Influence of geometric imperfections on the nonlinear forced vibration characteristics and stability of laminated angle-ply composite conical shells

Abstract

The forced vibration characteristic of laminated composite truncated conical shell has been analyzed by including von Karman kinematic non-linearity. The geometric imperfection is included in the analysis by providing an initial doubly sinusoidal transverse displacement. The finite element analysis has been carried out using the displacement field of FSDT and the constrained strain terms are interpolated using field consistent modified shape functions in order to avoid membrane/transverse shear locking. The steady state periodic response has been obtained by solving the governing equations in time domain using modified shooting method and arc length/pseudo-arc length continuation techniques. The main aim of the paper is to explore the effects of initial imperfections, fiber-angle and curvature on the nonlinear periodic response characteristics. Further, the stability of the periodic response has also been investigated and the ensuing bifurcations resulting in loss/gain of stability has been discussed. The parameters affecting the softening/hardening nonlinear behavior of the conical shells have also been assessed. The nonlinear frequency response reveal greater amplitude during inward half cycle due to destabilizing nature of the nonlinear membrane stress resultants during inward motion at large amplitudes. Multiple stress reversals is observed during a periodic cycle which has large ramifications on the fatigue design.