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1 Acta Mechanica et Automatica

1 2012

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Limitation of Cauchy Function Method in Analysis of Estimators of Frequency and Form of Natural Vibrations of Circular Plate with Variable Thickness and Clamped Edges

Jaroszewicz J., Żur K.

Acta Mechanica et Automatica

2012

Vol. 6, no. 2

53-57

In this paper the Berstein-Kieropian double estimators of basic natural frequency of circular plate with power variable thickness along the radius and clamped edges in diaphragm form were analyzed in a theoretical approach. The approximate solution of boundary problem of transversal vibration by means of Cauchy function and characteristic series method has been applied for chosen values of power indicator of variable thickness and material Poisson’s ratio has been chosen which led to exact form solutions. Particular attention has been given to a singularity arising from the uncertainty of estimates of Bernstein-Kieropian. Improving this method has been obtained the general form of Cauchy function for arbitrary values of and , which are physically justified. Therefore, the aim of the paper was to explore the reason why for a plate above a certain value = 3.97 exact solution, which Conway couldn’t receive (Conway, 1958a, b)