this controller is established using the Lyapunov theory. Additionally, the reward function within the reinforcement learning network is carefully crafted to align with key objectives, including minimising chattering, force error, position error, and control effort. A simulation performed using a 3-DOF Delta Robot illustrates the effectiveness of the RL-HC approach. Results indicate that RL-HC outperforms traditional methods, showcasing better performance and robustness when facing various external disturbances and uncertainties. Specifically, the findings highlight a significant reduction in position error, force error, total control effort, and chattering. The study also illustrates how different reward function designs impact the achievement of the desired objectives. © 2025 Informa UK Limited, trading as Taylor & Francis Group.
Abdi, F.,
Ghasemi, A.,
Ariaei, A.R.,
Eftekhari, S.A.,
Nasr, M.,
Khabaz, M.K.,
Salahshour, S. Heliyon (24058440)11(1)
This study considers Timoshenko beam theory and the isogeometric analysis method to investigate the free vibration and buckling of axially functionally graded (AFG) tapered beams. The governing equations are obtained from the kinematic assumptions of Timoshenko beam theory and Hamilton's principle. The isogeometric analysis approach is implemented to solve the motion equations. One-dimensional B-spline basis functions are used to estimate the displacement field, describe the geometry, and illustrate the deformed shapes of the beam. Due to suffering the isogeometric approach from the shear locking phenomenon, the selectively reduced integration is applied. It is shown that this method can mitigate the effect of shear locking. In this attempt, the effect of material non-homogeneity parameters, mass density, Young's modulus, and taper ratio on the critical buckling loads and natural frequencies are considered for various boundary conditions. Several numerical examples show the accuracy and reliability of this method. The obtained results are in accord with the ones in the related articles and can be adopted as future reference solutions. © 2024 The Authors
Measurement: Journal of the International Measurement Confederation (02632241)224
The mesh stiffness is a necessary and influential parameter in system dynamics modeling and vibration analysis of straight bevel gear systems (SBG). A new experimental method, employing a laser extensometer (LE) and an innovative setup, is developed to calculate the mesh stiffness in both healthy and cracked systems. An analytical method based on potential energy and tooth root crack modeling is also proposed. Both methods were implemented on healthy and cracked gear systems with varying crack depths. The new LE experimental method's results are compared with those obtained from the proposed analytical method. The results showed good agreement between both methods, indicating that the newly proposed experimental method considers all parts of mesh stiffness and is suitable for measuring mesh stiffness in both healthy and cracked SBG systems. © 2023
Measurement: Journal of the International Measurement Confederation (02632241)238
The mesh stiffness plays a crucial role in influencing the performance and behavior of straight bevel gear (SBG) systems. Precisely determining the mesh stiffness enables to assess the SBG system's dynamic behavior more accurately and anticipate potential concerns such as crack identification and noise reduction. A novel experimental method is developed, employing experimental modal analysis associated with metaheuristic algorithms and an innovative setup. This method effectively determines the mesh stiffness in healthy and cracked systems. Additionally, an analytical method based on the potential energy associated with crack modeling is proposed. Both methods are implemented on SBG systems with varying crack depths. The results obtained from the experimental method are compared with those from the analytical method, revealing good agreement between them. This demonstrates that the newly proposed experimental method effectively considers all parts of mesh stiffness and is appropriate for determining the mesh stiffness in healthy and cracked SBG systems. © 2024
IET Electric Power Applications (17518660)18(10)pp. 1200-1213
The vibration and acoustic noise of a permanent-magnet synchronous motor are analysed and evaluated. Acoustic noise sound levels, their prominent frequencies, and the noisiest motor speed range are predicted. According to many resources, the radial vibration of the stator system due to the magnetic attraction between rotor permanent magnets and stator iron teeth is the main reason for the acoustic noise propagation of the PMSMs. The dominant orders of the spatial circumferential harmonics of the radial magnetic forces (RMFs) have been investigated and compared. The complete and complicated mechanical components, materials, and harmonics of the magnetic forces of the motor and their interaction are simplified and equalised to a vibration model, which consists of the interaction between the stator system and the dominant harmonic orders of the RMFs. Based on this approach, the simplest and most adequate semi-analytical-FEM model for noise prediction in PMSMs is proposed. This model, in addition to simplification, clarifies the role of the main mechanical and electromagnetic origins of noise generation. The acoustic noise prediction, using the proposed method has been compared with the experimental results. There is a proper agreement between the analytical, the FEM, and measurement results. © 2024 The Author(s). IET Electric Power Applications published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology.
