刚-柔耦合的对称天线结构非线性主共振
高秀敏，金栋平，胡海岩
摘要: 本文研究了主共振激励下空间天线的非线性动态响应。考虑机械臂与天线的耦合，提出了一种由两级刚性臂与两根各向同性柔性梁组成的T-型梁式结构。采用Lagrange方程和假设模态方法，建立了T-型刚柔耦合天线面内四自由度非线性动力学方程。利用多尺度法获得主共振三次近似解，得出系统主共振幅频响应解析方程。对系统幅频响应进行分析，结果表明主共振响应存在多解和非线性跳跃现象，激励对模态幅值及非线性特性具有显著影响。随着激励的增大，系统出现由刚度硬特性向软特性的转变;当激励超过临界值时，系统幅频响应表现出刚度渐软特性，共振频率随简谐激励幅值的增大而减小。
关键词：刚柔耦合, 天线结构, 非线性共振, 四自由度, 假设模态
Nonlinear primary resonance of a rigid-flexible space symmetric antenna
XiuMin Gao, DongPing Jin, HaiYan Hu
Abstract：This paper studies the nonlinear response of a T-shape space antenna structure composed of two rigid arms jointed by a spring and two uniform beams made by isotropic material. Based on the Lagrange equation and the assumed modes method, the nonlinear dynamic equations of in-plane motion of the rigid-flexible coupled antenna are established, with four degrees of freedom. In order to reveal the dynamic characteristics of the nonlinear system, the method of multiple scales expressed in matrix form is used to solve the primary resonance responses of third-order approximation. Analyzing the frequency-amplitude response gives the jumping phenomenon in the primary resonance response. With increase of the excitation amplitude, the frequency-amplitude response curve would have a conversion between the hardening and softening types. Under small excitation amplitude, the frequency-response curve exhibits the hardening-type behavior, whereas the softening-type behavior would appear once the excitation amplitude is out to a critical value. In the case of softening-type behavior, the resonance frequencies decrease with increase of the excitation amplitudes.
Keyword：rigid-flexible coupled structures, space antenna, nonlinear resonance, four-degree-of-freedom, assumed modes method
原文链接：http://www.cnki.com.cn/Article/CJFDTOTAL-JGXK201710008.htm
