A new modified Lindstedt–Poincare method for nonlinear damped forced oscillations
Nonlinear damped forced oscillators are very importance in the fields of mechanical, electrical and other dynamical systems. Small oscillations are being investigated by classical perturbations. Earlier Cheung et al. presented a modified Lindstedt–Poincare method for large amplitude of oscillation;...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-08-01
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| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379723004667 |
| _version_ | 1827877754831372288 |
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| author | M.Z. Alam Md. Alal Hosen M.S. Alam |
| author_facet | M.Z. Alam Md. Alal Hosen M.S. Alam |
| author_sort | M.Z. Alam |
| collection | DOAJ |
| description | Nonlinear damped forced oscillators are very importance in the fields of mechanical, electrical and other dynamical systems. Small oscillations are being investigated by classical perturbations. Earlier Cheung et al. presented a modified Lindstedt–Poincare method for large amplitude of oscillation; but its mathematical manipulation is tremendously difficult. Moreover, it fails to determine the solutions when linear restoring force vanishes. In this article, a modification of the same method is made which greatly reduces mathematical calculations. On the other hand, it provides more accurate results and is used whether linear restoring force is present or not. |
| first_indexed | 2024-03-12T17:41:57Z |
| format | Article |
| id | doaj.art-afa368743e644b479e04bbb5fc145df5 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-03-12T17:41:57Z |
| publishDate | 2023-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-afa368743e644b479e04bbb5fc145df52023-08-04T05:47:13ZengElsevierResults in Physics2211-37972023-08-0151106673A new modified Lindstedt–Poincare method for nonlinear damped forced oscillationsM.Z. Alam0Md. Alal Hosen1M.S. Alam2Corresponding author.; Department of Mathematics, Rajshahi University of Engineering & Technology (RUET), Rajshahi 6204, BangladeshDepartment of Mathematics, Rajshahi University of Engineering & Technology (RUET), Rajshahi 6204, BangladeshDepartment of Mathematics, Rajshahi University of Engineering & Technology (RUET), Rajshahi 6204, BangladeshNonlinear damped forced oscillators are very importance in the fields of mechanical, electrical and other dynamical systems. Small oscillations are being investigated by classical perturbations. Earlier Cheung et al. presented a modified Lindstedt–Poincare method for large amplitude of oscillation; but its mathematical manipulation is tremendously difficult. Moreover, it fails to determine the solutions when linear restoring force vanishes. In this article, a modification of the same method is made which greatly reduces mathematical calculations. On the other hand, it provides more accurate results and is used whether linear restoring force is present or not.http://www.sciencedirect.com/science/article/pii/S2211379723004667Modified Lindstedt–Poincare methodNonlinear damped forced oscillatorsApproximate solutionsFrequency amplitude relation |
| spellingShingle | M.Z. Alam Md. Alal Hosen M.S. Alam A new modified Lindstedt–Poincare method for nonlinear damped forced oscillations Results in Physics Modified Lindstedt–Poincare method Nonlinear damped forced oscillators Approximate solutions Frequency amplitude relation |
| title | A new modified Lindstedt–Poincare method for nonlinear damped forced oscillations |
| title_full | A new modified Lindstedt–Poincare method for nonlinear damped forced oscillations |
| title_fullStr | A new modified Lindstedt–Poincare method for nonlinear damped forced oscillations |
| title_full_unstemmed | A new modified Lindstedt–Poincare method for nonlinear damped forced oscillations |
| title_short | A new modified Lindstedt–Poincare method for nonlinear damped forced oscillations |
| title_sort | new modified lindstedt poincare method for nonlinear damped forced oscillations |
| topic | Modified Lindstedt–Poincare method Nonlinear damped forced oscillators Approximate solutions Frequency amplitude relation |
| url | http://www.sciencedirect.com/science/article/pii/S2211379723004667 |
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