Gaussian white noise excited elasto-Plastic oscillator of several degrees of freedom

The Slepian model process method has turned out to be a powerful tool to obtain accurate approximations to the long run probability distributions of the plastic displacements of a one degree of freedom linear elastic-ideal plastic oscillator (EPO) subject to stationary Gaussian white noise excitation. The paper extends the method to the simplest EPO of more than one degree of freedom. This EPO contains only a single structural component that can yield. It is experienced by direct response simulation that the loss of the property of slowly varying amplitudes when extending to more than one degree of freedom tends to jeopardize the assumption that the position of the response amplitude at the end of any clump of plastic displacements has practically no influence on the distributional properties of the response just before the start of the next clump of plastic displacements. Under this restriction the obtained Slepian model results fit well with the results obtained by direct response simulations. Also it is observed that the restriction gets less importance for decreasing intensity of the white noise excitation. Keywords: Random vibrations, Slepian models, MDOF elasto-plastic oscillator, Earthquake incluced vibrations, Random plastic displacements.