A numerical evaluation of the method of equivalent nonlinearization

by Lin, Anne

Abstract (Summary)
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. 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)[...]-damping and the Van der Pol equation.
Bibliographical Information:

Advisor:Thomas Kirk Caughey

School:California Institute of Technology

School Location:USA - California

Source Type:Master's Thesis

Keywords:civil engineering


Date of Publication:12/21/1987

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