PSEUDOLINEAR VIBROIMPACT SYSTEMS - NONWHITE RANDOM-EXCITATION

Response analyses of vibroimpact systems to random excitation are grea tly facilitated by using certain piecewise-linear transformations of s tate variables, which reduce the impact-type nonlinearities (with velo city jumps) to nonlinearities of the ''common'' type - without velocit y jumps. This reduction permitted to obtain certain exact and approxim ate asymptotic solutions for stationary probability densities of the r esponse for random vibration problems with white-noise excitation. Mor eover, if a linear system with a single barrier has its static equilib rium position exactly at the barrier, then the transformed equation of free vibration is found to be perfectly linear in case of the elastic impact. The transformed excitation term contains a signature-type non linearity, which is found to be of no importance in case of a white-no ise random excitation. Thus, an exact solution for the response spectr al density had been obtained previously for such a vibroimpact system, which may be called ''pseudolinear'', for the case of a white-noise e xcitation. This paper presents analysis of a lightly damped pseudoline ar SDOF vibroimpact system under a non-white random excitation. Soluti on is based on Fourier series expansion of a signum function for narro w-band response. Formulae for mean square response are obtained for re sonant case, where the (narrow band) response is predominantly with fr equencies, close to the system's natural frequency; and for non-resona nt case, where frequencies of the narrow-band excitation dominate the response. The results obtained may be applied directly for studying re sponse of moored bodies to ocean wave loading, and may also be used fo r establishing and verifying procedures for approximate analysis of ge neral vibroimpact systems.