平稳非高斯激励下线性结构响应统计量的高阶虚拟激励法  

Statistics analysis for response of linear structure under stationary non-Gaussian excitation based on the higher-order pseudo-excitation method

作　　者：范文亮[1,2] Fan WenLiang(Key Laboratory of New Technology for Construction of Cities in Mountain Area of the Ministry of Education, Chongqing University, Chongqing 400045, China;School of Civil Engineering, Chongqing University, Chongqing 400045, China)

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

出　　处：《土木工程学报》2019年第10期30-35,共6页China Civil Engineering Journal

基　　金：国家重点研发计划项目(2018YFC0809400);国家自然科学基金项目(51678092);中央高校基本科研业务费(2019CDXYTM0032)

摘　　要：相比于经典随机振动理论的日益成熟,尤其是虚拟激励法的提出所引起的效率提升,非高斯激励下的结构随机振动分析仍具有相当大的挑战性。为此,文章针对平稳非高斯激励下线性结构响应的高阶统计量展开研究,力图发展切实可行的高效分析方法。首先,基于振型叠加法,推导多自由度线性结构响应的高阶矩的解析表达式,并经由 Fourier 变换获得高阶矩谱的解答,即完全高次组合方法。其次,借鉴常规虚拟激励法的思路,提出适用于高阶矩谱分析的高阶虚拟激励法,而传统的虚拟激励法则是建议方法的一个特例。对比分析可以发现:高阶虚拟激励法不仅具有计算方案选择上的多样性,在计算效率方面更具有显著的优势。The classical random vibration theory has been well developed with wide applications, and the efficiency of analysis for random vibration has been improved by the pseudo-excitation method. However, random analysis for structural vibration under non-Gaussian excitation has still been a great challenge. In this work, statistics for response of linear multiple degrees of freedom (MDOF) structure under stationary non-Gaussian excitation were analyzed, and an efficient and practical method is presented. Firstly, based on the mode superposition method, the analytical solution for higher-order statistical moment of response was derived, and then the solution for higher-order moment spectrum was obtained by the Fourier transformation of moments, which was named the complete higher-order combination method. Secondly, by following the idea of traditional pseudo-excitation method, the higher-order pseudo-excitation method was proposed for calculating the higher-order moment spectrum, while the traditional pseudo-excitation method is just a special case of the proposed method. A comparison discloses that the higher-order pseudo-excitation method is superior to the complete higher-order combination method not only from the perspective of the diversity of computational schemes, but also from the perspective of the computational efficiency.

关 键 词：非高斯 线性结构 高阶统计量 振型叠加法 高阶虚拟激励法 

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]