Chaotic and bifurcation dynamic behavior of a simply supported rectangular orthotropic plate with thermo-mechanical coupling

Abstract

This paper presents a novel analytical approach utilizing fractal dimension criteria and the maximum Lyapunov exponent to characterize the conditions which can potentially lead to the chaotic motion of a simply supported thermo-mechanically coupled orthotropic rectangular plate undergoing large deflections. The study commences by deriving the governing partial differential equations of the rectangular plate, and then applies the Galerkin method to simplify these equations to a set of three ordinary differential equations. The associated power spectra, phase plots, Poincaré map, maximum Lyapunov exponents, and fractal and bifurcation diagrams are computed numerically. These features are used to characterize the dynamic behavior of the orthotropic rectangular plate under various excitation conditions. The maximum Lyapunov exponents and the correlation dimensions method indicate that chaotic motion of the orthotropic plate occurs at η1 = 1.0, p¯=2.0, and δ¯=0.05 for an external force of f¯=5.0. The application of an external in-plane force of magnitude p¯=1.08 causes the orthotropic plate to perform bifurcation motion. Furthermore, when p¯>3.0, aperiodic motion of the plate is observed. Hence, the dynamic motion of a thermo-mechanically coupled orthotropic rectangular plate undergoing large deflections can be controlled and manipulated to achieve periodic motion through an appropriate specification of the system parameters and loads.