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...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202007019 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |