Bifurcation and Chaos of Functionally Graded Carbon Nanotube Reinforced Composite Cylindrical Shell with Piezoelectric Layer

This paper investigates bifurcation and chaos of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) cylindrical shells containing piezoelectric layer (PL) under combined electro-thermo-mechanical loads. We assumed that FG-CNTRC material properties were graded along thickness direction and determined them using mixtures' law. Governing equations of structures were derived according to the theory of von Karman nonlinear shell and PL with thermal effects. Next, the governing equations were transformed into second order nonlinear ordinary differential equations (SNODE) with cubic terms through Galerkin procedure and further into first order nonlinear ordinary differential equations (FNODE) through introducing additional state variables. Complex system dynamic behavior was qualitatively examined using fourth order Runge-Kutta method. The effects of different factors including applied voltage, volume fraction, temperature change, and distribution of carbon nanotubes (CNTs) on bifurcation and chaos of FG-CNTRC shells with PL were comprehensively studied.