Statistical Linearization of Duffing Oscillator Using Constrained Optimization Technique

Abstract

The present work aims to evaluate the response of Duffing oscillator using equivalent linearization. The stiffness and damping forces are proportional to the cube power of the displacement and velocity, respectively. The oscillator is excited by stationary process. The method suggested in this work aims to replace the original nonlinear system with an equivalent linear system by minimizing the difference in the displacement between the nonlinear system and the equivalent linear system in a least square sense using different constraints (e.g., restoring force, potential energy, complementary energy). Numerical results are presented to show the efficiency of the proposed linearization scheme. For this purpose, instantaneous mean square values of the displacement are evaluated and compared with simulation. A close agreement between the simulations and the proposed model is observed which, in turn, shows the efficiency and applicability of the proposed model. A discussion on the use of different constraint conditions and their relative importance is also presented.