The application of Wiener series in nonlinear random vibrations: An enhancment of Equivalent linearization

Equivalent Linearisation (EL) is a popular method used both in industry and academia for ana-lysing the response of nonlinear systems. EL aims to replace a nonlinear system with an equiva-lent linear system. In the case of stiffening nonlinearities in a system, EL fails to predict the re-sponse power spectrum despite the fact that it can determine the RMS value of the response as well as capturing the position of the resonance peaks very accurately. In this paper, the reason behind the failure of EL will be presented but most importantly an alter-native method to EL is to be suggested for nonlinear systems with white-noise input. The way to go forward with the latter is through the study and use of the Wiener series theory; a well-known but not widely used method for representing the response of the nonlinear systems under such input. It can be thought to be an extension of the impulse response representation from linear theory to nonlinear systems. This new representation requires an infinite number of 'impulse response functions' which are now called the Wiener kernels. The most important of the kernels is the first Wiener kernel due to the exclusive relation it has to the energy input in the system and the linear relation it has with the power spectrum of systems with linear damping and nonlinear stiffness. The first Wiener kernel is the cornerstone for the new methodology to be presented and which involves the computation of the first Wiener kernels of the nonlinear force in the system and that of the system's original response. In the final step, an appropriate curve fitting technique is re-quired which results in an accurate prediction of the first Wiener kernel and hence of the power spectrum of the system outperforming EL