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Accuracy Improvement of the Method of Multiple Scales for Nonlinear Vibration Analyses of Continuous Systems with Quadratic and Cubic Nonlinearities
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-01-19
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
This paper proposes an accuracy improvement of the method of multiple scales (MMSs) for nonlinear vibration analyses of continuous systems with quadratic and cubic nonlinearities.
As an example, we treat a shallow suspended cable subjected to a harmonic excitation, and investigate the primary resonance of the mth in-plane mode (Ω≈ωm) in which Ω and ωm are the driving and natural frequencies, respectively.
The application of Galerkin's procedure to the equation of motion yields nonlinear ordinary differential equations with quadratic and cubic nonlinear terms.
The steady-state responses are obtained by using the discretization approach of the MMS in which the definition of the detuning parameter, expressing the relationship between the natural frequency and the driving frequency, is changed in an attempt to improve the accuracy of the solutions.
The validity of the solutions is discussed by comparing them with solutions of the direct approach of the MMS and the finite difference method.
American Psychological Association (APA)
Abe, Akira. 2011. Accuracy Improvement of the Method of Multiple Scales for Nonlinear Vibration Analyses of Continuous Systems with Quadratic and Cubic Nonlinearities. Mathematical Problems in Engineering،Vol. 2010, no. 2010, pp.1-12.
https://search.emarefa.net/detail/BIM-505767
Modern Language Association (MLA)
Abe, Akira. Accuracy Improvement of the Method of Multiple Scales for Nonlinear Vibration Analyses of Continuous Systems with Quadratic and Cubic Nonlinearities. Mathematical Problems in Engineering No. 2010 (2010), pp.1-12.
https://search.emarefa.net/detail/BIM-505767
American Medical Association (AMA)
Abe, Akira. Accuracy Improvement of the Method of Multiple Scales for Nonlinear Vibration Analyses of Continuous Systems with Quadratic and Cubic Nonlinearities. Mathematical Problems in Engineering. 2011. Vol. 2010, no. 2010, pp.1-12.
https://search.emarefa.net/detail/BIM-505767
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-505767