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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.
In this paper, the nonlinear dynamic response of the space antenna under primary resonance excitation is studied. Considering the coupling between the arm and the antenna, a T-beam structure consisting of two rigid arms and two isotropic flexible beams is proposed. Lagrange equation and assumed modal method, a four-degree-of-freedom nonlinear dynamic equation of the T-shaped rigid-flexible coupling antenna is established, and the cubic resonance approximation solution of the main resonance is obtained by using the multi-scale method to obtain the analytical equation of the main resonance amplitude frequency response. The results of amplitude-frequency response analysis show that there exist multiple solutions and nonlinear jumps in the main resonance response, and the excitation has a significant effect on the amplitude and nonlinearity of the modal.With the increase of the excitation, When the excitation exceeds the critical value, the amplitude-frequency response of the system shows the gradual stiffness characteristics. The resonance frequency decreases with the increase of the harmonic excitation amplitude.