SUBHARMONIC TRAVELING WAVES IN A GEOMETRICALLY NONLINEAR CIRCULATE PLATE

The subharmonic motions of thin, axisymmetric, geometrically non-linear circular plates are analyzed. It is well known that such cyclic systems possess pairs of degenerate modes in ''1-1'' internal resonance, i.e. modes having equal linearized natural frequencies. The non-linear interaction of such a pair of modes is examined by discretizing the non-linear partial differential equations of motion and then investigating the resulting set of non-linear ordinary differential equations analytically and numerically. Two types of forced subharmonic motions are detected, namely subharmonic standing waves (SSW) and subharmonic travelling waves (STW). Moreover, it is found that for sufficiently large values of frequency detuning of the forcing function the STW lose stability in a Hopf bifurcation, leading to quasi-periodic motions of the plate, i.e. to oscillations on a two-torus. The analytical results are confirmed by numerical integrations of the equations of motion and by numerical Poincare maps. The results reported in this work are expected to have applicability on the dynamic analysis and design of thin, flexible disks, of the type used for data storage in the computer industry.