Nonlinear vibration responses of lattice sandwich beams with FGM facesheets based on an improved thermo-mechanical equivalent model

Abstract

An investigation on the nonlinear vibration behaviors of a lattice sandwich beam with pyramidal truss core and functionally graded material (FGM) facesheets under thermo-mechanical loads is performed with consideration of the temperature-dependency of material properties. In present work, an improved equivalent methodology is proposed to determine the transverse shear modulus of pyramidal core subjected to a non-uniform thermal field across thickness direction and makes lattice truss core transformed to a continuous layer. Finally, the lattice sandwich beam is modeled as a three-layered sandwich structure. The facesheets are made of FGMs with mixture of ceramics and metals in a pow-law form. The outer surfaces of facesheets are ceramic-rich, while the inner surfaces are metal-rich. The nonlinear strain–displacement relations are established based on the von Kármán large deflection and classical beam theory. The Lagrange method are implemented to yield equations governing the free and forced vibration behaviors. With the help of Newton-Raphson iteration technique as well as the Newmark-β method, the nonlinear time-independent responses of the sandwich beam under thermal environment are solved. A comprehensive parameter study is directed to address the effects of non-uniform thermal environment, FMG facesheets, external load, and lattice core on the nonlinear vibrations of the beams.