On the softening and hardening nonlinear behavior of laminated cylindrical shells

Abstract

The nonlinear dynamic response of laminated composite cylindrical shell under external periodic force with forcing frequency varied in the spectral vicinity of first and second natural frequency is presented. The governing equations of motion are solved to obtain the state vector representing the periodic response using Newmark time marching based shooting approach and arc length/pseudo-arc length continuation techniques. The main contributions of the paper is to explore the parameters influencing the transition between softening and hardening nonlinear behavior of cylindrical shell. In addition the nonlinear restoring force dynamics leading to differences in the positive and negative half cycle response amplitude have been explained using strain/stress distribution. Further, the upper and lower surfaces of the shell are subjected to tensile and compressive stresses for unequal time within a cycle. The periodic variation of the steady state stresses and its FFT reveal significantly large higher harmonic contributions detrimental to fatigue design of structures. Symmetric laminated shell depict greater response amplitude compared to antisymmetric ones owing to increase in restoring forces due to lamination scheme induced bending-stretching coupling for antisymmetric laminates. The deformed configuration of the shell corresponding to primary and secondary peak reveal modal interaction between first and higher modes.