Hostname: page-component-848d4c4894-4hhp2 Total loading time: 0 Render date: 2024-05-29T03:13:48.382Z Has data issue: false hasContentIssue false

Flexural Vibration of Rectangular Plates with Stiffeners Parallel to the Edges

Published online by Cambridge University Press:  04 July 2016

S. Mahalingam*
Affiliation:
Deportment of Mechanical Engineering, University of Ceylon

Summary

The basis of the procedure described in the paper is the replacement of the stiffeners by an approximately equivalent system of line springs. One of two methods may then be used to determine the natural frequencies. A rectangular plate with edge stiffeners, point-supported at the four corners, is used to demonstrate the application of the Rayleigh-Ritz method. Numerical results obtained are compared with known approximate solutions based on finite difference equations. A Holzer-type iteration is employed in the case of a plate with parallel stiffeners, where the two edges perpendicular to the stiffeners are simply supported, the other two edges having any combination of conditions.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society 1963

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Hoppmann, W. H.Bending of Orthogonally Stiffened Plates. Journal App. Mech., Vol. 22, p. 267, 1955.Google Scholar
2.Hoppmann, W. H., Huffington, N. J. and Magness, L. S.A Study of Orthogonally Stiffened Plates. Journal App. Mech., Vol. 23, p. 343, 1956.CrossRefGoogle Scholar
3.Simon, G.Determination of Characteristic Frequencies of Rectangular Plates with Stiffeners Parallel to the Edges and Navier Type Boundary Conditions. Stahlbau., Vol. 27, p. 309, 1958.Google Scholar
4.Kirk, C. L.Vibration Characteristics of Stiffened Plates. Journal Mech. Eng. Sci., Vol. 2, p. 242, 1960.Google Scholar
5.Mahalingam, S.Vibration of Stiffened Rectangular Plates. Journal of the Royal Aeronautical Society, Vol. 67, p. 305, 1963.CrossRefGoogle Scholar
6.Warburton, G. B.The Vibration of Rectangular Plates. Proc. Inst. Mech. Eng., Vol. 168, p. 371, 1954.Google Scholar
7.Cox, H. L. and Benfield, W. A.Vibration of Uniform Square Plates Bounded by Flexible Beams. Journal Acoust. Soc. Amer., Vol. 31, p. 963, 1959.Google Scholar
8.Veletsos, A. S. and Newmark, N. M. Determination of the Natural Frequencies of Continuous Beams on Flexible Supports. Proc. Second U.S. Nat. Cong. App. Mech., p. 147, 1954.Google Scholar
9.Mahalingam, S.An Improvement of the Myklestad Method for Flexural Vibration Problems. J. Aero. Sci., Vol. 26, p. 46, 1959.Google Scholar
10.Myklestad, N. O.A New Method of Calculating the Natural Modes of Uncoupled Bending Vibration of Airplane Wings and Other Types of Beams. Journal Aero. Sci., Vol. 11, p. 153, 1944.Google Scholar
11.Veletsos, A. S. and Newmark, N. M.Natural Frequencies of Continuous Flexural Members. Trans. Amer. Soc. Civ. Eng., Vol. 122, p. 249, 1957.CrossRefGoogle Scholar
12.Thomson, W. T.Matrix Solution for the Vibration of Non-uniform Beams. Journal App. Mech., Vol. 17, p. 337, 1950.Google Scholar