Improved formulation for spatial free vibration of thin-walled Al/Al2O3 FG sandwich beams with non-symmetric open, single- and double-cell sections

Abstract

In this study, an improved formulation is presented for the spatially coupled free vibration analysis of Al/Al2O3 thin-walled functionally graded (FG) sandwich beams with non-symmetric open, single- and double-cell sections. The thin-walled beam model is based on the Euler-Bernoulli beam theory for bending and the Vlasov theory for torsion. The FG beam consists of ceramic (Al2O3) and metal (Al) phases varying through the wall thickness. Three types of material distribution, which leads to the material coupling, are considered. The strain and kinetic energies are derived by introducing displacement parameters defined at the arbitrary chosen axis considering the effects of axial-flexural-torsional coupling and restrained warping. For finite element analysis, cubic polynomials are utilized as the shape functions of two-noded Hermitian beam element. Elastic stiffness and mass matrices for the non-symmetric cross-sections are precisely evaluated. In order to illustrate the accuracy of this formulation, the present finite element solutions of thin-walled sandwich beams with non-symmetric open, single- and double-cell sections are presented and compared with available results. Especially, the effects of various structural parameters of thin-walled FG sandwich beams such as gradient index, thickness ratios of ceramic in flanges and webs, and non-symmetricity of cross-section on the warping to torsion ratio of cross-section and the spatially coupled natural frequencies are parametrically investigated.