Frequencies of Continuous Plates by Moment‐Ratio Method
Publication: Journal of Structural Engineering
Volume 109, Issue 12
Abstract
The moment‐ratio method developed is a numerical procedure to determine the natural frequencies of continuous orthotropic and isotropic plates. The basic concept employs dynamic flexibility functions at the panel joints. The moment‐ratio function of a panel may be obtained from the transfer of the preceding one. A fixed number of computational steps equal to the number of panels is required for each cycle. One of the natural frequencies will be obtained when the terminal moment‐ratio vanishes. A sufficient number of times with assumed varying frequencies will determine one of the natural frequencies to a degree of desired accuracy. Three numerical examples are included. Some of the numerical solutions are compared with existing data. Four types of boundary conditions of continuous plates—partial constraint, simple‐simple, simple‐clamp, and clamp‐clamp—are developed. An equivalent analysis of continuous orthotropic and isotropic plate systems is presented and their numerical frequencies are compared. Frequency clusters formed in uniform systems are introduced in the moment‐ratio method.
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References
1.
Dickinson, S. M., and Warburton, G. B., “Natural Frequencies of Plate Systems Using the Edge‐Effect Method,” Journal of Mechanical Engineering Science, Vol. 9, 1967, pp. 318–329.
2.
Dill, E. H., and Pister, K. S., “Vibration of Rectangular Plates and Plate Systems,” Proceedings of the Third U.S. National Congress of Applied Mechanics, 1958.
3.
Elishakoff, I., and Stenberg, A., “Eigenfrequencies of Continuous Plates with Arbitrary Number of Equal Spans,” Journal of Applied Mechanics, Transactions, ASME, Vol. 46, Sept., 1979, pp. 656–662.
4.
Gaskel, R. E., “On Moment Balancing in Structural Dynamics,” Quarterly of Applied Mathematics, Vol. 1, 1943.
5.
Gupta, G. S., “Natural Flexural Waves and the Normal Modes of Periodically‐Supported Beams and Plates,” Journal of Sound and Vibration, Vol. 13, No. 1, 1970, pp. 89–101.
6.
Hayashi, Y., and Kanai, T., “On Vibrations of Continuous Plate,” 15th Structures, Structural Dynamics and Material Conference, 1973, pp. 25–28 (Japanese).
7.
Kalmanok, A., Structural Mechanics in Plates, Moscow, 1950 (Russian).
8.
Kurata, M., “On Vibration of Continuous Rectangular Plates,” Proceedings of the First Japan National Congress for Applied Mechanics, 1951.
9.
Lin, Y. K., “Free Vibrations of Continuous Skin‐Stringer Panels,” ASME Journal of Applied Mechanics, Vol. 27, 1960, pp. 669–676.
10.
Lin, Y. K., Brown, I. D., and Deutschle, P. C., “Free Vibrations of a Finite Row of Continuous Skin‐Stringer Panels,” Journal of Sound and Vibration, Vol. 1, 1964, pp. 14–27.
11.
Lin, Y. K., and Donaldson, B. K., “A Brief Survey of Transfer Matrix Techniques with Special Reference to the Analysis of Aircraft Panels,” Journal of Sound and Vibration, Vol. 10, 1969, pp. 103–143.
12.
McDaniel, T. J., and Henderson, J. P., “Review of Transfer Matrix Vibration Analysis of Skin‐Stringer Structure, Part I,” The Shock and Vibration Digest, Vol. 6, 1974, pp. 13–19.
13.
Mercer, C. A., and Searey, C., “Prediction of Natural Frequencies and Normal Modes of Skin‐Stringer Panel Rows,” Journal of Sound and Vibration, Vol. 6, 1967, pp. 149–162.
14.
Moskalenko, V. N., “On the Vibrations of Multispan Plates,” Strength Analysis, Vol. 14, 1969, pp. 360–367 (Russian).
15.
Moskalenko, V. N., and Chien, De‐Lin, “On the Natural Vibrations of Multispan Plates,” Practical Mechanics, Vol. 1, No. 3, 1965, pp. 59–66 (Russian).
16.
Mukhopashyay, M. A., “A Semi‐Analytic Solution for Free Vibration of Rectangular Plates,” Journal of Sound and Vibration, Vol. 60, No. 1, Sept., 1978, pp. 71–85.
17.
Myklestad, N. O., “New Method of Calculating Natural Modes of Coupled Bending‐Torsion Vibration of Beams,” Transaction ASME, Vol. 67, pp. 61–67, 1945.
18.
Qin, B. S., “Calculation of Continuous Plates and Study on Their Properties Under the Harmonic Disturbing Force,” thesis presented to Tong‐Ji University, at Tong‐Ji, in 1965, in partial fulfillment of the requirements for Graduate Diploma, The People's Republic of China (Chinese).
19.
Sakata, T., “Eigenvalues of Orthotropic Continuous Plates with Two Opposite Sides Simply Supported,” Journal of Sound and Vibration, Vol. 47, No. 4, 1976.
20.
Solukin, N. S., Dynamic Computation of Structures of Factory Building, 1956 (Russian).
21.
Szilard, Rudolph, Theory and Analysis of Plates, Prentice‐Hall, New York, N.Y., 1959.
22.
Takahashi, K., and Chishaki, T., “Free Vibrations of a Rectangular Plate on Oblique Supports,” Journal of Sound and Vibration, Vol. 60, No. 2, Sept., 1978, pp. 299–304.
23.
Thomson, W. T., “Matrix Solution for the Vibration of Nonuniform Beams,” Journal of Applied Mechanics, Vol. 17, No. 3, pp. 337–339, 1950.
24.
Timoshenko, S. P., and Woinowsky‐Krieger, S., Theory of Plates and Shells, McGraw‐Hill, New York, N.Y., 1959.
25.
Ungar, E. E., “Free Oscillations of Edge‐Connected Simply Supported Plate Systems,” ASME Journal of Engineering for Industry, Vol. 83, 1961, pp. 434–440.
26.
Veletsos, A. S., and Newmark, N. M., “Natural Frequencies of Continuous Flexural Members,” Proceedings, ASCE, Paper No. 735, July, 1955, 620.6 a/mo3.
27.
Veletsos, A. S., and Newmark, N. M., “Determination of Natural Frequencies of Continuous Plates Hinged Along Two Opposite Edges,” Journal of Applied Mechanics, Vol. 23, 1956.
28.
Wu, C. L., and Chenng, Y. K., “Frequency Analysis of Rectangular Plates Continuous in One or Two Directions,” Journal of Earthquake Engineering and Structural Dynamics, Vol. 3, 1974, pp. 3–14.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 109 • Issue 12 • December 1983
Pages: 2905 - 2921
Copyright
Copyright © 1983 ASCE.
History
Published online: Dec 1, 1983
Published in print: Dec 1983
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