Dynamic analysis of functionally graded sandwich shells resting on elastic foundations

Abstract

Free vibrations of sandwich shallow shells resting on elastic foundations are investigated. It is assumed that shell consists of three layers of the different thickness. Different schemes of arrangement of layers are considered. Namely, the core is made of ceramics or metals , and the upper and lower layers are made of FGM. The volume fractions of metal and ceramic are described by the power law. Shear deformation shell theory of the first (FSDT) that includes interaction with elastic foundations is applied. To study shells with an arbitrary plan form the R-functions theory combined with the variational Ritz method are used. Validation of the proposed method and developed software has been examined on test problems for FG shell with rectangular plan form. New results for shallow shells with complex plan form were obtained. Effects of the power law index, boundary conditions, thickness of core and face sheet layers, elastic foundations on fundamental frequencies are studied in this work.