On Natural Frequency of Finite Element Modeled Geometrically Imperfect Shear Deformable Functionally Gradient Sandwich Arches in Thermal Environment

Abstract

In the present study, the natural frequency of finite element modeled geometrically imperfect shear deformable functionally gradient (FG) sandwich arches in the thermal environment has been studied. The formulation is based on the higher-order shear deformation theory. The upper layer of the sandwich arch is considered to be ceramics, whereas the lower layer is made of metal. The core of the sandwich arch is made of gradient materials. The material properties of the sandwich arches are varying continuously in the thickness direction only by a simple power-law distribution in terms of volume fractions of the constituents. Comparison and convergence studies have been performed to validate the present formulation with the limited available literature. Parametric studies have been performed to study the effect of various influencing parameters on the frequency of the FG sandwich arches, i.e., volume fraction index, thickness-to-length ratio, imperfection amplitude, and opening angle. New results are presented which can be treated as benchmark solutions for future researches.