Isogeometric analysis of small-scale effects on the vibration of functionally graded porous curved microbeams based on the modified strain gradient elasticity theory

Abstract

This paper presents a size-dependent study on the free vibration behaviour of the functionally graded (FG) porous curved microbeams. Based on the different higher-order shear deformation models and the modified strain gradient theory, the governing equations are derived using Hamilton’s principle. Then, the isogeometric analysis approach is employed to solve these equations. Besides, the material properties and the material length scale parameters (MLSPs) vary along the thickness direction of the FG curved microbeams according to the rule of mixture scheme. Also, two types of porosity distributions across the thickness, including even and uneven, are considered. By increasing the order of the non-uniform rational b-spline (MLSPs) basis functions, the C2-continuity requirement can be easily achieved. To establish the validity of the proposed method, the present results are compared with those from the previous studies. Finally, the effects of the variable MLSPs, porosity parameter, material gradient indices, curvature and different boundary conditions on free vibration response of circular, elliptical and parabolic FG porous microbeams are investigated. The obtained results reveal that the size-dependent effects increase the natural frequency as well as porosity decreases it because of decreasing the stiffness. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature.