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A numerical evaluation of the method of equivalent nonlinearization

Citation

Lin, Anne (1988) A numerical evaluation of the method of equivalent nonlinearization. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-11082007-084824

Abstract

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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.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Major Option:Civil Engineering
Thesis Availability:Restricted to Caltech community only
Thesis Committee:
  • Caughey, Thomas Kirk (chair)
Defense Date:21 December 1987
Record Number:CaltechETD:etd-11082007-084824
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-11082007-084824
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4460
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:28 Nov 2007
Last Modified:26 Dec 2012 03:08

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