A Numerical Evaluation of the Method of Equivalent Nonlinearization

Author: Lin, Anne

Year: 1988

Degree: Dissertation (Ph.D.)

Advisor: Caughey, Thomas Kirk

Committee Members: Caughey, Thomas Kirk; Jennings, Paul C.; Housner, George W.; Knowles, James K.; Iwan, Wilfred D.

Option: Civil Engineering

DOI: 10.7907/31g4-p045

Abstract

The Method of Equivalent Nonlinearization, an approach for determining the approximate steady-state probability density function for the random response of nonlinear systems, is evaluated based on numerical simulations.

The approach is a natural extension of the well-known Method of Equivalent Linearization, and is based on approximating the original nonlinear system by an equivalent nonlinear system. As such, the approach relies on the existence of exact solutions for the steady-state probability density function of nonlinear systems.

The approach is applied to a class of systems with nonlinear damping, for which there are no exact solutions. The results show an excellent agreement between simulated and predicted probability density functions for displacement, velocity and energy-based envelope. Several examples were solved, including the case of (velocity)m-damping and the Van der Pol equation.

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