Nonlinear Dynamics (0924090X)112(14)pp. 11945-11970
The tooth crack identification through the effect of the tooth root crack on nonlinear vibration behaviors in a straight bevel gear (SBG) system is sought. The mesh stiffness is evaluated through an analytical method based on the potential energy and Tredgold approximation associated with tooth root crack modeling. A 10-dof model is developed for the SBG system where the backlash nonlinearity is of concern. To assess the nonlinear vibration behaviors of the SBG system, first, the dynamic response is extracted analytically with the proposed dynamic model, and experimentally with a designed setup, then the extracted response is assessed based on the different crack identification statistical factors. Results indicate that the Skewness is the most effective factor in identifying the crack in the SBG system with backlash nonlinearity, compared to other investigated factors. The nonlinear vibration response as a time history, phase diagram, Poincaré map, modal analysis, and mesh stiffness FFT spectrum is analyzed and recommended as an appropriate indicator for tooth root cracks. The modeled mesh stiffness and simulated SBG system are verified by applying FEM and the experimental method. Graphical abstract: (Figure presented.) © The Author(s), under exclusive licence to Springer Nature B.V. 2024.
Archive of Applied Mechanics (14320681)93(8)pp. 3045-3049
The published article consists of part of Fig. 4. It must be published as, (Figure presented.) Some of the mode shapes of the system The original article has been corrected. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
Archive of Applied Mechanics (14320681)93(8)pp. 3025-3043
An analytical solution is presented for determining the natural frequencies, mode shapes, and forced responses of a system of elastically connected annular plates with general boundary conditions. By applying the Kirchhoff’s plate theory, the motion of n elastically connected plates is described through a set of n differential equations. These equations are coupled, thus, hard to solve. A new variable change is presented to uncouple the equations and obtain one decoupled equation for each plate. These equations are solved separately and analytically, and the natural frequencies, mode shapes, and forced responses of the separated plates are obtained. The frequencies of the original system are those calculated analytically for the decoupled system, and the mode shapes and forced responses are obtained by applying the inverse transform. A three plates system with clamped edges is solved to demonstrate this approach. The effects of stiffness coefficients of elastic layers, inner edge radius of the plates, and the frequency of the external harmonic force on the answers are assessed. Applying ABAQUS software, the analytical solution is validated, where a good agreement is observed. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
Earthquake Engineering and Engineering Vibration (16713664)21(4)pp. 947-967
A new procedure is proposed to ease the analyses of the free vibration of an elastically connected identical plates system with respect to Kirchhoff plate theory. A structure of n parallel, elastically connected rectangular plates is of concern, whereby the motion is explained by a set of n coupled partial differential equations. The method involves a new change in variables to uncouple equations and form an equal system of n decoupled plates, while each is assumed to be elastically connected to the ground. The differential quadrature method is adopted to solve the decoupled equations. To unravel the original system, the inverse transform is applied. Decoupling the equations enables one to solve them based on the solution methods available for a single plate system. This also diminishes the computational costs of such problems. By considering different boundary conditions, a case study is run to present the method and to validate the results with its counterparts, for which excellent agreement is observed. Assessing the influence of dimensionless thickness, aspect ratio, and stiffness coefficients on the frequencies reveals the different effects of them at the low order of dimensionless natural frequencies in comparison with high orders and for different boundary conditions. © 2022, Institute of Engineering Mechanics, China Earthquake Administration.
