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

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Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (8) : 20-27.

SHI Junlei1,2,3，DING Zhe1,2,3，ZHANG Lei1,2,3，ZHANG Yan1,2,3

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Abstract

Calculating the first-order derivatives of Power Spectrum Density (PSD) function with respect to design variables is a prerequisite for random responses when gradient-based optimization algorithms are adopted. Unlike viscous damping model, which assumes that the damping force is proportional to the velocity, the damping force of non-viscous damping model depend on the past history of motion via convolution integrals over some suitable kernel functions. Therefore, the non-viscous damping model is more accurate to modelling the energy dissipation behaviors of viscoelastic materials. This paper considers the design sensitivity analysis of PSD function for non-viscously damped systems subjected stationary stochastic excitations. The governing equations of the non-viscously damped system under stationary random excitations are transformed into a deterministic harmonic response problem based on Pseudo-Excitation method (PEM). The expressions of the first-order derivatives of the PSD function is derived by direct differentiate method. Three numerical methods, namely complex-mode based first- and second-order approximation method (PEM-FAM, PEM-SAM) and real-mode based iterative method (PEM-IM), are proposed to calculate the sensitivity of the PSD function. The computational accuracy and efficiency of the three methods are compared by two numerical methods. The results indicate that the PEM-IM would be the best candidate to compute the sensitivities of the PSD function of non-viscously damped systems, especially for large-scale problems.

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power spectral density / sensitivity analysis / non-viscous damping model / stationary stochastic excitations；Pseudo-excitation method

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SHI Junlei1,2,3，DING Zhe1,2,3，ZHANG Lei1,2,3，ZHANG Yan1,2,3. Sensitivity analysis of the power spectrum density function for non-viscously damped systems subject to stationary stochastic excitations[J]. Journal of Vibration and Shock, 2023, 42(8): 20-27

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