Nonlinear transient response of porous FGM sandwich beams with elastically restrained ends in a thermal environment

Abstract

This study executes a semi–analytical investigation on the combined effects of pores, tangential ends constraints, initial geometric imperfection, foundation interaction, and high temperatures on the nonlinear transient response of functionally graded material (FGM) sandwich beams subjected to suddenly applied uniform transverse loads in thermal environments. Two types of sandwich beams corresponding to FGM face sheets and core layer are examined. The pores are distributed into FGM layers according to even and uneven types. The effective properties of porous FGM are estimated employing a modified rule of mixture. The motion equations are formulated on the basis of the first order shear deformation beam theory taking into consideration von Kármán nonlinear terms, initial geometric imperfection and interaction from elastic foundations. The derived equations are treated by means of analytical solutions along with Galerkin method to attain a time–dependent nonlinear ordinary differential equation. This differential equation is numerically treated by means of fourth–order Runge–Kutta scheme to trace nonlinear displacement–transient time paths. Parametric studies are performed to evaluate diverse effects on the nonlinear transient response curves of FGM sandwich beams. The results indicate that the pores and foundations have detrimental and beneficial effects on the dynamical bending resistance capability of sandwich beams, respectively. The study also finds that the tangential end restraints make the dynamical deflection of beams exposed to thermal environments deeper. Besides, the initial geometric imperfection decreases and increases the dynamic deflection of the beams placed at room and elevated temperatures, respectively.