A study of bending waves in infinite and anisotropic plates

Ove Lindblom; Reinhold Näslund; Lars-Erik Persson; Karl-Evert Fällström

Applications of Mathematics (1997)

  • Volume: 42, Issue: 3, page 213-232
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Lindblom, Ove, et al. "A study of bending waves in infinite and anisotropic plates." Applications of Mathematics 42.3 (1997): 213-232. <http://eudml.org/doc/32977>.

@article{Lindblom1997,
abstract = {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.},
author = {Lindblom, Ove, Näslund, Reinhold, Persson, Lars-Erik, Fällström, Karl-Evert},
journal = {Applications of Mathematics},
keywords = {Kirchoff plate equation; bending waves; anisotropic plates; orthotropic plates; isotropic plates; the Fourier transform; Boussinesq formula; Kirchhoff plate equation; Fourier transform; Boussinesq formula},
language = {eng},
number = {3},
pages = {213-232},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A study of bending waves in infinite and anisotropic plates},
url = {http://eudml.org/doc/32977},
volume = {42},
year = {1997},
}

TY - JOUR
AU - Lindblom, Ove
AU - Näslund, Reinhold
AU - Persson, Lars-Erik
AU - Fällström, Karl-Evert
TI - A study of bending waves in infinite and anisotropic plates
JO - Applications of Mathematics
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 42
IS - 3
SP - 213
EP - 232
AB - 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.
LA - eng
KW - Kirchoff plate equation; bending waves; anisotropic plates; orthotropic plates; isotropic plates; the Fourier transform; Boussinesq formula; Kirchhoff plate equation; Fourier transform; Boussinesq formula
UR - http://eudml.org/doc/32977
ER -

References

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  10. 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. (1994) 
  11. Green’s method applied to the plate equation in mechanics, Comment. Math. Prace Mat 33 (1993), 119–133. (1993) 
  12. The Use of Integral Transforms, McGraw-Hill Company, Inc., New York, 1972. (1972) Zbl0237.44001
  13. The Symmetrical Vibrations of a Thin Elastic Plate, Proceedings of the Cambridge Philosophical Society, Volume 41, Cambridge University Press, 27–42, 1945. (1945) Zbl0063.07102MR0011882
  14. The Fourier Transform Solution of an Elastic Wave Equation, Proceedings of the Cambridge Philosophical Society, Volume 41, Cambridge University Press, 1945, pp. 239–243. (1945) Zbl0063.07103MR0013505
  15. Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, New Yersey, 1971. (1971) MR0304972
  16. The Theory of Functions, Second Edition, Oxford University Press, 1939. (1939) 

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