非平稳非高斯激励下线性结构响应统计量的高阶分析方法  

Higher-order analysis method of statistics analysis for response of linear structure under non-stationary and non-Gaussian excitations

作　　者：盛向前 范文亮[1,2] 李正良[1,2] SHENG Xiangqian;FAN Wenliang;LI Zhengliang(School of Civil Engineering,Chongqing University,Chongqing 400045,China;Key Laboratory of New Technology for Construction of Cities in Mountain Area of the Ministry of Education,Chongqing University,Chongqing 400045,China)

机构地区：[1]重庆大学土木工程学院,重庆400045 [2]重庆大学山地城镇建设与新技术教育部重点实验室,重庆400045

出　　处：《建筑结构学报》2023年第6期254-262,共9页Journal of Building Structures

基　　金：国家自然科学基金项目(51678092,52178455)。

摘　　要：传统随机振动中最为常用的以频域分析方法为基础的时-频域分析方法,对于非平稳非高斯激励下结构随机振动分析尚无行之有效的解决途径。为此,通过推导的非平稳随机激励的高阶矩谱表达式,提出非平稳非高斯激励下线性结构响应时变高阶矩谱的计算方法,并结合圆频率的离散值和时域显式法,给出结构响应高阶矩谱的高效计算方法,并通过4层平面框架结构和6层三维框架结构将建议方法与时域数值模拟结果进行对比。研究结果表明:建议的高阶分析方法能够准确地计算线性结构在非平稳非高斯激励下响应的高阶矩谱和时变高阶矩;相比于时域数值模拟法,该方法计算结果比较稳定且不受样本随机性的影响,同时,建议方法的计算耗时远小于时域数值模拟法;在非高斯激励下,6层三维框架结构相比于4层平面框架结构,其响应的非高斯特性更加明显;6层三维框架结构在非高斯激励作用下,其剪力的非高斯特性最明显,位移的非高斯特性次之,弯矩的非高斯特性最不明显。The time-frequency domain analysis method based on the frequency domain analysis method is most commonly used in traditional random vibration,but has no practical solution for the analysis of structural random vibration under non-stationary and non-Gaussian excitation.To this end,a computation method for the response of the linear structure under non-stationary and non-Gaussian excitation was proposed through the derived expression of the higher-order moment spectrum of non-stationary random excitation,and the efficient computation method of the high-order moment spectrum of response was presented according to the discrete frequency value and the time-domain explicit formulation method.The proposed method was compared with the results of the time-domain numerical simulations by a 4-story planar frame structure and a 6-story 3D frame structure.The results show that,the proposed higher-order analysis method can accurately calculate the higher-order moment spectrum and time-varying higher-order moments of the response for the linear structure under non-stationary and non-Gaussian excitation;compared with the time-domain numerical simulation method,the results of the proposed method are more stable and not affected by the randomness of the sample.Meanwhile,the calculation time of the proposed method is much less than that of the time-domain numerical simulation method;the non-Gaussian characteristics of the response are more pronounced for the 6-layer 3D frame structure compared to the 4-layer planar frame structure under non-Gaussian excitation;the 6-story 3D frame structure has the most pronounced non-Gaussian characteristics for shear,the second most pronounced non-Gaussian characteristics for displacement,and the least pronounced non-Gaussian characteristics for bending moment under non-Gaussian excitation.

关 键 词：线性结构 非平稳 非高斯 高阶矩谱 振型叠加法 

分 类 号：TU311.3[建筑科学—结构工程] O324[理学—一般力学与力学基础]