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1 Technical Sciences / University of Warmia and Mazury in Olsztyn

1 2016

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The general formula for calculation of fundamental frequency of axisymmetric vibrations of circular plates with linearly variable thickness

Jaroszewicz J., Radziszewski L.

Technical Sciences / University of Warmia and Mazury in Olsztyn

2016

nr 19(4)

401--410

This work has derived the general formula, sufficiently precise for engineering calculations of base frequency of axisymmetric free vibrations of uniform, circular diaphragm type plates clamped at the edge with linearly variable thickness. To solve the boundary problem, the Cauchy’s function method and characteristic series have been applied. The above formula has been derived on the basis of Dunkerley’s formula which is based on the first major term of the characteristic series and results in the simplest, lower bound estimator. The analysis of the formula shows that the base frequency coefficient for diaphragm plates clamped at the edge depends to only a small extent on the Poisson’s ratio, and therefore it may be averaged in the case of construction materials. Comparison of the calculations results of the simplest lower bound estimators for the base frequency obtained by using proposed method, with the results known from the literature as precise solutions, including Conway method, confirmed the high accuracy of the proposed method.