实模态参数的二阶灵敏度算法与对比分析

精确计算实模态参数灵敏度的方法包括模态法、代数法和直接法。为了提高其工程应用性,并比较三者的精度,提出了实模态参数的二阶灵敏度的代数法、全模态法及与全模态法相对应的截模态算法,其中截模态算法的截断准则简单高效,更具有工程价值。数值算例检验了所提出的全部算法的正确性及有效性。同时,数值结果也显示三种精确算法具有相同的精度,并且截模态算法也具有较高精度,是非常实用的灵敏度分析算法。

The second-order sensitivity algorithm and their comparison analysis for real modal parameters

The sensitivity of real modal parameters can be obtained by means of Modal Method,Algebraic Method and Direct Method.The theories of real modal parameters and its sensitivity analysis are introduced,including Friswell''s direct algorithm.In a previous paper,the first-order sensitivity analysis in Algebraic Method was reported.This paper extends the approach to the second-order sensitivity analysis.Meanwhile,following the classical idea of Modal Method,the second-order sensitivity algorithms are proposed not only by the full-mode case but also by the truncated modal case,where the truncation rule is simple and efficient.And the truncated algorithm proposed here has important engineering value.The numerical example is demonstrated to verify the correctness and efficiency of all proposed algorithms of the paper.In addition,the numerical results indicate that the algebraic,full-mode and direct methods have the similar accuracies and the truncated modal algorithm has high accuracy as desired.