High-order sensitivity analysis of complex modal parameters and their comparison.

In terms of the first- and second-order sensitivities of the complex mode for a symmetric damped linear discrete dynamic system with respect to design parameters, the algebraic method, direct method, full-mode method and truncated modal method corresponding to full-mode method are proposed. These four algorithms insist on using the expression forms in N-dimensional vector space, which provide the convenience in engineering application. In the numerical examples, the correctness and validity of all the proposed algorithms are demonstrated for the single-frequency, closed-frequency and multiple-frequency systems. The algebraic method, direct method and full-mode method are accurate algorithms. No statement is made that one method is absolutely superior to the other, but this paper provides the chance to compare their efficiency and accuracies of all the three accurate algorithms. Truncated modal method proposed here is an approximate algorithm. The truncation criterion is simple and efficient, which is a more competitive alternative to the full-mode method, and it is shown that the truncated modal method has high precision and good convergence speed for sensitivity analysis by numerical examples. [ABSTRACT FROM AUTHOR]