Sensitivity Analysis of Nonlinear Transient Response Based on Perturbation in the Complex Domain

Author:

Cao Zhifu1,Fei Qingguo1,Jiang Dong2,Zhu Rui1,Jin Hui3

Affiliation:

1. Jiangsu Engineering Research Center of Aerospace Machinery, School of Mechanical Engineering, Southeast University, Nanjing 211189, China

2. Jiangsu Engineering Research Center of Aerospace Machinery, School of Mechanical Engineering, Southeast University, Nanjing 211189, China; School of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037, China

3. Department of Engineering Mechanics, Southeast University, Nanjing 211189, China

Abstract

Abstract Sensitivity analysis of transient response plays a crucial role in structural dynamics optimization. In this paper, the sensitivity analysis method for calculating the first-order derivatives of the nonlinear transient response using the real-imaginary perturbations (RIP) in the complex domain is proposed. Independent design parameters are synchronously perturbed using real and imaginary perturbations, respectively. The complex variable finite element method is employed to compute the complex transient response of the perturbed model. The nonlinear transient response sensitivities with respect to each parameter are obtained by separately extracting the real and imaginary responses. The computational accuracy and efficiency of the proposed method are demonstrated by employing a nonlinear multidegree-of-freedom system and a cantilever beam with nonlinear elastic supports. Results show that the response sensitivity with respect to multiple design parameters is obtained accurately by using the proposed method, the computational efficiency of which is increased compared with the complex variable method (CVM). The stability of the transient response sensitivity is significantly affected by the parameter perturbations in the real and imaginary parts. The RIP-imaginary-based response sensitivity is feasible even for an extremely small perturbation in the imaginary part; the RIP-real-based response sensitivity is stable only within a limited real perturbation range.

Funder

National Natural Science Foundation of China

Publisher

ASME International

Subject

Applied Mathematics,Mechanical Engineering,Control and Systems Engineering,Applied Mathematics,Mechanical Engineering,Control and Systems Engineering

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