This paper considers a probabilistic description of the random response of linear structures which is described by a finite number of coordinates. Such a description differs from those available in the literature, where random response is usually either assumed Gaussian or is described on the basis of correlation and spectral theories of random functions; it is based on the response probability density distribution freed from the previous assumptions. The development of the response density function is the main task of this work. Given the characteristics of a structure and the density distribution of a random input, stationary or nonstationary, a response density distribution is derived.

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