An analysis of free vibrations of isotropic, circular plates with the Mindlin plate theory

We study non-axially symmetric vibrations of isotropic, circular plates with free edges. Mindlin´s first-order equations governing the coupled thickness-shear, flexural, and thickness-twist modes are obtained for circular plates in cylindrical coordinates by following the derivation of Mindlin plate equations in Cartesian coordinates. The equations are successfully solved by Bessel functions. Numerical results for dispersion relations, frequency spectra, and mode shapes are obtained as parts of the validation and solution procedure. The calculated results of frequency spectra are in good agreement with Mindlin´s earlier studies. It is our first step to analyze high frequency vibrations of circular plates in a systematic manner for applications in circular quartz crystal resonators.