Determination the Spectral Response for Non-Linear Oscillators with the Nonlinear Characteristic

In many practical applications, the vibrations are not linear. They have a nonlinear character. For example, the cars wheel vibrations are random vibrations linear raceways. These occur due to irregularities of the runways who are described by random functions. The essential problem is here in finding the power spectral density of the response. In theory seismic or levees are all nonlinear vibrations. 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. The method of the stochastic equivalent linearization is based on the idea that a nonlinear system may be replaced by a linear system by minimizing the mean square error of the two systems. This paper studies the nonlinear vibrations of a single degree of freedom Duffing oscillator with elastic characteristics sinusoidal type. The computations are illustrated with graphs that represent the power spectral density of the frequency response function. The power spectral density of response functions so obtained show non-linear features such as multiple resonant peaks.