NORMAL MULTI-MODES OF NONLINEAR EULER BEAMS

For a strongly non-linear multi-degree-of-freedom system, in general, one cannot consider one mode at a time as in linear modal analysis. In the absence of external excitation, the natural vibration often invol ves more than one mode at a time resulting in quasi-periodic or multi- periodic (toroidal) vibration. The normal multi-mode in free vibration have been formulated by means of the action-angle transformation and the resulting ordinary differential equations embedded in partial diff erential equations. Final multi-periodic solutions have been obtained by extending the newly developed Toeplitz Jacobian matrix method with multi-periodic fast Fourier transforms. (C) 1997 Academic Press Limite d.