Journal of Sound and Vibration (10958568)535
In this article, a novel multi-objective modified fractional-order nonsingular terminal sliding mode (MFONTSM) controller is designed for the flexible spacecraft attitude control and passive vibration suppression, assuming the control torque saturation in the system dynamics. Then, by considering the effects of flexible components on the appendages modal equation as an external disturbance, an active FONTSM controller is designed separately to suppress any residual vibrations using piezoelectric actuators. The practical fixed-time stability of the closed-loop system is analyzed and proved using the Lyapunov theorem. Finally, the proposed controllers’ performance has been tested in the presence of uncertainties, external disturbances, and the absence of the damping matrix to study the proposed method's effectiveness. It was observed that the proposed passive and active control strategies were able to achieve fast attitude stabilization while providing substantial vibration suppression under uncertainty and disturbance even in the absence of any damping terms in the system. © 2022 Elsevier Ltd
Mechanical Systems and Signal Processing (08883270)177
The focus of this study is on multi-beam piezoelectric energy harvester (MPEH) network optimization with respect to its configuration. Indeed, the harvested power in the single piezoelectric energy harvesters (SPEHs) may not meet the power level necessary to many applications. In case of constraint in the beam dimensions, the issue of sufficient power generation can be undertaken by arranging a definite number of those harvester units as an MPEH network. The versatility of network configurations presented in the literature, consisting of the harvester beams and their series/parallel interconnections, are limited to only two scenarios including all-series and all-parallel connections of the beams. As will be shown, these classic configurations are not necessarily the optimum ones for a given vortex shedding (VS) frequency. In fact, the harvested power as a function of VS frequency can be maximized by adopting a special network configuration, referred to as the optimum network configuration (ONC). In this study, the general form of the harvested power for each VS frequency is presented in a closed-form expression as a function of the network parameters. An optimization problem is formulated to maximize the harvested power and to obtain the ONC, which is solved through a proposed algorithm named the network configuration optimizer (NETCOOP). In the proposed MPEH structure, electrical switch blocks are used to implement the ONC and to reconfigure the network according to each VS frequency. The obtained VS frequency-dependent ONC enables the designers to develop the best configuration at each fluid flow velocity. To highlight the advantages of this proposed algorithm, the performance of the ONC is compared with other configurations like the all-series and the all-parallel configurations. In the simulation results, the optimum harvested power is obtained for different VS frequencies and load resistances by applying the brute-force approach. It is revealed that the harvested power obtained by the NTECOOP algorithm matches the optimum performance. © 2022 Elsevier Ltd
ISA Transactions (00190578)128pp. 162-173
In this study, a new adaptive fractional-order nonsingular terminal sliding mode (AFONTSM) controller is presented. A novel multi-purpose sliding surface is constructed, with the aim of bringing the reaction wheels in to rest after every attitude stabilization maneuver, utilizing the fractional-order difference of the quaternion error and the reaction wheels angular momentum error. The closed-loop system's practical fixed-time stability is investigated using the Lyapunov theorem under uncertainty and external disturbance. The AFONTSM controller's performance is compared with the existing nonsingular terminal sliding mode (NTSM), full-order NTSM, and fractional-order sliding mode controllers. Finally, the proposed AFONTSM controller's effectiveness is studied in close-to-reality situations through practical experiments on the spacecraft attitude control subsystem simulator under internal/external disturbance and uncertainty; then, the results are compared with previous studies. © 2021 ISA
This study aimed to improve the control scheme incorporated into the unknown system dynamics estimator (USDE) to deal with unknown dynamics and external disturbances. In comparison with the nonlinear disturbance observer (NDO) that requires calculating the inverse of the inertia matrix, USDE can be easily implemented, and their parameter tuning is more straightforward. We use the super twisting sliding mode algorithm (STA) to achieve a faster convergence rate and increase tracking performance. The closed-loop stability of the new composite controller is proved. Finally, the improvement of the new hybrid proposed controller is confirmed by using numerical simulation and experimental tests on a DELTA robot. Then the performance of the new controller is compared with the previous method. © 2022 IEEE.
The leader-following attitude consensus problem for multiple rigid spacecraft formation systems (MSF) with uncertainties, external disturbances, and actuator saturation is addressed in this paper. The first step to solve this problem is to assume that all parameters of the rigid spacecraft system and networks communication links are known. At first, the leader-following consensus problem is redefined to well defined error system by utilizing a nonlinear distributed observer for the leader spacecraft. Then by composing a high order disturbance observer (HODO) and adaptive super twisting algorithm (ASTA) the control problem is solved for each spacecraft. Finally, a simulation example is given with one leader and four followers. © 2021 IEEE.
Jordan Journal Of Mechanical And Industrial Engineering (19956665)13(2)pp. 69-74
Spur gear systems are widely used in power transmission systems in the industry. One of the common defects of the gears is tooth crack. Tooth crack increases the vibration and also generates noise. Previous studies have shown that tooth stiffness will decrease due to any crack and it is important to estimate the magnitude of reduction of tooth stiffness. This research suggests a new analytical approach for crack modeling and determining the reduction of time-varying gear mesh stiffness by Elastic Spring Method (ESM). Based on this approach, two or more cracks can be considered in one tooth. However, previous studies have primarily concentrated on one crack. In addition, it should be voted that each crack is replaced by one linear and one torsional spring in the present study. The results that were obtained from this method are validated through a comparison with Limit Line Method (LLM) and Finite Element Method (FEM). © 2019 Jordan Journal of Mechanical and Industrial Engineering. All rights reserved.
