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Kirchoff plate equation; bending waves; anisotropic plates; orthotropic plates; isotropic plates; the Fourier transform; Boussinesq formula
In this paper we present a unified approach to obtain integral representation formulas for describing the propagation of bending waves in infinite plates. The general anisotropic case is included and both new and well-known formulas are obtained in special cases (e.g. the classical Boussinesq formula). The formulas we have derived have been compared with experimental data and the coincidence is very good in all cases.
[1] A. Das, K. Roy: Note on the forced vibration of an orthotropic plate on an elastic foundation. Journal of Sound and Vibration 66(4) (1979), 521–525. DOI 10.1016/0022-460X(79)90696-5
[2] M. Engliš, J. Peetre: A Green’s function for the annulus. Research report 95/7002, Department of Mathematics, Lund University (ISRN LUTFD2/TFMA) (53 pages), submitted (1995). MR 1441874
[3] K.-E. Fällström: Material parameters and defects in anisotropic plates determined by holografic Interferometry. Ph.D. Thesis 1990: 86 D, Department of Physics, Luleå University of Technology, 1990.
[4] K.-E. Fällström, O. Lindblom: Material parameters in anisotropic plates determined by using transient bending waves. Research report. Luleå University of Technology (10 pages), submitted 1996.
[5] I.S. Gradshteyn, I.M. Ryzhik: Table of Integrals, Series and Products. Academic Press, 1965.
[6] S.G. Lekhnitskii: Anisotropic Plates, translated by S.W. Tsai and T. Cheron. Gordon and Breach Science Publishers, 1944.
[7] J. Malmquist, V. Stenström, S. Danielsson: Mathematical Analysis, III. Almqvist & Wiksell, 1954, pp. 584–594. (Swedish)
[8] L. Meirovitch: Analytical Methods in Vibration. The MacMillan Company, New York, 1967.
[9] S.V. More: The symmetrical free vibrations of a thin elastic plate with initial conditions as a generalized function. Indian J. Pure Appl. Math. 10(4) (1979), 431–436. MR 0527355
[10] Kenneth Olofsson: Pulsed holographic interferometry for the study of bending wave propagation in paper and in tubes. Ph.D. Thesis 1994:144 D, Department of Physics, Luleå University of Technology, 1994.
[11] L.-E. Persson, T. Strömberg: Green’s method applied to the plate equation in mechanics. Comment. Math. Prace Mat 33 (1993), 119–133.
[12] I.N. Sneddon: The Use of Integral Transforms. McGraw-Hill Company, Inc., New York, 1972. Zbl 0237.44001
[13] I.N. Sneddon: The Symmetrical Vibrations of a Thin Elastic Plate. Proceedings of the Cambridge Philosophical Society, Volume 41, Cambridge University Press, 27–42, 1945. MR 0011882 | Zbl 0063.07102
[14] I.N. Sneddon: The Fourier Transform Solution of an Elastic Wave Equation. Proceedings of the Cambridge Philosophical Society, Volume 41, Cambridge University Press, 1945, pp. 239–243. MR 0013505 | Zbl 0063.07103
[15] E.M. Stein, G. Weiss: Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press, New Yersey, 1971. MR 0304972
[16] E.C. Titchmarsch: The Theory of Functions, Second Edition. Oxford University Press, 1939.
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