运动板的非线性振动和混沌

项目名称： 运动板的非线性振动和混沌

项目编号： No.11202135

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 唐有绮

作者单位： 上海应用技术学院

项目金额： 26万元

中文摘要： 应用和发展经典非线性振动理论和现代非线性动力学理论，研究运动黏弹性板的非线性振动及其稳定性和混沌。在建模、分析和仿真各环节，聚焦运动黏弹性板的本质特征，控制方程中的陀螺项。考虑von Karman非线性薄板理论，建立复杂约束情况下运动黏弹性板面内及面外振动的数学模型；分别通过解析和数值仿真方法求解运动板的振动固有频率和模态函数；并以此为基础利用近似方法研究系统非线性振动的稳态响应及其稳定性；考察运动板从平衡失稳到周期运动再分岔进入混沌的全过程，采用数值仿真技术研究运动黏弹性板的分岔特性和混沌形态等非线性行为。通过本项目的实施，构建运动黏弹性板非线性振动分析的理论框架，拓展非线性振动理论和非线性动力学理论的应用范围，发展和完善非线性连续体(特别是陀螺体)的近似解析和数值解法，深化人们对运动黏弹性板非线性振动特性、分岔特征和混沌性态的理解，为相应工程系统的分析和设计提供理论基础和技术储备。

中文关键词： 运动黏弹性板；非线性振动；稳定性；混沌；

英文摘要： The classical nonlinear vibration theory and the modern nonlinear dynamics theory are applied and developed to investigate nonlinear vibration, stability and chaos of moving viscoelastic plates. In modeling, analysis and simulation, the essential characteristics of the moving viscoelastic plates which are gyro in the governing equation are focused on. Considering the nonlinear von Karman plate theory, the mathematical model of the in-plane vibration and surface vibration of the moving viscoelastic plates with complex constraint case is established. The natural frequencies and mode functions are solved by the analytical and numerical simulation methods. The steady state response and stability of the system are studied by the use of the approximate methods. The whole process of moving plates from instability to a periodic motion to the balance of the bifurcation and then into chaos is investigated. The nonlinear behavior (the bifurcated features and chaos) of the moving viscoelastic plates are studied by the use of numerical simulation. Through the implementation of this project, the theoretical framework of the non-linear vibration analysis of the moving viscoelastic plates is built; the scopes of application of the non-linear vibration theory and nonlinear dynamics theory are expanded; the approximate analytical

英文关键词： Moving viscoelastic plate；Nonlinear vibration；Stability；Chaos；