Chaotic and Bifurcation Dynamics of a Thermo-Elastic Axisymmetric Circular Plate in Large Deflection

摘要

This paper presents the conditions that can possibly lead to chaotic motion and bifurcation behavior for a simply-supported large deflection thermo-elastic circular plate by utilizing the criteria of fractal dimensions, maximum Lyapunov exponents and bifurcation diagrams. The governing partial differential equation of the simply supported thermo-elastic circular plate is reduced by means of Galerkin and single-mode method. Several different features including Fourier spectra, phase plot, Poincare map and bifurcation diagrams are numerically computed. These features are used to characterize the dynamic behavior of the plate subjected to various excitations of lateral loads and thermal loads. Numerical examples are presented to verify the conditions that lead to chaotic motion and the effectiveness of the proposed modeling approach. Numerical modeling results indicate that large deflection motion of a thermo-elastic circular plate possesses chaotic motions, bifurcation motion and some jump phenomena under different lateral loads and thermal loads. The simulation results also indicate that the denominator of the ratio of "thermal loading frequency to lateral loading frequency turns out to be the period number. The dynamic motion of the circular plate is periodic if the frequency of lateral load is within a specific range or the thermal load is less than a specific critical value. The modeling results show that the proposed method can be employed to predict the nonlinear dynamics of any axisymmetric circular plate in large deflection.