Application of Non-classical Shells Theories for Free Vibration Analysis of Annular Plates

In the present paper, the problem of evaluation natural frequencies of a transversely isotropic circular plate is considered and the impact of the material properties of the plate on its natural frequencies is studied. The classical Kirchhoff-Love (KL) theory only takes into account material properties of the midplane. That is why the fundamental frequencies for isotropic and transversely isotropic plates are equal for the classical theory. The Ambartsumyan (A) theory of anisotropic shells takes into account the impact of the shear deformation in the thickness direction on the stress-strain state of the plate. In the general case, the theory of anisotropic plates and shells developed by Rodionova, Titaev, and Chernykh (RTC) permits one to take into account not only the transverse shears, but also the deformation of normals to the midplane. In the present paper, the problem of determining the fundamental frequencies is solved both with A and RTC theories, which improve the KL theory. To study the impact of the radial inhomogeneity on the plate fundamental frequencies, the calculations are carried out using the commercial finite element software COMSOL Multiphysics (v. 5.0). It is shown that the inhomogeneity of the plate affects greatly the fundamental (lowest) frequency of the plate, while the plate non-isotropy has a greater influence on the second and higher vibration modes