Journal of Intelligent Material Systems and Structures (1045389X)30(18-19)pp. 2651-2669
In this study, the influence of carbon nanotubes agglomeration is investigated on the electroelastic dynamic behavior of a sandwich plate. The smart sandwich plate consists of functionally graded porous layer as the core and piezoelectric layers as the face sheets, which is subjected to the harmonic electrical loading. In order to take into account the continuum model for the silica aerogel foundation of the smart structure, the modified Vlasov’s model is applied. The porosity distribution of the core layer varies non-uniformly throughout the thickness due to the non-uniform function. The equivalent material properties of nanocomposite core layer are determined using the Eshelby–Mori–Tanaka approach, in which the influence of carbon nanotube agglomeration is considered. For modeling the electroelastic fact sheets behavior, the piezoelasticity theory is adopted. On the basis of non-polynomial shear and normal deformation theory, the governing equations of motion are inferred applying the Hamilton’s principle and the obtained equations are solved by an iterative procedure. The verification is accomplished through the available results in the literature and the influences of carbon nanotube agglomeration, different geometrical parameters, porosity index, and applied voltage are assessed on the dynamic deflection of nanocomposite sandwich plate. © The Author(s) 2019.
Applied Mathematical Modelling (0307904X)66pp. 472-485
Free and forced vibration analysis of a Timoshenko beam on viscoelastic Pasternak foundation featuring coupling between flapwise bending and torsional vibrations is studied in this article. The system motion is described through a coupled set of three partial differential equations. The differential transform method, DTM, as an efficient mathematical technique is adopted to obtain the natural frequencies and the mode shapes. The system force response is assessed for a moving concentrated load with a constant velocity. Two different methods are studied and applied in obtaining forced vibration response of the system: (1) the same time functions, STF, by setting out the orthogonality conditions derived in this article and (2) the different time functions, DTF. The difference between the responses of the system is assessed by applying STF and DTF for a constant moving load. The effects of some parameters on the system response are probed. A numerical example is solved to validate the results obtained here with the available ones and a close agreement is found. It is observed that the time functions in DTF and STF are almost identical for transverse displacement and bending angle and are significant for torsion angle, recommending the application of DTF when the bending-torsion coupling is of concern. © 2018 Elsevier Inc.
Archive of Applied Mechanics (14320681)88(7)pp. 1041-1057
Free vibration and buckling of a set of parallel Timoshenko beams joined by intermediate flexible connections under axial loading are assessed in this paper. The numbers of beams and intermediate connections are arbitrary. Through axial loading, a new set of equations is extracted, applicable in solving the axial loading problems. The existence of the intermediate connections and the related compatibility equations allow for the introduction of coupled partial differential equations. The solution involves a change of variables to uncouple the governing differential equations. The natural frequencies and mode shapes are calculated through the transfer matrix method. By presenting an appropriate equation, it is observed that the general formulation studied here, regarding the separated flexible connections, can easily cover the issue of parallel beams joined by Winkler elastic layers in a continuous manner presented in the literature. The effects of different parameters such as the number of beams, number and stiffness of elastic connections and axial loading are assessed on the natural frequencies and the critical buckling force. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
Journal of Applied Physics (00218979)120(5)
The free vibration analysis of a multiple rotating nanobeams' system applying the nonlocal Eringen elasticity theory is presented. Multiple nanobeams' systems are of great importance in nano-optomechanical applications. At nanoscale, the nonlocal effects become non-negligible. According to the nonlocal Euler-Bernoulli beam theory, the governing partial differential equations are derived by incorporating the nonlocal scale effects. Assuming a structure of n parallel nanobeams, the vibration of the system is described by a coupled set of n partial differential equations. The method involves a change of variables to uncouple the equations and the differential transform method as an efficient mathematical technique to solve the nonlocal governing differential equations. Then a number of parametric studies are conducted to assess the effect of the nonlocal scaling parameter, rotational speed, boundary conditions, hub radius, and the stiffness coefficients of the elastic interlayer media on the vibration behavior of the coupled rotating multiple-carbon-nanotube-beam system. It is revealed that the bending vibration of the system is significantly influenced by the rotational speed, elastic mediums, and the nonlocal scaling parameters. This model is validated by comparing the results with those available in the literature. The natural frequencies are in a reasonably good agreement with the reported results. © 2016 Author(s).
