A Caltech Library Service

A numerical evaluation of the method of equivalent nonlinearization


Lin, Anne (1988) A numerical evaluation of the method of equivalent nonlinearization. Dissertation (Ph.D.), California Institute of Technology.


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.

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:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4460
Deposited By: Imported from ETD-db
Deposited On:28 Nov 2007
Last Modified:02 Mar 2017 00:30

Thesis Files

[img] PDF (Lin_a_1988.pdf) - Final Version
Restricted to Caltech community only
See Usage Policy.


Repository Staff Only: item control page