Free vibration of FGM layered beams by various theories and finite elements

Abstract

The Carrera Unified Formulation (CUF) is used to perform free-vibrational analyses of functionally graded (FG) structures. CUF is a hierarchical formulation for obtaining refined structural theories that account for variable kinematic description. These theories can be obtained by expanding the unknown displacement variables over the beam section axes by adopting any kind of function. The number of the terms in the expansions is a free parameter of the analysis. For Taylor-like expansions, the linear case can result in classical beam theories. For the first time in the 1D CUF framework, the Finite Element method is used to solve the governing equations of functionally graded beams which are derived in a weak form by means of the Principle of Virtual Displacements. These equations are written in terms of f¨undamental nuclei.¨ Their forms do not depend on the expansions used. Several structures are considered, including a sandwich beam with FG core, laminated beams, thin- and thick-walled boxes as well as sandwich cylinders. The results are shown in terms of natural frequencies and compared with those available in existing literature.