Sensitivity analysis of the power spectrum density function for non-viscously damped systems subject to stationary stochastic excitations [平稳随机激励下非黏滞阻尼系统功率谱密度函数的灵敏度分析]

作者：Shi J.; Ding Z.; Zhang L.; Zhang Y.

来源：Journal of Vibration and Shock, 2023, 42(8): 20-27 and 37.

DOI：10.13465/j.cnki.jvs.2023.08.002

• non-viscous damping model
• power spectral density (PSD)
• pseudo-excitation method (PEM)
• sensitivity analysis
• stationary stochastic excitations

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.

• 单位
  武汉科技大学