The Spreading Residue Harmonic Balance Method for Strongly Nonlinear Vibrations of a Restrained Cantilever Beam
Joint Authors
Yao, Minghui
Qian, Y. H.
Pan, J. L.
Chen, S. P.
Source
Advances in Mathematical Physics
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-04-10
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
The exact solutions of the nonlinear vibration systems are extremely complicated to be received, so it is crucial to analyze their approximate solutions.
This paper employs the spreading residue harmonic balance method (SRHBM) to derive analytical approximate solutions for the fifth-order nonlinear problem, which corresponds to the strongly nonlinear vibration of an elastically restrained beam with a lumped mass.
When the SRHBM is used, the residual terms are added to improve the accuracy of approximate solutions.
Illustrative examples are provided along with verifying the accuracy of the present method and are compared with the HAM solutions, the EBM solutions, and exact solutions in tables.
At the same time, the phase diagrams and time history curves are drawn by the mathematical software.
Through analysis and discussion, the results obtained here demonstrate that the SRHBM is an effective and robust technique for nonlinear dynamical systems.
In addition, the SRHBM can be widely applied to a variety of nonlinear dynamic systems.
American Psychological Association (APA)
Qian, Y. H.& Pan, J. L.& Chen, S. P.& Yao, Minghui. 2017. The Spreading Residue Harmonic Balance Method for Strongly Nonlinear Vibrations of a Restrained Cantilever Beam. Advances in Mathematical Physics،Vol. 2017, no. 2017, pp.1-8.
https://search.emarefa.net/detail/BIM-1123206
Modern Language Association (MLA)
Qian, Y. H.…[et al.]. The Spreading Residue Harmonic Balance Method for Strongly Nonlinear Vibrations of a Restrained Cantilever Beam. Advances in Mathematical Physics No. 2017 (2017), pp.1-8.
https://search.emarefa.net/detail/BIM-1123206
American Medical Association (AMA)
Qian, Y. H.& Pan, J. L.& Chen, S. P.& Yao, Minghui. The Spreading Residue Harmonic Balance Method for Strongly Nonlinear Vibrations of a Restrained Cantilever Beam. Advances in Mathematical Physics. 2017. Vol. 2017, no. 2017, pp.1-8.
https://search.emarefa.net/detail/BIM-1123206
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1123206