Nonnormal Accelerations Due to Yielding in a Primary Structure

Keywords: System Response to Excitation, Dynamic Loading of Structural Systems, Dynamic Response, Nonnormal Accelerations, Displacement Nonnormality, and Random Excitation Of Structures.

Abstract: Response nonnormality is investigated for a yielding primary structure subjected to a normally distributed ground acceleration. This is a preliminary step in the nonlinear investigation of primary-secondary systems, since this primary acceleration is the base excitation of a light secondary system. The nonlinearity considered is bilinear hysteretic yielding in the primary structure. Results are presented from simulation, and from analysis of a simplified nonhysteretic substitute structure. This study of the nonnormality of acceleration is an extension of previous investigations which focused on displacement nonnormality. The nonlinear but nonhysteretic substitute structural model used here is a substantially improved version of an earlier model. The substitute structure is one for which the stationary Fokker-Planck equation can be solved to obtain values for probability distribution and moments of response. The coefficient of excess is used as a measure of the nonnormality. Analytical and numerical results for the substitute structure are compared with those from simulation of the bilinear hysteretic system. Such comparisons are made for both the relative displacement and the absolute acceleration of the primary structure, and include both the mean squared levels and the coefficients of excess of those responses. The agreement between the two sets of results for acceleration is shown to be quite good.