Chaotic dynamics of a non-autonomous nonlinear system for a smart composite shell subjected to the hygro-thermal environment

In this research, nonlinear dynamic behaviors of multiscale composites doubly curved shells have been investigated by employing multiple scales Perturbation Method. Three-phase composites shells with polymer/Carbon nanotube/fiber (PCF) according to Halpin–Tsai model have been assumed. The displacement- strain of nonlinear vibration of multiscale laminated doubly curved shells via higher order shear deformation (HSDT) theory and using Green–Lagrange nonlinear shell theory is obtained. The governing equations of composite doubly curved shell have been derived by implementing Hamilton’s principle and shell considered to be simply supported. For investigating correctness and accuracy, this paper is validated by other previous researches. Finally, bifurcation diagram, phase portraits and Poincare maps are investigated. The results indicate different dimensionless force; curvature ratio and kind of distribution pattern have strong influence on nonlinear vibration control of the composite multiscale doubly curved shell.