This paper concerns random vibration testing on electrodynamic shakers, which is specified by prescribing the power spectral density (PSD) of the generated excitation and its kurtosis if the latter needs to be higher or lower than that provided by the PSD simulation on its own. A special procedure of windowing and overlapping considered in this paper is performed by shaker controllers based on inverse fast Fourier transform (IFFT) in order to suppress discontinuities at data block boundaries and to introduce randomness into the initially generated periodic IFFT signal. The windowing operation is the same as in random signal analysis, but, combined with the overlapping, it affects the initial kurtosis value of the generated data blocks. This kurtosis transformation is discussed, and the relationship between input and output kurtosis values is proved to be linear. A precise algebraic equation for the output kurtosis has been derived for the Hann window function with various overlapping numbers. Numerical examples of signal time histories with high kurtosis after windowing and overlapping are demonstrated.

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