线性随机参变振动的谱分解法
A Spectral Resolving Method for Analyzing Linear Random Vibrations with Variable Parameters
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摘要: 本文是[1]文的一个发展.考虑如下的随机方程:(t)+2β?(t)+ω02Z(t)=(a0+alZ(t)).I(t)+c,激励I(t)和响应到Z(t)都是随机过程,并设它们相互独立.如[1],设I(t)=a(t)I0(t),a(t)是已知的时间函数,IO(t)是平稳随机过程.本文考虑了以上随机方程的谱分解形式,数值求解方法以及一些特殊情况的解式.Abstract: This paper is a development of Ref.[1].Consider the following random equation:(t)+2?(t)+02Z(t)=(a0+alZ(t)).I(t)+c,in which excitation I0(t)and response Z(t)are both random processes, and it is proposed that they are mutually independent.Suppose that I(t)=a(t)I0(t),a(t)is a known function of time and IO(t)is a stationary random process.In this paper, the spectral resolving form of the random equation stated above, the numenca solving method and the solutions in some special cases are considered.
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[1] 金问鲁,线弹性结构非平稳随机振动分析的有限元方法.应用数学和力学,3,6(1982). [2] 蔡国强,电磁激振器的随机参变振动.浙江大学研究生论文,(1983). [3] 张炳根、赵玉芝,《科学与工程中的随机微分方程》,海洋出版社.(1980). [4] 《数学手册》编写组,《数学手册》,人民教育出版社.(1979). [5] 星谷胜.《榷率论手法による振动分析》.地震出版社.常宝琦译本. -
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