Free vibrations of circular plates with axisymmetric thickness variation

Abstract

The integral equation method is developed for vibration analysis of solid circular plates with arbitrary thickness variation along the radius. General boundary conditions are considered. The problem is formulated in terms of displacements. The resulting fourth-order linear hyperbolic equation with variable coefficients is solved using the analogue equation method of Katsikadelis. According to this method the linear governing differential equation is replaced by a linear equation of a substitute beam with unit bending stiffness, under a fictitious load distribution. Numerical examples are presented for plates with various thickness variation laws, which illustrate the method and demonstrate its efficiency and accuracy.

Keywords

circular plate vibrations variable thickness boundary elements integral equation method analogue equation method

Get full access to this article

View all access options for this article.

References

Avalos

Laura

P. A. A.

Larrondo

H. A.

Vibrating circular plates with stepped thickness over a concentric circular region: A general, approximate solution. J. Acoust. Soc. Am., 1988, 84, 1181–1185.

Yeh

K.-Y.

Kue

J.-H.

Rimrott

F. P. J.

On the nonaxisymmetric loading of nonhomogeneous annular plates of variable thickness. J. Appl. Mechanics, 1997, 64, 307–312.

Azimi

Free vibration of circular plates with elastic or rigid interior support. J. Sound Vibr., 1988, 120, 37–52.

Azimi

Free vibration of circular plates with elastic edge supports using the receptance method. J. Sound Vibr., 1988, 120, 19–35.

Romanelli

Rossi

R. E.

Laura

P. A. A.

Gutierrez

R. H.

Transverse vibrations of a circular annular plate with an intermediate circular support and a free inner edge. J. Sound Vibr., 1998, 212, 564–571.

Leissa

A. W.

Vibration of plates, NASA SP 160, 1969 (US Government Printing Office, Washington, DC).

Timoshenko

S. P.

Woinowsky-Krieger

Theory of plates and shells, 1959 (McGraw-Hill, New York).

Conway

H. D.

An analogy between flexural vibrations of a cone and a disc of linearly varying thickness. Z. Angew. Math. Mechanik, 1957, 37, 406–407.

Singh

Saxena

Axisymmetric vibration of a circular plate with double linear variable thickness. J. Sound Vibr., 1995, 179, 879–897.

10.

Singh

Tyagi

D. K.

Transverse vibrations of an elliptic plate with variable thickness. J. Sound Vibr., 1985, 99, 379–391.

11.

Singh

Chakraverty

Use of orthogonal characteristic polynomial in two dimension for tranverse vibration of elliptical and circular plates with variable thickness. J. Sound Vibr., 1994, 173, 35–42.

12.

Singh

Hassan

Tranverse vibration of a circular plate with arbitrary thickness variation. Int. J. Mech. Sci., 1998, 40, 1089–1104.

13.

Singh

Saxena

Axisymmetric vibration of a circular plate with exponential thickness variation. J. Sound Vibr., 1996, 192, 35–42.

14.

T. Y.

Liu

G. R.

Free vibration analysis of circular plates with variable thickness by the generalized differential quadrature rule. Int. J. Solids Structs, 2001, 38, 7967–7980.

15.

Nerantzaki

M. S.

Katsikadelis

J. T.

An analog equation solution to dynamic analysis of plates with variable thickness. Engng Analysis Boundary Elements, 1996, 17, 145–152.

16.

Katsikadelis

J. T.

Tsiatas

C. G.

Buckling load optimization of beams. Arch. Appl. Mechanics, 2005, 74, 790–799.