THE POWER SPECTRAL DENSITY OF THE STATIONARY RESPONSE OF DUFFING OSCILLATOR WITH NONLINEAR ELASTIC CHARACTERISTIC

Abstract

We present a method for estimating the power spectral density of the stationary response of oscillator with a nonlinear restoring force under external stochastic wide-band excitation. If a non-linear mathematical model of the system under consideration is adopted, together with a random process model of the excitation, then one is faced with the problem of predicting the system response. Non-mechanical system are completely linear, but linearization around the equilibrium position is acceptable in many cases-at least within some range of deformation. Linearization is important because linear functions are easier to deal with. Using linearization, one can estimate function values near known points. The statistical linearization technique can also tackle a wide variety of problems and also provides approximate information on the frequency domain characteristics of the stochastic response.