Calculating resonant frequencies of axisymmetric oscillations of isotropic cylindrical disks

Resonant axisymmetric oscillations of cylindrical disks made of isotropic materials are analytically considered in accordance with the Kog theory. Relationships of dimensionless resonant frequencies to the geometrical dimensions of the disks and the dynamic characteristics of the material (Poisson’s ratio and shear wave velocity) are presented in a form convenient for calculations. Digital values of resonant frequencies are calculated and summarized in tables at different Poisson’s ratios ranging between 0.20 and 0.45, with a step of 0.05, for a number of discrete thickness-to-diameter ratios ranging from 0 to 0.853145 and from 0 to 0.30 when oscillations of the first and second modes are exited, respectively. The estimation of method errors in resonant frequency calculations based on the comparison with the known results obtained by the RayleighRitz method has proved their high repeatability. Instrumental errors in determining the dynamic characteristics of the material are calculated in relation to experimental results obtained in a number of well-known studies.