具有随机路径的振动传递路径系统的随机响应分析

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振动与冲击 ›› 2009, Vol. 28 ›› Issue (2) : 99-101,.

论文

具有随机路径的振动传递路径系统的随机响应分析

赵薇,张义民

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RESPONSE OF VIBRATION TRANSFER PATH SYSTEMS WITH UNCERTAIN PATHS

Zhao Wei,Zhang Yimin

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摘要

基于Kronecker代数、矩阵微分理论、向量值和矩阵值函数的二阶矩技术、矩阵摄动理论和概率统计方法，实用有效地提出了时域内振动传递路径系统的随机响应分析方法。在考虑传递路径参数,包括质量、阻尼、刚度、位置参数不确定性的条件下，对振动传递路径系统的随机响应问题进行了理论分析和数值计算，给出了系统随机振动响应的一阶矩和二阶矩的一般数学表达式，据此可以考虑工程实际中大量的传递系统中固有的不确定性，以便为解决不确定振动传递路径系统的问题提供有效方便的途径。通过算例表明，该法数值分析结果与Monte Carlo随机模拟结果比较，具有理想的精度。

Abstract

This paper is based on the Kronecker algebra, the matrix calculus, the generalized second moment technique of vector-valued functions and matrix-valued functions, the matrix perturbation theory, the probability and statistics. The effective approach for stochastic response analysis for vibration transfer path systems in time range is presented, and the random responses of the vibration transfer path systems with uncertain paths，which include mass, damping, stiffness and position, are analyzed theoretically and computed numerically, and the mathematical expressions of the first order and second order moments for the random vibration response of random path systems are obtained. Thus, in practical project, the most uncertain factors in vibration transfer systems can be considered so as to give the effective way for solving the vibration transfer path systems with uncertain factors. The results of calculation are consistent with the results of Monte-Carlo simulation by the numerical examples.