Legendre-meshfree vibration analysis of cross-ply laminated elliptical shell of revolution considering the effect of drop-off ply

Abstract

In this study, the vibration investigations on cross-ply laminated closed elliptical shell introducing the effect of symmetrical and unsymmetrical drop-off ply are performed by using a Legendre moving least squares (Legendre-MLS) meshfree method. Several uniformly subshells of uniform thickness without drop-off plies are assembled rigidly in order to consider the drop-off ply included in the elliptical shell, and the corresponding theoretical formulations is derived following the first-order laminated shell theory (FSDT). The boundary conditions of elliptical shell and continuity relationship between adjacent interfaces of substructures are imposed by artificial springs having variable stiffness. On the basis of meshfree theory, Legendre-MLS shape function in conjunction with circumferential Fourier series is developed to approximate the displacement variables. Thus, boundary equations and the governing equations are discretized to obtain the vibration solutions of cross-ply laminated elliptical shell of revolution considering the effect of symmetrical and unsymmetrical drop-off ply. The applicability of the Legendre-meshfree model is clarified by carrying out some comparative evaluations of current results and those from archived literature and finite element simulation models. And then, some parametric studies for the influence of structural boundaries, geometric dimensions, lamination schemes etc., on the vibration properties are performed.