Numerical covariance analysis of MDoF hysteretic non- linear mechanical system subjected to modulated stochastic inputs

Structural systems subjected to random dynamic actions, response evaluation must be based on a stochastic approach. If nonlinear mechanical behaviour is considered, only in very few cases complete exact solutions exist. In this work, a numerical procedure is proposed, providing an expression of response in the state space that in our best knowledge has not yet been presented in literature, by using a formal justification with reference to seismic input processes modelled as linear filtered white noise with time varying parameters. Structural nonlinearities are modelled by the hysteretic differential Bouc-Wen model (BWM). The non-linear differential equation of the response covariance matrix is then solved by using a numerical algorithm, which updates the equivalent linear system coefficients at each step. Numerical computational effort is minimized by taking into account symmetry characteristic of state space covariance matrix. As application of the proposed method, both a single degree of freedom system and multi-storey shear type buildings are analysed to obtain the response in terms of standard deviation of displacements and its sensitivity. Finally, the mean value of dissipated hysteretic energy and time variation of integration steps are evaluated.