非经典阻尼体系复振型随机反应分析  

COMPLEX-MODE STOCHASTIC ANALYSIS FOR NON-CLASSICALLY DAMPED SYSTEMS

作　　者：秦佳会 胡聿贤[1] 

机构地区：[1]国家地震局地球物理研究所

出　　处：《地震工程与工程振动》1990年第4期5-19,共15页Earthquake Engineering and Engineering Dynamics

摘　　要：本文将复杂的复振型随机反应分析化为各阶振型单自由度体系的随机反应求解和复振型叠加的有关系数计算。此方法始终将体系位移和速度反应作为一个整体来考虑,可同时得到体系位移和速度反应功率谱、相关函数和谱矩的解析表达式。文中将位移反应的高阶函数转化为速度反应的低阶函数来处理,推导出非经典阻尼体系在有色谱输入下体系反应和振型反应间相关函数的解析表达式以及在白噪声输入下的解析解。文中还给出了在白噪声输入下体系平稳反应的功率谱前三阶自谱矩的解析精确解。文中采用的分析方法物理意义明确,可直接利用现有单自由度体系随机反应分析的成熟结果,而且解析表达式简单,振型反应的计算量减少了一半,简化了现有的复振型随机反应分析方法。A method suggested in this paper solves the very complicated problem of complex-mode random response in two steps: 1. decomposition of system random responses in terms of the responses of each mode; 2. the calculations of some parameters in complex-mode decomposition and superposition. This approach considers the displacement and velocity responses of the system as a whole, and derives the general expressions for power spectra, correlation functions and spectral moments of the displacement and velocity responses. By making use of lower-rank functions of velocity responses for higher-rank functions of displacement responses, general expressions of power spectra and correlation functions are obtained in simpler forms than current methods, and new results are obtained for cross-correlation functions of system responses and between mode responses which have not been given before for systems under non-white input.The main advantage of this method is to directly apply the given results of the random responses of one-degree-of -freedom systems and thus the formulas are very simple and explicit. The calculations of mode responses are reduced by half.

关 键 词：复振型 随机反应 非经典 阻尼体系 

分 类 号：P315.9[天文地球—地震学]