Approximate Analysis of Nonlinear Systems under Narrow Band Random Inputs

Abstract

Dynamic analysis of systems with nonlinear stiffness characteristics is important in many earthquake engineering problems. Eventhough the base seismic excitation could be modelled as a wideband random process, due to the filtering action of the primary structure, the excitation to the equipments at higher floor levels are narrowbanded. This problem has received considerable attention in recent years [1, 2, 3]. While, under a broadband excitation, atleast simple nonlinear oscillators can be solved, the corresponding solutions under a narrowband input are not available. Since a gaussian narrowband process is essentially a filtered whitenoise, the dimensionality of the system response vector would be atleast four. The Fokker-Planck (FP) equation for the transitional probability density can be easily written down, but obtaining a solution to this equation is a formidable task. The stochastic averaging technique reduces the number of variables to three [4], but the resulting FP equation is still difficult to handle. Thus equivalent linearization or closure methods have to be used to get approximate solutions. However, in the absence of solution error estimates these methods can only be evaluated with reference to extensive numerical simulations.