分数阶导数系统非平稳随机振动灵敏度分析的时域显式方法  

Explicit time-domain method for sensitivity analysis of nonstationary random vibration of systems with fractional derivatives

作　　者：冼剑华 苏成[1,2] XIAN Jian‑hua;SU Cheng(School of Civil Engineering and Transportation,South China University of Technology,Guangzhou 510640,China;State Key Laboratory of Subtropical Building Science,South China University of Technology,Guangzhou 510640,China)

机构地区：[1]华南理工大学土木与交通学院,广东广州510640 [2]华南理工大学亚热带建筑科学国家重点实验室,广东广州510640

出　　处：《振动工程学报》2022年第5期1058-1067,共10页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(51678252);广州市科学研究计划重点项目(201804020069)。

摘　　要：分数阶导数模型是描述黏弹性材料本构关系的理想模型。进行了分数阶导数线性系统非平稳随机振动的灵敏度分析。建立分数阶导数系统动力响应的时域显式表达式;采用灵敏度分析的直接求导法或伴随变量法,推导系统动力响应灵敏度的时域显式表达式;提出分数阶导数系统响应统计矩灵敏度高效计算的时域显式方法。所提出的基于直接求导法和伴随变量法的时域显式方法,分别适用于少设计变量和多设计变量两种情况下的响应统计矩灵敏度分析。以非平稳地震激励下设置分数阶导数黏弹性阻尼器的层剪切结构为数值算例,验证了所提方法的计算精度和计算效率。Fractional derivative models are capable of describing the constitutive behaviors of viscoelastic materials.This paper is devoted to the sensitivity analysis of nonstationary random vibration of linear systems comprising fractional derivative terms.The explicit time-domain expressions of dynamic responses are firstly established for the system with fractional derivatives.The sensitiv‐ities of dynamic responses are then derived using the direct differentiation method(DDM)or the adjoint variable method(AVM).On the basis of the explicit expressions of dynamic responses and their sensitivities,an explicit time-domain method(ETDM)is proposed for efficient calculation of the sensitivities of statistical moments of responses.The proposed DDM-and AVM-based ET‐DM are applicable to the scenarios with less and more design variables,respectively.A numerical example involving a shear-type structure under nonstationary seismic excitations and with viscoelastic dampers modelled by fractional derivatives is presented to validate the computational accuracy and efficiency of the proposed method.

关 键 词：随机振动灵敏度 分数阶导数 时域显式方法 直接求导法 伴随变量法 

分 类 号：O324[理学—一般力学与力学基础] TU311.3[理学—力学]