粘弹性轴向运动板的分数阶本构关系建模及非线性动力学分析

项目名称： 粘弹性轴向运动板的分数阶本构关系建模及非线性动力学分析

项目编号： No.11202140

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： 杨天智

作者单位： 沈阳航空航天大学

项目金额： 23万元

中文摘要： 发展和应用分数阶非线性动力系统理论，研究具有分数阶粘弹性本构关系的轴向运动板的建模、非线性振动特性、分岔和混沌等动力学行为。考虑到工程中的动力传送带大多数是由橡胶等聚合物材料制造，本课题以von Karmen 非线性薄板理论和分数阶粘弹性本构关系为基础，建立几类一般约束和一般载荷下轴向运动板的面内和面外振动的数学模型；利用半解析方法和数值方法求解线性自由振动的固有频率和模态函数；并以此为基础用近似解析方法研究系统的非线性振动解。用数值方法研究系统的分岔和时间-空间混沌等复杂非线性动力学行为；其中，重点研究分数阶粘弹性板在轴向运动中的非线性振动机理，用近似解析方法建立失稳判断准则；讨论超薄轴向运动板与流体相互作用下的动力学特性及其稳定性；探索含有分数导数动力系统的分岔和混沌现象。本研究的成果将会发展和完善分数阶非线性动力学理论，为工程中存在的分数阶粘弹性轴向运动连续体提供理论基础和设计准。

中文关键词： 分数阶；轴向运动梁；稳定性；振动；

英文摘要： The proposed research is based on fractional nonlinear nonlinear dynamics theory, which to be investigate nonlinear vibration, stability ,bifurcation and chaos of axially moving plates constituted by a fractional law. By considering the power transmission belts are constitutived by rubber and polymers, this proposal uses nonlinear von Karmen thin plate theory and fractional viscoelastic constitutive relation to derive some mathematical models of the in-plane and out-plane vibration of the axially moving plates with some general boundary conditions and subjected to excitations. Semi-analytical and numerical methods will be used to solve the natural frequencies and the mode functions for the linear vibration. Then, based on the obtained linear solutions, the solution to the nonlinear oscillation would be found by using some approximate analytical methods. The main focus of the proposed research is the study of the nonlinear vibration mechanism of the plate which is constituted by fractional viscoelastic materials. Establish instability rule by approximate analytical method. Discuss the dynamical property and stability of the axially moving viscoelastic ultra-thin plates interacting with surrounding fluid. Great efforts will be made to discuss the complex dynamical behaviors, such as bifurcation and spatiotemporal

英文关键词： Fractional；axially moving beam；Stability；vibration；