| Abstract: | A relatively simple and straightforward procedure is given for representing analytically defined or data-based covariance kernels of arbitrary random processes in a compact form that allows its convenient use in later analytical random vibration response studies. The method is based on the spectral decomposition of the random process by the orthogonal Karhunen-Loeve expansion and the subsequent use of least-squares approaches to develop an approximating analytical fit for the data-based eigenvectors of the underlying random process. The resulting compact analytical representation of the random process is then used to derive a closed-form solution for the non-stationary response of a damped SDOF harmonic oscillator. The utility of the method for representing the excitation and calculating the mean-square response is illustrated by the use of an ensemble of acceleration records from the 1971 San Fernando earthquake. |
