On the Approximate Analytical Solution to Non-Linear Oscillation Systems
This study describes an analytical method to study two well-known systems of nonlinear oscillators. One of these systems deals with the strongly nonlinear vibrations of an elastically restrained beam with a lumped mass. The other is a Duffing equation with constant coefficients. A new implementation...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.3233/SAV-2012-0726 |
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| _version_ | 1832547466545725440 |
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| author | Mahmoud Bayat Iman Pakar |
| author_facet | Mahmoud Bayat Iman Pakar |
| author_sort | Mahmoud Bayat |
| collection | DOAJ |
| description | This study describes an analytical method to study two well-known systems of nonlinear oscillators. One of these systems deals with the strongly nonlinear vibrations of an elastically restrained beam with a lumped mass. The other is a Duffing equation with constant coefficients. A new implementation of the Variational Approach (VA) is presented to obtain highly accurate analytical solutions to free vibration of conservative oscillators with inertia and static type cubic nonlinearities. In the end, numerical comparisons are conducted between the results obtained by the Variational Approach and numerical solution using Runge-Kutta's [RK] algorithm to illustrate the effectiveness and convenience of the proposed methods. |
| format | Article |
| id | doaj-art-d29f555a5f8344a5b80259b5e1e5ee5e |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-d29f555a5f8344a5b80259b5e1e5ee5e2025-02-03T06:44:45ZengWileyShock and Vibration1070-96221875-92032013-01-01201435210.3233/SAV-2012-0726On the Approximate Analytical Solution to Non-Linear Oscillation SystemsMahmoud Bayat0Iman Pakar1Department of Civil Engineering, Mashhad Branch, Islamic Azad University, Mashhad, IranDepartment of Civil Engineering, Mashhad Branch, Islamic Azad University, Mashhad, IranThis study describes an analytical method to study two well-known systems of nonlinear oscillators. One of these systems deals with the strongly nonlinear vibrations of an elastically restrained beam with a lumped mass. The other is a Duffing equation with constant coefficients. A new implementation of the Variational Approach (VA) is presented to obtain highly accurate analytical solutions to free vibration of conservative oscillators with inertia and static type cubic nonlinearities. In the end, numerical comparisons are conducted between the results obtained by the Variational Approach and numerical solution using Runge-Kutta's [RK] algorithm to illustrate the effectiveness and convenience of the proposed methods.http://dx.doi.org/10.3233/SAV-2012-0726 |
| spellingShingle | Mahmoud Bayat Iman Pakar On the Approximate Analytical Solution to Non-Linear Oscillation Systems Shock and Vibration |
| title | On the Approximate Analytical Solution to Non-Linear Oscillation Systems |
| title_full | On the Approximate Analytical Solution to Non-Linear Oscillation Systems |
| title_fullStr | On the Approximate Analytical Solution to Non-Linear Oscillation Systems |
| title_full_unstemmed | On the Approximate Analytical Solution to Non-Linear Oscillation Systems |
| title_short | On the Approximate Analytical Solution to Non-Linear Oscillation Systems |
| title_sort | on the approximate analytical solution to non linear oscillation systems |
| url | http://dx.doi.org/10.3233/SAV-2012-0726 |
| work_keys_str_mv | AT mahmoudbayat ontheapproximateanalyticalsolutiontononlinearoscillationsystems AT imanpakar ontheapproximateanalyticalsolutiontononlinearoscillationsystems |