SUBHARMONIC RESPONSES IN HARMONICALLY EXCITED RECTANGULAR-PLATES WITHONE-TO-ONE INTERNAL RESONANCE

Non-linear flexural vibrations of a rectangular plate with uniform str etching are studied for the case when it is subharmonically excited at nearly three times one of the linear natural frequencies. The interes t here is in the subharmonic response of the plate when two distinct l inear modes are near one-to-one internal resonance. Using the method o f averaging, it is shown that, depending on the spatial distribution o f the external forces, the plate can undergo harmonic motions, subharm onic motions in the directly excited spatial mode, or subharmonic moti ons in which both the internally resonant modes participate. The coupl ed-mode subharmonic oscillations can also undergo Hopf bifurcation to complicated amplitude-modulated subharmonic solutions which exhibit pe riod-doubling route to chaos. Numerical results are presented specific ally for one-to-one resonance in the (1,2) and (3,1) plate modes. The two-mode discretization of the von Karman plate equations are also dir ectly simulated to verify some of the predictions of the averaged equa tions. (C) 1997 Elsevier Science Ltd.