A wavelet-Galerkin procedure to investigate time-periodic systems: Transient vibration and stability analysis

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 coefficients. Numerical comparisons, achieved with a Run ge-Kutta method, emphasize that the wavelet-based procedure is reliable eve n in the case of problems involving both smooth or non-smooth parametric ex citations and a relatively large number of degrees of freedom. The procedur e is then applied to study the vibrations of some theoretical parametricall y excited systems. Since problems of stability analysis of non-linear syste ms are often reduced after linearization to problems involving linear diffe rential systems with time-varying coefficients, the method is shown to be e ffective for the computation of the Floquet exponents that characterize sta ble/unstable parameters areas and consequently allows estimators for stabil ity/instability levels to be provided. Stability diagrams of some theoretic al examples including a sin.-le-degree-of-freedom Mathieu oscillator and a two-degree-of-freed om parametrically excited system, illustrate the releva nce of the method. Finally, future studies are outlined for the extension o f the wavelet method to the non-linear case. (C) 2001 Academic Press.