Resonant frequency calculations using a hybrid perturbation-galerkin technique / James F. Geer, Carl M. Anderson.

Format:

Book

Government document

Author/Creator:

Geer, James F.

Contributor:

Anderson, Carl M.

Institute for Computer Applications in Science and Engineering

Series:

ICASE report ; no. 91-68.

NASA contractor report ; NASA CR-187632.

ICASE report ; no. 91-68

NASA contractor report ; 187632

Language:

English

Subjects (All):

Nonlinear systems.

Perturbation (Mathematics).

Physical Description:

1 online resource (i, 27 pages) : illustrations

Place of Publication:

Hampton, Va. : Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, [1991]

Summary:

A two step hybrid perturbation-Galerkin technique is applied to the problem of determining the resonant frequencies of one- or several degree(s) of freedom nonlinear systems involving a parameter. In step one, the Lindstedt- Poincare method is used to determine perturbation solutions which are formally valid about one or more special values of the parameter (e.g. for small or large values of the parameter). In step two, a subset of the perturbation coordinate functions determined in step one is used in a Galerkin type approximation. The technique is illustrated for several one-degree-of-freedom systems, including the Duffing and van der Pol oscillators, as well as for the compound pendulum. For all of the examples considered, it is shown that the frequencies obtained by the hybrid technique using only a few terms from the perturbation solutions are significantly more accurate than the perturbation results on which they are based, and they compare very well with frequencies obtained by purely numerical methods.

Notes:

Title from title screen (viewed on December 6, 2011).

"September 1991."

Includes bibliographical references (pages 23-24).

OCLC:

227773976

Access Restriction:

APPROVED FOR PUBLIC RELEASE.