Dynamic Analysis of Layered Functionally Graded Viscoelastic Deep Beams with Different Boundary Conditions Due to a Pulse Load

Abstract

This paper studies the dynamic viscoelastic response of functionally graded (FG) thick 2D cantilever and simply supported beams under dynamic pulse load, for the first time. A point load applied at a specific spatial point is described as a time-pulse sinusoidal load. Two-dimensional plane-stress constitutive equation is exploited to describe the local stress-strain relation through the beam. The gradation of material is depicted by generalized power law function through the layer thickness across beam thickness. The Kelvin-Voigt viscoelastic model is proposed to describe material damping of structure. Lagrange's equation is employed to derive governing motion equation. A finite element method (FEM) is exploited to discretize the spatial domain of 2D beam structure by using 12-node 2D plane element. Numerical Newmark implicit time integration method is proposed to solve the equation of motion incrementally and get the response of beam structure. Two types of boundary conditions are considered in the numerical examples. In numerical results, effects of stacking sequence, geometry parameters and material gradation index and viscoelasticity coefficients on the displacement-time response of layered functionally graded viscoelastic deep beams for different boundary conditions.