An Analytical Approximation Method for Strongly Nonlinear Oscillators
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-02-27
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
An analytical method is proposed to get the amplitude-frequency and the phase-frequency characteristics of free/forced oscillators with nonlinear restoring force.
The nonlinear restoring force is expressed as a spring with varying stiffness that depends on the vibration amplitude.
That is, for stationary vibration, the restoring force linearly depends on the displacement, but the stiffness of the spring varies with the vibration amplitude for nonstationary oscillations.
The varied stiffness is constructed by means of the first and second averaged derivatives of the restoring force with respect to the displacement.
Then, this stiffness gives the amplitude frequency and the phase frequency characteristics of the oscillator.
Various examples show that this method can be applied extensively to oscillators with nonlinear restoring force, and that the solving process is extremely simple.
American Psychological Association (APA)
Shimin, Wang& Lechang, Yang. 2012. An Analytical Approximation Method for Strongly Nonlinear Oscillators. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-9.
https://search.emarefa.net/detail/BIM-993884
Modern Language Association (MLA)
Shimin, Wang& Lechang, Yang. An Analytical Approximation Method for Strongly Nonlinear Oscillators. Journal of Applied Mathematics No. 2012 (2012), pp.1-9.
https://search.emarefa.net/detail/BIM-993884
American Medical Association (AMA)
Shimin, Wang& Lechang, Yang. An Analytical Approximation Method for Strongly Nonlinear Oscillators. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-9.
https://search.emarefa.net/detail/BIM-993884
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993884