正交異向平板受熱激振之非線性分析

Analysis of a Nonlinear Orthotropic Plate Subjected to Thermal Excitation

本論文探討正交異向平板受熱激振之非線性分析，採用馮卡門平板理論（von Kármán plate theory），獲得非線性偏微方程式；以蓋里奇方法（Galerkinmethod）運算後，簡化為非線性常微方程式；提出以J 積分值為指標，用來建立J 積分值的分歧圖表現多解共存及初始空間的吸引子盆地圖。正交異向平板受熱激振有週期倍增至混沌響應及豐富的響應類型出現；配合以Poincarè 切面圖、相圖、頻譜圖和Lyapunov 指數，說明響應類型。

In this paper, we study a nonlinear orthotropic plate subjected tothermal excitation. The governing equations are derived from von Kármánplate theory. From them, the simplified nonlinear ordinary differentialequations are then obtained by employing Garlerkin’s method. We haveprovided an effective index J integral, which constructs the J bifurcationand basins of attraction to evaluate the influence of parameters and toobserve the characteristics of these systems. Chaotic motion and basins ofattraction are distinguished by J integral with assistance of Ponincarésection, phase portraits, frequency spectrum, and Lyapunov exponent.