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本文作为“客车振动系统模拟的研究”和“随机振动及其异出过程响应谱的计算”的续篇,运用随机振动理论和方法推导了线性系统在多个激励下产生多个响应的矩阵公式。同时推导了相关矩阵,谱密度矩阵和频率响应矩阵。还推导了多重凝聚函数和噪声谱。作为实例讨论了两个输入和两个输出的车辆模型的计算。在线性系统随机振动理论的国内外专著中,对多输入多输出最普遍的矩阵公式难得见到给于详细推导和证明,因此给工程技术人员带来一定的困难,并时有发生误用现象。为此本文对上述矩阵公式进行了详细推导和证明。
In this paper, as a sequel of “Study on Vibration System Simulation of Passenger Car” and “Calculation of Response Spectrum of Stochastic Vibration and Its Outgoing Process”, the matrix formula of multiple response of linear system under multiple stimuli is deduced by stochastic vibration theory and method. At the same time, the correlation matrix, spectral density matrix and frequency response matrix are deduced. Multiple coherence functions and noise spectra are also derived. The calculation of a vehicle model with two inputs and two outputs is discussed as an example. In the domestic and foreign monographs of stochastic vibration theory of linear systems, the most common matrix formula of multiple input and multiple output is rare to be deduced and proved, so it brings some difficulties to engineering technicians and sometimes misuse . In this paper, the above matrix formula has been derived and proved in detail.