Sensitivity analysis of the power spectrum density function for non-viscously damped systems subject to stationary stochastic excitations

被引：0
|
作者：
Shi J. [1 ,2 ,3 ]
Ding Z. [1 ,2 ,3 ]
Zhang L. [1 ,2 ,3 ]
Zhang Y. [1 ,2 ,3 ]
机构：
[1] Key Laboratory of Metallurgical Equipment and Control Technology of Ministry of Education, Wuhan University of Science and Technology, Wuhan
[2] Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering, Wuhan University of Science and Technology, Wuhan
[3] Precision Manufacturing Institute, Wuhan University of Science and Technology, Wuhan
来源：
Zhendong yu Chongji/Journal of Vibration and Shock | 2023年 / 42卷 / 08期
关键词：
non-viscous damping model; power spectral density (PSD); pseudo-excitation method (PEM); sensitivity analysis; stationary stochastic excitations;
D O I：
10.13465/j.cnki.jvs.2023.08.002
中图分类号：
学科分类号：
摘要：
Calculating the first-order derivatives of the power spectrum density (PSD) function with respect to design variables is a prerequisite for random responses when gradient-based optimization algorithms are adopted. Unlike a viscous damping model, which assumes that the damping force is proportional to the velocity, the damping force of non-viscous damping model depends on the past history of motion via convolution integrals over some suitable kernel functions. Therefore, a non-viscous damping model is more accurate to modelling the energy dissipation behaviors of viscoelastic materials. The design sensitivity analysis of PSD function for non-viscously damped systems subjected stationary stochastic excitations was considered. The governing equations of the non-viscously damped system under stationary random excitations were transformed into a deterministic harmonic response problem based on the pseudo-excitation method (PEM). The expressions of the first-order derivatives of the PSD function were derived by the direct differentiate method. Three numerical methods, namely complex-mode based first-and second-order approximation method and pseudo-excitation method-iterative method (PEM-IM), were proposed to calculate the sensitivity of the PSD function. The computational accuracy and efficiency of the three methods were compared by two numerical methods. The results indicate that the PEM- IM is the best candidate to compute the sensitivities of the PSD function of non-viscously damped systems, especially for large-scale problems. © 2023 Chinese Vibration Engineering Society. All rights reserved.
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页码：20 / 27and37
页数：2717
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