One-floor building as elasto-plastic oscillator subject to and interacting with Gaussian base motion

Abstract

The Slepian model process method has turned out to be a powerful tool to obtain accurate approximations to the probability distributions of the plastic displacements of a one degree of freedom linear elastic-ideal plastic oscillator subject to Gaussian white noise excitation. In the present paper the Slepian method is applied to obtain approximate distributions in closed analytical form of the plastic displacements of the top floor of an n-floor shear wall building. The top floor is modeled as an elasto-plastic oscillator whereas all the other floors are modeled as linear elastic modally damped oscillators. The excitation is stationary Gaussian white noise acting at the bottom floor. This model set-up is an attempt to model a one-floor shear wall building as an elasto-plastic oscillator subject to a stationary non-white Gaussian excitation represented by the random vibration of the (n−1)th floor. Moreover, the model simulates the soil-structure interaction through the exchange of energy between the top floor and the elastic structure below the top floor. The obtained distribution approximations are checked by comparison with direct simulation results using an autoregressive approximate representation of the response. It is thereby revealed that the neglect of dependency in the sequence of displacements causes only small error in the predicted distribution of the second and the following plastic displacements in a clump of consecutive plastic displacements of opposite sign. However, in the derivation of the distribution of the first plastic displacement in a clump there is no neglect of dependency and the approximation is observed to be satisfactory. It is possible to take the dependency into account by a simulation procedure of weighted outcomes. However, this topic is not treated in the present paper.