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Application of Green's function method in frequency analysis of axisymmetric vibration of annular plates with elastic ring supports

Kukla S., Szewczyk M.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2005

Vol. 4, nr 1

79-86

The paper concerns the axisymmetric vibration of annular plates with concentric elastic ring supports. The formulation and solution to the problem take into account the plates with one edge clamped and another one free and arbitrary number of circular supports. The Green's function method is applied to obtain the exact solution of the problem in an analytical form. Presented numerical examples show the influence of the parameters characterizing the system on its free vibration frequencies.

The Green's functions for vibration problems of circular plates with elastic ring supports

Kukla S., Szewczyk M.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2004

Vol. 3, nr 1

67--72

The paper deals with axisymmetric free vibration of a circular uniform plate. The formulation and solution of the problem take into account an arbitrary number of elastic concentric rings supporting the plate. The Green's function method was applied to solve the free vibration problem. The Green's functions were obtained to various boundary conditions. The obtained exact solution was used in a numerical analysis of an influence of the parameter characterizing the system on its free vibration frequencies.