重频结构模态灵敏度分析的高精度截模态算法

基于全模态展开定理,提出了计算重频阻尼结构模态灵敏度的全模态算法和高精度截模态算法。首先通过引入松驰因子的移频法克服了重频现象对模态灵敏度分析的影响,给出了重频模态灵敏度的全模态算法,并从理论上分析了这种算法的误差来源及控制方法;其次通过分析各阶模态在模态灵敏度的全模态线性展开式中的贡献作为截断准则来实施截断,从而提出了重频结构模态灵敏度分析的高精度截模态算法,并给出了其误差分析方法。提出的高精度截模态算法仅需少量模态,即可获得对称及非对称系统任一重频模态的灵敏度信息,无论是理论分析还是数值计算的结果均表明了该算法的正确性及高效性。

A high accuracy truncated modal algorithm of sensitivity analysis for multiple-frequency structure

Based on Full-mode Linear Expansion Theory, the article puts forward two new algorithms which are called the full-mode algorithm and the high accuracy truncated modal algorithm for computing modal sensitivity of multiple-frequency damping structure. Firstly, through introducing the relaxation factors, the new full-mode algorithm proposed eliminates the influence of multiple frequency on modal sensitivity analysis. The article also theoretically analyzes the source of error and the controlling method of the full-mode algorithm. Secondly, the high accuracy truncated modal algorithm and its error analysis are proposed through analyzing the contributions of all modes, which are regarded as the truncation criterion, in the full-mode linear expansion subject to the sensitivity analysis of multiple-frequency mode. According to the high accuracy truncated modal algorithm, the fewer modes can obtain the certain information of multiple-frequency modal sensitivity in symmetrical or asymmetrical system, the facts show that not only the theoretical analysis but also numerical calculations indicate the correctness and efficiency of this algorithm.