Determination op frequencies of natural vibrations of circular plates: PMM vol. 40, n≗1, 1976, pp. 112–119

Abstract

A method to construct an asymptotic process to find the axisymmetric vibration frequencies of a circular plate is proposed. Cases of symmetric vibrations relative to the middle surface (tension-compression vibrations) and of antisymmetric (bending) vibrations are considered. The asymptotic process for a plate with free endfaces has been studied in detail under mixed boundary conditions on the side surface. This problem can be considered as a model on which the practical convergence of the method proposed is analyzed and the accuracy of finding the frequencies at each step of the process is estimated. Furthermore, problems about the natural vibrations of a circular plate under other boundary conditions on the side surface, hinged-support and rigidly fixing, are solved by the proposed method. The purpose of this investigation is to develop a method of determining the natural vibration frequencies of a “medium” thickness plate. The question of finding the higher frequencies, even for thin plates, as well as the lowest vibration frequencies of medium thickness plates cannot be solved within the framework of existing applied theories. Hence, it is interesting to formulate a sequence of approximate theories which would permit determination of any, previously assigned, number of the first frequencies with sufficient accuracy for medium thicknesses.