Parametrically excited nonlinear systems: a comparison of two methods
Subharmonic resonance of two-degree-of-freedom systems with cubic nonlinearities to multifrequency parametric excitations in the presence of three-to-one internal resonance is investigated. Two approximate methods (the multiple scales and the generalized synchronization) are used to construct a firs...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2002-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202007019 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832561879206068224 |
|---|---|
| author | A. F. El-Bassiouny |
| author_facet | A. F. El-Bassiouny |
| author_sort | A. F. El-Bassiouny |
| collection | DOAJ |
| description | Subharmonic resonance of two-degree-of-freedom systems with cubic nonlinearities to multifrequency parametric excitations in the
presence of three-to-one internal resonance is investigated. Two
approximate methods (the multiple scales and the generalized
synchronization) are used to construct a first-order nonlinear
ordinary differential equations governing the modulation of the
amplitudes and phases. Steady state solutions and their stability
are computed for selected values of the system parameters. The
results obtained by the two methods are in excellent agreement.
Numerical solutions are carried out and graphical representations
of the results are presented and discussed. |
| format | Article |
| id | doaj-art-e53e648d1a4b4013a6dda1bfa6a29442 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e53e648d1a4b4013a6dda1bfa6a294422025-02-03T01:24:00ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-01321273976110.1155/S0161171202007019Parametrically excited nonlinear systems: a comparison of two methodsA. F. El-Bassiouny0Mathematics Department, Faculty of Science, Benha University, Benha 13518, EgyptSubharmonic resonance of two-degree-of-freedom systems with cubic nonlinearities to multifrequency parametric excitations in the presence of three-to-one internal resonance is investigated. Two approximate methods (the multiple scales and the generalized synchronization) are used to construct a first-order nonlinear ordinary differential equations governing the modulation of the amplitudes and phases. Steady state solutions and their stability are computed for selected values of the system parameters. The results obtained by the two methods are in excellent agreement. Numerical solutions are carried out and graphical representations of the results are presented and discussed.http://dx.doi.org/10.1155/S0161171202007019 |
| spellingShingle | A. F. El-Bassiouny Parametrically excited nonlinear systems: a comparison of two methods International Journal of Mathematics and Mathematical Sciences |
| title | Parametrically excited nonlinear systems: a comparison of two methods |
| title_full | Parametrically excited nonlinear systems: a comparison of two methods |
| title_fullStr | Parametrically excited nonlinear systems: a comparison of two methods |
| title_full_unstemmed | Parametrically excited nonlinear systems: a comparison of two methods |
| title_short | Parametrically excited nonlinear systems: a comparison of two methods |
| title_sort | parametrically excited nonlinear systems a comparison of two methods |
| url | http://dx.doi.org/10.1155/S0161171202007019 |
| work_keys_str_mv | AT afelbassiouny parametricallyexcitednonlinearsystemsacomparisonoftwomethods |