Non-Gaussian random vibration testing with kurtosis control is considered in the paper as a way of increasing or decreasing the excitation crest factor. An increase of crest factor is required for more accurate simulation of ground vehicle vibrations and the opposite action of crest factor decrease is useful in other applications, such as modal testing. Implementing kurtosis as an additional test specification leads to closed-form solutions for the requirement of the excitation high peak behavior being controlled simultaneously with the traditional power spectral density (PSD) control. A method of subjecting Gaussian signals to polynomial transformation is simpler but has an inherent tendency of introducing frequency distortions jeopardizing the PSD simulation. There is no such difficulty with another approach of phase manipulation in the inverse fast Fourier transform since the power spectrum is not influenced by the phases. A universal phase selection procedure capable of modeling non-Gaussian random excitations with a high or low kurtosis has been developed. Because of the analytical solution advantage, the proposed phase method can be implemented in automatic shaker testing systems with closed-loop control. This paper is the first in a series of two publications. Part II will present numerical and experimental results.
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