A WAVELET-GALERKIN PROCEDURE TO INVESTIGATE TIME-PERIODIC SYSTEMS: TRANSIENT VIBRATION AND STABILITY ANALYSIS
✍ Scribed by S. PERNOT; C.-H. LAMARQUE
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 932 KB
- Volume
- 245
- Category
- Article
- ISSN
- 0022-460X
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✦ Synopsis
A wavelet-Galerkin procedure is introduced in order to obtain transient and periodic solutions of multi-degree-of-freedom (d.o.f.s) dynamical systems with time-periodic coe$cients. Numerical comparisons, achieved with a Runge}Kutta method, emphasize that the wavelet-based procedure is reliable even in the case of problems involving both smooth or non-smooth parametric excitations and a relatively large number of degrees of freedom. The procedure is then applied to study the vibrations of some theoretical parametrically excited systems. Since problems of stability analysis of non-linear systems are often reduced after linearization to problems involving linear di!erential systems with time-varying coe$cients, the method is shown to be e!ective for the computation of the Floquet exponents that characterize stable/unstable parameters areas and consequently allows estimators for stability/instability levels to be provided. Stability diagrams of some theoretical examples including a single-degree-of-freedom Mathieu oscillator and a two-degree-of-freedom parametrically excited system, illustrate the relevance of the method. Finally, future studies are outlined for the extension of the wavelet method to the non-linear case.
2001 Academic Press