Shape of dispersion curves in the Rayleigh--Lamb spectrum

• Autorzy: Ahmad F.
• Języki publikacji: EN

Abstrakty

EN

The following features of the symmetric Lamb modes in an elastic waveguide are well known: 1. There exists no mode with phase speed less than cR. 2. There is only one mode whose speed asymptotically approaches cR. 3. A horizontal line above c = cT (including the line c = cL) cannot be an asymptote to any of the modes. 4. Phase speed of all modes, except the lowest mode, approaches cT as the frequency becomes very large. The above features characterize the spectrum which is obtained numerically or experimentally but are not fully understood analytically. We analyze the Rayleigh-Lamb equation and provide analytical explanation for the above features.

Słowa kluczowe

EN

dispersion curve; Rayleigh-Lamb spectrum; analytical solution

PL

krzywa rozproszenia; widmo Rayleigh-Lamb'a

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2004
• Tom: Vol. 56, nr 2
• Strony: 157--165
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Ahmad F.

• Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 Saudi Arabia,

Bibliografia

• 1. J. D. AcHENBAcH, Wave propagation in elastic solids, North-Holland, Amsterdam 1980.
• 2. Lord RAYLEIGH,O n the /ree vibrations oj an infinite plate oj homogeneousis otropic elastic matter, Proc. London Math. Soc., 20, 225-235, 1889.
• 3. H. LAMB, On the flexure of an elastic plate, Proc. London Math. Soc., 21, 1889, 70-90.
• 4. R. D. MINDLIN, Waves and vibrations in isotropic elastic plates, [in:) First Symposium on Structural Mechanics, 1958, J. N. GOODIER and N. J. HOFF [Eds.), 199-232, Pergamon, Oxford 1960.
• 5. H. UBERALL, Surface waves in acoustics, W. P. MASON and R. N. TRURSTON [Eds.), Physical Acoustics, 10, 1-60, Academic Press, New York 1973.
• 6. B. A. AULD, Acoustic fields and waves in solida, 2, Krieger, 1990.
• 7. J. L. ROSE, Ultrasonic waves in solid media, Cambridge University Press, 1999.
• 8. F. ARMAD, A simple formula for the Lamb modes in a plate, J. Acoust Soc. Am. 111, 1974-75,2002.
• 9. F. ARMAD, A simple formula for the longitudinal modes in a cylinder, J. Acoust. Soc. Am., 115,475-477,2004 (in press).