梁型结构非线性动力学理论和实验研究

项目名称： 梁型结构非线性动力学理论和实验研究

项目编号： No.10802001

项目类型： 青年科学基金项目

立项/批准年度： 2009

项目学科： 交通运输

项目作者： 曹东兴

作者单位： 北京工业大学

项目金额： 26万元

中文摘要： 机械柔性梁类结构在航空航天、机械、交通等工程领域应用广泛，本项目以L型和T型两个结构为研究对象，通过理论分析、数值计算和实验验证研究了两个结构的非线性动力学特性。主要成果包括：考虑几何大变形，利用Langange方程建立了L型梁结构和T型梁结构的非线性动力学方程，并利用Galerkin截断方法把偏微分方程离散为多自由度非线性系统，然后利用多尺度方法对其进行摄动分析得到平均方程，基于平均方程数值计算了系统的频率响应曲线、波形图、相图、Poincare映射和功率谱，详细分析了L型梁结构和T型梁结构的分叉、脉冲跳跃和混沌现象；建立了机械柔性梁结构的振动实验平台，实验研究了L型梁结构和T型梁结构的非线性振动特性，发现了系统存在跳跃、分叉和混沌等复杂非线性现象，并通过波形图、相图和频谱分析，讨论了激励频率和激励幅值对结构振动形式的影响，确定了系统周期运动和混沌运动的振动形式，给出了实验条件下两个结构产生混沌运动的参数条件,验证了理论分析结果。

中文关键词： 柔性梁结构；分叉；混沌动力学；振动实验

英文摘要： Mechanical flexible beam structures are important components and very significant models in engineering applications, such as space stations, mechanical engineering and vehicles. In this program, the theoretical method, numerical simulation and experimental method were applied, and the bifurcations and chaotic dynamics of two beam structures like L-shape beam structure and T-shape beam structure were studied. The main contents include: The nonlinear governing equations of planar vibrations for the L-shape beam structure and T-shape beam structure were established firstly using Lagrange method. The Galerkin method was used to discrete partial differential equation, then, the method of multiple scales was utilized obtained the averaged equations. Numerical method was applied to get waveform, phase portrait, Poincare map and power spectrum. The nonlinear vibrations, bifurcations and chaotic dynamics were analyzed in detail for the mechanical flexible L-shape beam structure and T-shape beam structure. In the other hand, we set up the experimental equipments, the influence of the excitation frequency and excitation amplitude for the two beam structures were discussed and the nonlinear phenomena like jumping, bifurcation and chaos were found. The periodic motions and chaotic motions were described through waveform, phase portraits and power spectrum. The experimental solution validated the theoretical analysis.

英文关键词： flexible beam structure; bifurcation; chaotic dynamics; vibration experiment