一种新的非高斯随机振动数值模拟方法  

A novel approach for numerical simulation of a non-Gaussian random vibration

作　　者：蒋瑜[1] 陶俊勇[1] 王得志[1] 陈循[1] 

机构地区：[1]国防科技大学机电工程与自动化学院机电工程研究所,长沙410073

出　　处：《振动与冲击》2012年第19期169-173,共5页Journal of Vibration and Shock

基　　金：国家自然科学基金项目(50905181)

摘　　要：在振动工程领域,采用蒙特卡洛仿真方法求解复杂随机动力学问题时需要精确模拟各种随机振动激励信号。当随机振动激励具有显著的非高斯特征时,用传统的高斯振动去近似将产生较大的分析误差,需要研究精确的非高斯振动数值模拟技术。现有各种非高斯随机模拟方法一般只能模拟具有高峰值特征的随机振动,即超高斯随机振动,并且算法复杂不够直观,需要进行多次反复迭代,模拟精度和效率都有待提高。本文提出了一种新的基于幅值调制和相位重构的非高斯随机振动数值模拟方法,算法简洁直观,并充分利用快速傅里叶变换算法提高模拟效率,不仅可以模拟具有指定统计特性和频谱特性的超高斯随机振动,还能模拟亚高斯随机振动,具有广泛的适应性。数值仿真实验验证了该方法的有效性和精确性。Using Monte Carlo simulation method for solving complex dynamic problems in vibration engineering requires accurate simulation of various random vibrations. In situations where a random vibration has a significant non- Gaussian feature, using traditional Gaussian vibration to approximate a non-Gaussian vibration will result in a larger error, so techniques for accurate simulation of a non-Gausian vibration must be available. The various existing simulation methods of a non-Gaussian vibration generally can only simulate a super-Gaussian vibration with high-peak characteristics. And most of these methods are very complicated, not sufficiently intuitive, requiring repeated iterations, they have lower simulation accuracy and efficiency. Here, a novel approach for simulation of a non-Gaussian random vibration was presented with prescribed statistical and spectral characteristics using amplitude modulation and phase reconstruction, it was simple and intuitive and could simulate both super-Gaussian and sub-Gaussian random vibrationa. Another attractive feature of the method was that its processing could be implemented efficiently using the fast Fourier transformation technique. Several simulation examples demonstrated the efficiency and accuracy of the proposed algorithm.

关 键 词：非高斯随机振动 数值模拟 幅值调制 相位重构 

分 类 号：O324[理学—一般力学与力学基础] O242[理学—力学]