含多项式非线性关节的平面周期结构多谐波等效建模

Multi-harmonic equivalent modeling for a planar repetitive structure with polynomial-nonlinear joints

大型结构中的非线性关节对结构的影响是一类值得研究的重要问题.针对含大量非线性关节的平面周期结构,建立了一种基于高阶谐波的等效方法.首先,在单元层面上,非线性关节采用多谐波描述函数法进行建模,关节-梁-关节单元在动态缩聚后得到混合梁单元.然后,在结构层面上,使用位移等效原理获得平面周期结构的多谐波等效欧拉梁单元模型.其次,使用伪弧长法来跟踪频响函数的轨迹.之后,设计了一个实验来验证理论模型的正确性,同时考虑了悬挂系绳的影响和空气阻力.仿真结果揭示了这类含非线性关节周期结构的非线性特性与单自由度非线性系统特性的相似之处.最后,说明了在预测共振频率和幅值时考虑高阶谐波的重要性.

How nonlinear joints affect the response of large space structures is an important problem to investigate.In this paper,a multi-harmonic equivalent modeling method is presented to establish a frequency-domain model of planar repetitive structures with nonlinear joints.First,at the local level,the nonlinear joint is modeled by the multi-harmonic describing function matrix.The element of the hybrid beam is obtained by the dynamic condensation of the beam-joint element.Second,at the global level,the displacement-equivalence method is used to model the multi-harmonic Euler continuum beam equivalent to the planar repetitive structure.Then,the pseudo-arc-length continuation method is applied to track the multi-harmonic trajectory of response.Afterwards,an experiment is conducted to validate the correctness of the modeling method,considering the effect of hanging rope and air damping.In the numerical studies,several simulation results indicate the similarity of response between a single-degree-of-freedom system with a single nonlinear joint and the system of the planar repetitive structure with a large number of nonlinear joints.Finally,the component of higher-order harmonics is shown to be important for predicting the resonance frequencies and amplitudes.