Analysis of the influence of elasticity constants and material density on the base frequency of axi-symmetrical vibrations with variable thickness plates

In the paper, the influence of Young's modulus and Poisson ratio as well as mass density of a material on the base frequency of circular plates of the diaphragm type with variable thickness is
discussed. In order to solve the boundary-value problem, the Cauchy function method and double Bernstein-Kieropian estimators were applied. An analytical form of Cauchy's influence function was found and used to construct the characteristic equation in the form of a power series with respect to a frequency parameter. Application of this method allowed a functional dependency of the base frequency on material constants of the plates to be established. The results of calculations for plates made of duralumin and tin were mentioned as examples. Comparison of the obtained results with those found in scientific literature indicated high accuracy of the method applied therein.