International Journal of Mechanical Sciences (00207403)107pp. 93-109
A new procedure for determining natural frequencies and mode shapes of a system of elastically connected multiple rotating tapered beams is presented through a differential transform method. These identical double tapered beams are assumed to rotate at a constant speed and their deformation is obeying the Timoshenko beam theory. The motion of the system is described by a coupled set of 2n partial differential equations. A substantial change of variables is employed to uncouple the governing differential equations. Thereafter, a new equivalent system of n decoupled Timoshenko beams is formed where each beam appears elastically connected to the ground, resulting to a bunch of similar equations. The inverse transform is applied to extract the solution of the original system in terms of the original variables. The results are validated against those reported in the literature and then the effects of the rotational speed, hub radius, taper ratios, rotary inertia, shear deformation, slenderness ratio and elastic layers stiffness coefficients on the natural frequencies are discussed. The natural frequencies are in excellent agreement with the reported results. © 2016 Elsevier Ltd. All rights reserved.
This article describes the construction of a five spacecraft flight simulator based on an air bearing system, which was designed and instrumented in university of Isfahan laboratory to evaluate and to perform research in the field of Attitude Determination and Control Systems for spacecraft. This simulator is modeled in Autodesk-Inventor software package to design the simulator component precisely. The hardware and software components of the testbed are detailed in this article. the constraints for the construction and final realization of this attitude simulator testbed are depicted. It describes all modifications needed to reconfigure the simulator system testbed. © 2016 IEEE.
Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology (13506501)230(5)pp. 591-599
Micropitting is a surface fatigue failure of the gear tooth that occurs due to repeated loading and unloading of the tooth surface in a manner that the contact stresses exceed the surface fatigue strength of the material. The micropitting process in essence is a fatigue problem and thus it occurs during millions of cycles of operation. Micropitting can lead to problems such as wearing of the gear tooth, vibrations, noise, and misalignment. Therefore, micropitting life prediction is necessary for design, performance, and reliability improvements. The present study predicts the coefficient of friction for each point along the line of action of the pinion and gear using the load-sharing concept. The subsurface stresses are then calculated and the Von Mises stresses at each point are obtained. Then, the pitting life is predicted by employing a model which was developed by Zaretsky. The predicted pitting lives are compared with the experimental data from the literature. A parametric study on the effect of applied load, speed, and surface roughness on the micropitting life of a pair of spur gears is conducted. It is shown that increasing the applied load results in the decrease in the micropitting life of the gear. Increase in the speed, on the other hand, results in formation of a better lubricant film and therefore the micropitting life increases. An increase in the surface roughness leads to a decrease in the micropitting life. © IMechE 2015.
Journal Of Applied And Computational Mechanics (23834536)1(4)pp. 181-186
This study introduces the Differential Transform Method (DTM) in the analysis of the free vibration response of a rotating closed section composite, Timoshenko beam, which features material coupling between flapwise bending and torsional vibrations due to ply orientation. The governing differential equations of motion are derived using Hamilton's principle and solved by applying DTM. The natural frequencies are calculated and the effects of the bending-torsion coupling, the slenderness ratio and several other parameters on the natural frequencies are investigated using the computer package, Mathematica. Wherever possible, comparisons are made with the studies in open literature. © 2015, Shahid Chamran University of Ahvaz.
Archive of Applied Mechanics (09391533)85(5)pp. 555-572
An analytical method is presented to determine the vibration characteristics of a rotating Timoshenko beam with variable cross section and intermediate flexible connections using the differential transform method. Based on the application of Timoshenko beam theory on separate beams and the compatibility requirements on each connection point, the correlations between every two adjacent spans are obtained. The formulation is extended to a point where it would be able to evaluate the cases with internal and external flexible connections. The results will be validated against those reported in the literature and compared with the ones from the modal test. A number of parametric studies are conducted to assess the stiffness of elastic connections, rotating speed, hub radius and tapered ratio effects on the beam natural frequencies and mode shapes. It is observed that by changing the stiffness of the intermediate springs, the general formulation developed here can cover a large array of problems such as cracked or intermediately constrained beams. © 2014, Springer-Verlag Berlin Heidelberg.
