Contour Vibrations of Isotropic Circular Plates

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Abstract
A mathematical analysis has been done according to Love's theory. The results are: (a) The coefficients of the dilatation and the rotation are equal in amount regardless of Poisson's ratio only for the modes whose circumferential order is one. (b) The first mode whose order is two has the lowest natural frequency. This mode is practically equivoluminal, while the second mode is dilatational. (c) Locations of nodes are considered. Circular nodal lines can exist only for the radial and the tangential modes. (d) Frequencies and displacements of the most important modes are calculated. Applying the above results to bariumtitanate vibrators, we find that only the radial modes can be excited with full electrodes and the compound modes with split or partial electrodes, while the tangential modes can never be excited. Such an excitation of compound modes provides a convenient means for measuring Poisson's ratio of the material. Equivalent series inductances of the radial modes are calculated. Vibrations of thick circular plates are also considered. It is shown that vibrations of certain compound modes which are practically equivoluminal can be approximated by the rotation only. Comparisons between these solutions and the above results are made to reveal that the accuracy of approximation is satisfactory.

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