Modal Interactions and Complex Responses in Weakly Nonlinear Multi-Degree-of-Freedom Mechanical Systems

摘要

The analysis of forced nonlinear response of mechanical and structural systems,subjected to harmonic excitations, is considered in this report. It is shown that the presence of internal resonances on the various linear modes of vibration of the structure can result in quite complex dynamical motions and the motion may not settle down to either a periodic or a sub/super-harmonic response. Internal resonances, which allow for the exchange of energy between the participating modes give rise to beat-like fluctuations in the amplitudes of vibration. The nonlinear amplitude variation is very slow and can be either periodic or chaotic, depending on the level of forcing, damping and the nonlinearity coefficients. The analytical and numerical results are derived for the nonlinear vibrations of a thin rectangular plate, the response of the pendulum vibration absorber, and a double pendulum. Some experimental results of the measured response for a harmonically forced rectangular plate are also presented and compared to analytical predictions. (AN).