Nonlinear Oscillations of Mechanical Systems under Multifrequency Parametric Excitation.

摘要

Various problems related to the nonlinear oscillations of mechanical and structural systems were investigated. They involved the following topics: (1) Resonances in weakly nonlinear systems subjected to multifrequency parametric and/or external excitation, with one case being a self-excited system; (2) Dynamic behavior of cracked bars and rotating shafts, for the purpose of detecting cracks; (3) Vibrations of cylindrical membranes, with applications to inflatable dams; (4) Vibrations and stability of structures whose support resistance changes as the structure is loaded: (5) Dynamic instability of laminated composite plates under in-plane harmonically-varying loads; (6) Application of vibration data to nondestructively predict buckling loads; (7) Nonlinear oscillations of slender cantilevered beams under harmonically-varying loads; and (8) Prediction of a large jump in deflection, such as snap-through instability, under harmonically-varying loads. The results improve our understanding of the dynamics of mechanical and structural systems, and will be useful in the prevention of excessively large motions and unstable behavior.