基于刚柔耦合动力学的功能梯度柔性体的频率转向特性研究

项目名称： 基于刚柔耦合动力学的功能梯度柔性体的频率转向特性研究

项目编号： No.11302096

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 方建士

作者单位： 南京工程学院

项目金额： 23万元

中文摘要： 频率转向和振型转换是做大范围运动复杂连续柔性体（梁、板结构）的一类耦合振动问题。深入研究这一类耦合振动问题的机理对结构的振动测试和断裂故障诊断具有重要意义。基于刚柔耦合系统动力学的一次近似耦合模型，提出一种误差可控、高效的模型离散方法。随着功能梯度材料在柔性结构中的广泛应用，如何深入理解材料性能的梯度变化对对结构固有振动特性的影响，是当前刚柔耦合系统动力学的一个巨大挑战。本课题的主要研究内容：1.针对做大范围运动的柔性体，分析有限元法、假设模态法和B样条插值等方法的优点，提出一种误差可控、高效的模型离散方法。2.建立基于刚柔耦合动力学的做大范围运动柔性体的自由振动微分方程，重点考虑非线性耦合变形量和大范围运动对其频率转向特性和模态振型的影响。3.系统研究材料性能（包括弹性模量、切变模量和材料密度等）的梯度变化对做大范围运动柔性体的动力学仿真结果和频率转向特性等方面的影响。

中文关键词： 旋转梁板；刚柔耦合动力学；功能梯度材料；自由振动；频率转向

英文摘要： Frequency veering and mode shape interaction is a type of coupling vibration problems for the complex continuous flexible bodies (i.e. beams and plates) undergoing large overall motion. The in-depth study of this type of coupling vibration problems has important significances in the structure vibration testing and fracture failure diagnosis. A error controllable and efficient model discretization method is proposed, and applied to the first approximation coupling model based on the rigid-flexible coupling system dynamics. With the wide application of functionally graded materials in flexible structures, how to understand the effects of the gradient of material properties on the natural vibration characteristics of the structures is a huge challenge of the current rigid-flexible coupling system dynamics. The main contents of the subject are described as follows. Firstly, A error controllable and efficient model discretization method is proposed based on the advantages of the finite element method, assumed mode method and B-spline interpolation method for the flexible bodies undergoing large overall motion. Then by basing on rigid-flexible coupling system dynamics, a free vibration differential equation is derived for the flexible bodies undergoing overall motion, the effects of non-linear coupling deformation and

英文关键词： Rotating beams/plates；rigid-flexible coupling dynamics；functionally graded materials；free vibration；frequency veering