Damping out and non-linearities in modal methods

The precise numerical simulation of the dynamic behaviour of industrial components using the finite elements methods leads to big size models. Modal methods are currently used when dynamic excitations are of low or medium frequency. Spectral methods represent a particular type of modal methods used for seismic risk assessment. In these Rayleigh-Ritz type methods, the vibratory movement is projected into the vectorial space associated with a characteristic functions base of the system. Classically, the vectorial space corresponds to the real eigenvectors of a conservative system with symmetrical matrices. Because of the linearity of the system and of the particular damping forms, the uncoupled equations are verified by the generalized coordinates. These two hypotheses are often too restrictive, and some extensions of modal methods adapted to the study of industrial situations are presented (turbo-alternator, motor-driven primary coolant circuit pump..). The hardening and damping matrices are not necessarily symmetrical. (J.S.). 7 refs., 8 figs., 4 tabs