一种中高频激励下动力系统响应的级数展开改进算法

Improved Series Expand Method for Dynamics System Response under Medium and High Frequency Excitations

针对频率响应函数的级数展开法在中高频激励时计算发散的问题,提出一种新的级数展开改进算法。将系统的结构模态划分为低阶和截断的高阶模态,在模态叠加分析的基础上,将频率响应函数进行泰勒级数展开。根据高低阶模态对质量矩阵和刚度矩阵的耦合特性,用低阶模态及系统矩阵表达高阶模态对响应的影响。研究结果表明,该算法将频率响应函数的级数展开法扩展到高频激励和中频激励范围阶段,在非完备模态条件下提高了频率响应函数的计算精度,数值计算检验了该方法准确可靠并有很好的收敛性。

Aiming at the computational divergence in the series expand method of frequency response function under medium and high frequency excitations, a new improved algorithm for dynamics system response is proposed. Structural modes are divided into available low-order modes and truncated higher-order modes. On the basis of modal superposition analysis, the frequency response function of high order truncation modes is expanded by Taylor series. According to the coupling characteristics between low-order and high-order modes, the contribution of truncated high-order modes to the frequency response function is expressed by low-order modes and system matrix. The improved algorithm extends the series expand method for the range of high frequency and medium frequency excitations; the calculation accuracy of the frequency response function is improved under the non-complete modal conditions. Numerical results validate the feasibility and convergence.