SLAVING THE INPLANE MOTIONS OF A NONLINEAR PLATE TO ITS FLEXURAL MOTIONS - AN INVARIANT MANIFOLD APPROACH

We show that the in-plane motions of a nonlinear isotropic plate can b e decoupled from its transverse motions. We demonstrate this decouplin g by showing analytically and numerically the existence of a global no nlinear invariant manifold in the phase space of three nonlinearly cou pled fundamental oscillators describing the amplitudes of the coupled fundamental modes. The invariant manifold carries a continuum of slow periodic motions. In particular, for any motion on the slow invariant manifold the transverse oscillator executes a periodic motion and it s laves the in-plane oscillators into periodic motions of half its perio d. Furthermore, as the energy level of a motion on the slow manifold i ncreases, the frequency of the largest harmonic of the in-plane motion approaches the in-plane natural frequencies.