Archive of Applied Mechanics (14320681)83(9)pp. 1257-1272
An analytical transfer matrix method is presented to determine the effect of intermediate flexible constraints on the dynamic behavior of a multi-span beam subject to a moving mass. By using the Timoshenko beam theory on separate beams and applying the compatibility requirements on each constraint point, the relationships between every two adjacent spans can be obtained. By using a transfer matrix method, eigensolutions of the entire system can be determined. The forced responses can then be calculated by the modal expansion theory using the determined eigenfunctions. Some numerical results are presented to show the effects of intermediate constraints and locations on the dynamic response of the multi-span beams. It will be seen that the general formulation developed here can cover a large array of problems such as cracked or intermediately constrained beams. © 2013 Springer-Verlag Berlin Heidelberg.
Archive of Applied Mechanics (14320681)81(3)pp. 263-281
Based on Timoshenko beam theory, the dynamic response of an elastically connected multiple-beam system is investigated. The identical prismatic beams are assumed to be parallel and connected by a finite number of springs. Assuming n parallel Timoshenko beams, the motion of the system is described by a coupled set of 2n partial differential equations. The method involves a change of variables and modal analysis to decouple and to solve the governing differential equations, respectively. A case study is solved in detail to demonstrate the methodology and several plots of the midpoint deflections of beams are given and investigated for different values of moving load velocity and the stiffness of elastic connections. From the numerical results it is observed that the maximum deflection of the multiple Timoshenko beam system is always smaller than one of a single beam. © 2010 Springer-Verlag.
International Journal of Mechanical Sciences (00207403)52(8)pp. 1074-1091
This paper presents an analytical method for the application of piezoelectric patches for the repair of cracked beams subjected to a moving mass. The beam equations of motion are obtained based on the Timoshenko beam theory by including the dynamic effect of a moving mass traveling along a vibrating path. The criterion used for the repair is altering the first natural frequency of the cracked beam towards that of the healthy beam using a piezoelectric patch. Conceptually, an external voltage is applied to actuate a piezoelectric patch bonded on the beam. This affects the closure of the crack so that the singularity induced by the crack tip will be decreased. The equations of motion are discretized by using the assumed modes method. The cracked beam is modeled as number of segments connected by two massless springs at the crack locations (one, extensional and the other, rotational). The relationships between any two spans can be obtained by considering the compatibility requirements on the crack section and on the ends of the piezoelectric patch. Using the analytical transfer matrix method, eigensolutions of the system can be calculated explicitly. Finally, numerical simulations are performed with respect to different conditions such as the moving load velocity. It is seen that when the piezoelectric patch is used, the maximum deflection of the cracked beam approaches maximum deflection of the healthy beam. © 2010 Elsevier Ltd.
Journal of Sound and Vibration (10958568)326(3-5)pp. 709-724
This paper presents an analytical approach, as well as a calculation method for determining the dynamic response of the undamped Euler-Bernoulli beams with breathing cracks under a point moving mass using the so-called discrete element technique (DET) and the finite element method (FEM). First, the standard DET formulation is modified to consider the effects of Coriolis and centrifugal forces. Next, the formulation is extended to be able to evaluate the cases with open and breathing cracks under moving masses. The results will be validated against those reported in the literature and also compared with results from the finite element method. The effects of the moving mass velocity, location, and size of the crack on beam deflection will be investigated. Natural frequencies of the beam under the effect of crack will also be studied to compare the results with those of a beam without crack. It is observed that the presence of crack results in higher deflections and alters beam response patterns. In particular, the largest deflection in the beam for a given speed takes longer to build up, and a discontinuity appears in the slope of the beam deflected shape at the crack location. The effects of crack and load depend on speed, time, crack size, crack location, and the moving mass level. © 2009 Elsevier Ltd. All rights reserved.
Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics (14644193)221(4)pp. 551-556
The current article presents an analytical approach, as well as a calculation method for determining the dynamic response of Timoshenko beams under uniform partially distributed moving masses, using the so-called discrete element technique (DET). It is shown that the proposed methodology offers a compact and computationally efficient way of conducting parametric studies to evaluate the dynamic response of the beam-like structures with arbitrary boundary conditions such as railway and road bridges. First, a formulation is presented in a matrix form for beams under partially distributed masses. The results have been validated against analytical formulations, finite difference, and finite element results. A number of parametric studies were conducted to assess the effects of the moving mass velocity and moving mass length on the beam deflection. A major aspect of the work is the study of successive travelling masses for which the transient effects are important. Both analytical and DET results showed that the critical speeds were affected for successive moving masses. Finally, the effects of rotary inertia were studied for a range of inertia values to quantify the error arising from using the Bernoulli-Euler formulation for beams with large inertias. © IMechE 2007.
