Nonlinear Forced Vibration of a Viscoelastic Buckled Beam with 2 : 1 Internal Resonance
Joint Authors
Chen, Li-Qun
Zhang, Guo-Ce
Ding, Hu
Xiong, Liu-Yang
Source
Mathematical Problems in Engineering
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-01-08
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
Nonlinear dynamics of a viscoelastic buckled beam subjected to primary resonance in the presence of internal resonance is investigated for the first time.
For appropriate choice of system parameters, the natural frequency of the second mode is approximately twice that of the first providing the condition for 2 : 1 internal resonance.
The ordinary differential equations of the two mode shapes are established using the Galerkin method.
The problem is replaced by two coupled second-order differential equations with quadratic and cubic nonlinearities.
The multiple scales method is applied to derive the modulation-phase equations.
Steady-state solutions of the system as well as their stability are examined.
The frequency-amplitude curves exhibit the steady-state response in the directly excited and indirectly excited modes due to modal interaction.
The double-jump, the saturation phenomenon, and the nonperiodic region phenomena are observed illustrating the influence of internal resonance.
The validity range of the analytical approximations is assessed by comparing the analytical approximate results with a numerical solution by the Runge-Kutta method.
The unstable regions in the internal resonance are explored via numerical simulations.
American Psychological Association (APA)
Xiong, Liu-Yang& Zhang, Guo-Ce& Ding, Hu& Chen, Li-Qun. 2014. Nonlinear Forced Vibration of a Viscoelastic Buckled Beam with 2 : 1 Internal Resonance. Mathematical Problems in Engineering،Vol. 2014, no. 2014, pp.1-14.
https://search.emarefa.net/detail/BIM-507003
Modern Language Association (MLA)
Xiong, Liu-Yang…[et al.]. Nonlinear Forced Vibration of a Viscoelastic Buckled Beam with 2 : 1 Internal Resonance. Mathematical Problems in Engineering No. 2014 (2014), pp.1-14.
https://search.emarefa.net/detail/BIM-507003
American Medical Association (AMA)
Xiong, Liu-Yang& Zhang, Guo-Ce& Ding, Hu& Chen, Li-Qun. Nonlinear Forced Vibration of a Viscoelastic Buckled Beam with 2 : 1 Internal Resonance. Mathematical Problems in Engineering. 2014. Vol. 2014, no. 2014, pp.1-14.
https://search.emarefa.net/detail/BIM-507003
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-507003