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

10.29507/JT.200506.0001

簡守謙(Shoou-Chian Jen)；趙榮輝(Jung-Hui Chao)

平板 ； 分歧圖 ； 混沌 ； plate ； bifurcation diagram ； chaos

技術學刊

20卷2期（2005 / 06 / 01）

107 - 114

繁體中文

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(Galerkin method)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 to thermal excitation. The governing equations are derived from von Kármán plate theory. From them, the simplified nonlinear ordinary differential equations are then obtained by employing Garlerkin's method. We have provided an effective index J integral, which constructs the J bifurcation and basins of attraction to evaluate the influence of parameters and to observe the characteristics of these systems. Chaotic motion and basins of attraction are distinguished by J integral with assistance of Ponincaré section, phase portraits, frequency spectrum, and Lyapunov exponent.