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  

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

作　　者：史俊磊 丁喆 张磊[1,2,3] 张严 SHI Junlei;DING Zhe;ZHANG Lei;ZHANG Yan(Key Laboratory of Metallurgical Equipment and Control Technology of Ministry of Education,Wuhan University of Science and Technology,Wuhan 430081,China;Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering,Wuhan University of Science and Technology,Wuhan 430081,China;Precision Manufacturing Institute,Wuhan University of Science and Technology,Wuhan 430081,China)

机构地区：[1]武汉科技大学冶金装备及其控制教育部重点实验室,武汉430081 [2]武汉科技大学机械传动与制造工程湖北省重点实验室,武汉430081 [3]武汉科技大学精密制造研究院,武汉430081

出　　处：《振动与冲击》2023年第8期20-27,37,共9页Journal of Vibration and Shock

基　　金：国家自然科学基金(51805383);中国博士后科学基金(2021M692486,2018T110810)。

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。区别于黏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PSD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PSD函数的灵敏度表达式;分别引入基于复模态的一阶、二阶近似法和基于实模态的迭代法构建PSD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PSD函数的灵敏度求解。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.

关 键 词：功率谱密度(PSD) 灵敏度分析 非黏滞阻尼模型 平稳随机激励 虚拟激励法(PEM) 

分 类 号：TH113.1[机械工程—机械设计及理论]