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

史俊磊1,2,3,丁喆1,2,3,张磊1,2,3,张严1,2,3

振动与冲击 ›› 2023, Vol. 42 ›› Issue (8) : 20-27.

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (8) : 20-27.
论文

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

  • 史俊磊1,2,3,丁喆1,2,3,张磊1,2,3,张严1,2,3
作者信息 +

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

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

功率谱密度(power spectral density, PSD)函数的灵敏度分析是实现结构系统在随机激励下梯度优化算法的基础。区别于粘性阻尼模型假设阻尼力正比于瞬时速度,非黏滞阻尼模型的阻尼力与质点的时间历程相关,因而能够更加准确地描述黏弹性材料的耗能特性。针对卷积型非黏滞阻尼系统功率谱密度函数的灵敏度求解问题,利用虚拟激励法(pseudo-excitation method, PEM)将平稳随机激励下非黏滞阻尼系统的随机响应问题等效转化为确定性的简谐响应问题;利用直接微分法推导出功率谱密度函数的灵敏度表达式;分别引入基于复模态的一、二阶近似法和基于实模态的迭代方法构建功率谱密度函数的灵敏度算法;通过数值算例比较三种方法的计算精度和效率。结果表明,迭代法更适合大规模非黏滞阻尼系统功率谱密度函数的灵敏度求解。

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.

关键词

功率谱密度 / 灵敏度分析 / 非黏滞阻尼模型 / 平稳随机激励 / 虚拟激励法

Key words

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

引用本文

导出引用
史俊磊1,2,3,丁喆1,2,3,张磊1,2,3,张严1,2,3. 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[J]. 振动与冲击, 2023, 42(8): 20-27
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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