Nonlinear Vibration of Functionally Graded Porous-Cellular Timoshenko Beam Subjected to In-Plane Periodic Loading

Abstract

The present study deals with an open cell shear deformable functionally graded porous beam subjected to in-plane periodic loading to analyze its nonlinear vibration behaviour. The porous beam in this study is modelled based on Timoshenko beam theory i.e., first-order shear deformation theory (FSDT). The porosities are dispersed throughout the thickness of the beam considering uniform and non-uniform symmetric distribution models. For the two distribution systems, the mass density and elasticity moduli of porous beams are considered to vary in the thickness direction. Using Hamilton’s principle, the partial differential equations (PDEs) governing the behaviour of porous beams are derived for the simply supported boundary condition. Then, Galerkin’s method is employed to convert the PDEs to nonlinear ordinary differential equations (ODEs). Further to trace the non-linear vibration behaviour (frequency-amplitude curve) of the porous beam, these ODEs are solved by Incremental Harmonic Balance (IHB) method. A parametric study is presented to assess the influence of porosity, static and dynamic load factors on the vibrational characteristics of the porous beams. As anticipated, the porous beam with non-uniformly symmetric distribution exhibited a higher critical buckling load compared to the uniform distribution of porosity