Tuning of the natural frequency spectrum of a circular plate by in-plate stress

Abstract

Initial stresses are often introduced deliberately into centrally clamped, peripherally free circular plates to increase the plate natural frequencies. Increased natural frequencies in the critical modes extend the range of stable rotation speed. Current axisymmetric initial stressing schemes increase the natural frequencies of the zero nodal circle, two and higher nodal diameter vibration modes, but the zero and one nodal diameter natural frequencies decrease. For sufficiently large initial stress, the zero nodal diameter natural frequency vanishes and the plate experiences divergence buckling, thereby limiting the initial stress that can be induced. In this paper a new initial stressing method is presented whereby the natural frequencies of all zero nodal circle modes increase simultaneously, thus avoiding buckling of the plate through excessive initial stress. The stress field is induced by applying uniform pressure to the boundaries of eccentric interior holes. Through proper location of the holes, the critical natural frequencies increase monotonically with increased pressure, and the magnitudes of the frequency shifts increase with the introduction of additional stressed holes. The initial stressing schemes can be directed towards optimal increases in specific vibration modes. Calculations predict natural frequency increases between 35% and 90% depending on the vibration mode. Experimental measurements are consistent with the model predictions.