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Extensional vibrations of rectangular crystal plates

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3 Author(s)
Lee, P.C.Y. ; Department of Civil Engineering, Princeton University, Princeton, New Jersey 08544 ; Nakazawa, M. ; Hou, J.P.

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A system of one‐dimensional equations governing the extensional (contour) modes of vibrations in rectangular crystal plates is derived from the Cauchy–Voigt two‐dimensional equations of extensional motion of anisotropic, elastic plates. The system of equations is further divided into two groups of equations governing, separately, the symmetric (contour extensional) and antisymmetric (contour shear) modes of vibrations, by setting the elastic stiffness coefficients γ15 = γ35 = 0 in order to neglect the coupling effect between the two groups. Closed form solutions of contour extensional vibrations are obtained for rectangular crystal plates satisfying the traction‐free conditions at four edges. Dispersion relation and frequency equation are obtained in explicit form for the first three contour extensional modes. Resonance frequencies, for various contour extensional modes, are computed as a function of the length‐to‐width ratio (a/c) of plates. Predicted results are compared with the detailed measurements for rectangular GT cuts with close agreement. Two‐dimensional vibration patterns have also been calculated at resonances for different values of a/c ratio.

Published in:

Journal of Applied Physics  (Volume:53 ,  Issue: 6 )