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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. doi:10.7907/31g4-p045.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Civil Engineering
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Civil Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Caughey, Thomas Kirk
Thesis Committee:
  • Caughey, Thomas Kirk (chair)
  • Jennings, Paul C.
  • Housner, George W.
  • Knowles, James K.
  • Iwan, Wilfred D.
Defense Date:21 December 1987
Funding AgencyGrant Number
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:16 Apr 2021 23:00

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