Influence of additional mass rings on frequencies of axi-symmetrical vibrations of clamped circular plates of linearly variable thickness

The aim of this paper is to analyze the influence of values and radius of an additional mass ring on the continuous distribution of mass of a clamped circular plate of linearly variable thickness. The linear theory of thin plates is used for description of small buckling vibrations. The authors applied the partial discretization method which is based on the discretization of the continuous mass and continuous buckling rigidity function. It is also based on the method of Cauchy's influence function, which gives particularly exact effects for distributed-continuous systems such as that presented in this paper. It is shown that an approximate result leads to the exact value with the discretization degree of less than 5, and it is not dependent on the value and radius of the concentrated mass. Exact results of calculations lead to accurate values discovered by Conway for plates of linearly variable thickness without an additional mass and to accurate values discovered by Roberson for plates of constant thickness with the mass concentrated in the center.