Damped forced vibration analysis of layered functionally graded thick beams with porosity

Abstract

The following article presents the damped forced vibration of layered functionally graded thick beams including material porosities. In case of very thick beams, beam theories fail to satisfy boundary conditions and to predict the mechanical response accurately. So, the two-dimensional (2D) plane continuum model is exploited to model a thick functionally graded layered beam. The beam is composed from three- layers with functionally graded porous materials. The porosity is described by three different distribution models through the layer thickness. Applied forces to the functionally graded beam are assumed to be sinusoidal harmonic point load in time domain. The Kelvin-Voigt viscoelastic constitutive model is used to simulate damping effect. The governing equations are obtained by using Lagrange's equations. In frame of finite element analysis, twelve -node 2D plane element is exploited to discretize the space domain of thick beam. In the solution of the dynamic problem, the Newmark average acceleration method is used. Numerical studies illustrate effects of porosity distribution, stacking sequence, and graduation constant on the dynamic responses of layered functionally graded porous thick beams. The results show that the porosity function, stacking sequences and the damping ratio have a vital role in dynamic response of functionally graded beams. The proposed model can be used in nuclear, marine, and aerospace technologies.