Stability and Bifurcation for a Simply Supported Functionally Graded Material Plate with One-to-One Internal Resonance
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-05-26
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
Stability and bifurcation behaviors for a model of simply supported functionally graded materials rectangular plate subjected to the transversal and in-plane excitations are studied by means of combination of analytical and numerical methods.
The resonant case considered here is 1 : 1 internal resonances and primary parametric resonance.
Two types of degenerated equilibrium points are studied in detail, which are characterized by a double zero and two negative eigenvalues, and a double zero and a pair of pure imaginary eigenvalues.
For each case, the stability regions of the initial equilibrium solution and the critical bifurcation curves are obtained in terms of the system parameters which may lead to Hopf bifurcation and 2D torus.
With both analytical and numerical methods, bifurcation behaviors on damping parameters and detuning parameters are studied, respectively.
A time integration scheme is used to find the numerical solutions for these bifurcation cases, and numerical results agree with the analytic predictions.
American Psychological Association (APA)
Zhang, Dongmei& Chen, Fangqi. 2014. Stability and Bifurcation for a Simply Supported Functionally Graded Material Plate with One-to-One Internal Resonance. Journal of Applied Mathematics،Vol. 2014, no. 2014, pp.1-11.
https://search.emarefa.net/detail/BIM-470300
Modern Language Association (MLA)
Zhang, Dongmei& Chen, Fangqi. Stability and Bifurcation for a Simply Supported Functionally Graded Material Plate with One-to-One Internal Resonance. Journal of Applied Mathematics No. 2014 (2014), pp.1-11.
https://search.emarefa.net/detail/BIM-470300
American Medical Association (AMA)
Zhang, Dongmei& Chen, Fangqi. Stability and Bifurcation for a Simply Supported Functionally Graded Material Plate with One-to-One Internal Resonance. Journal of Applied Mathematics. 2014. Vol. 2014, no. 2014, pp.1-11.
https://search.emarefa.net/detail/BIM-470300
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-470300