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Research Papers

Extensional and Transversal Wave Motion in Transversely Isotropic Thermoelastic Plates by Using Asymptotic Method

[+] Author and Article Information
J. N. Sharma, P. K. Sharma

S. K. Rana

Department of Mathematics,  National Institute of Technology, Hamirpur 177005, Indiasanjeevrananit@gmail.com

J. Appl. Mech 78(6), 061022 (Sep 30, 2011) (11 pages) doi:10.1115/1.4003721 History: Received April 01, 2010; Revised November 19, 2010; Accepted February 28, 2011; Published September 30, 2011; Online September 30, 2011

The present investigation is concerned with the study of extensional and transversal wave motions in an infinite homogenous transversely isotropic, thermoelastic plate by using asymptotic method in the context of coupled thermoelasticity, Lord and Shulman (1967, “The Generalized Dynamical Theory of Thermoelasticity,” J. Mech. Phys. Solids, 15 , pp. 299–309), and Green and Lindsay (1972, “Thermoelasticity,” J. Elast., 2 , pp. 1–7) theories of generalized thermoelasticity. The governing equations for extensional, transversal, and flexural motions have been derived from the system of three-dimensional dynamical equations of linear thermoelasticity. The asymptotic operator plate model for extensional motion in a homogeneous transversely isotropic thermoelastic plate leads to sixth degree polynomial secular equation that governs frequency and phase velocity of various possible modes of wave propagation at all wavelengths. It is shown that the purely transverse motion (SH mode), which is not affected by thermal variations, gets decoupled from rest of the motion. The Rayleigh–Lamb frequency equation for the plate is expanded in power series in order to obtain polynomial frequency equation and velocity dispersion relations. Their validation has been established with that of asymptotic method. The special cases of short and long wavelength waves are also discussed. The expressions for group velocity of extensional and transversal modes have been derived. Finally, the numerical solution is carried out for homogeneous transversely isotropic plate of single crystal of zinc material. The dispersion curves of phase velocity and attenuation coefficient are presented graphically.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Phase velocity of extensional modes versus angle of incidence in CT plate for Rh=2

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Figure 2

Phase velocity of extensional modes versus angle of incidence in CT plate theory (Rayleigh–Lamb equation) for Rh=2

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Figure 3

Phase velocity of extensional modes versus wave number for CT plate for α=75 deg

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Figure 4

Phase velocity of extensional modes versus wave number in CT plate (Rayleigh–Lamb equation) α=75 deg

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Figure 5

Attenuation coefficient of extensional modes versus angle of in CT plate for Rh=2

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Figure 6

Attenuation coefficient of extensional modes versus wave number (Rh) in CT plate for α=75 deg

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Figure 7

Normalized phase velocity (V1) and attenuation coefficient (Q1) of extensional modes versus wave number in thermoelastic plate α=75 deg

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Figure 8

Normalized phase velocity (V2) and attenuation coefficient (Q2) of extensional modes versus wave number in thermoelastic plate for α=75 deg

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Figure 9

Normalized phase velocity (V3) and attenuation coefficient (Q3) of extensional modes versus wave number in thermoelastic plate α=75 deg

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Figure 10

Normalized phase velocity (V4) and attenuation coefficient (Q4) of extensional motion versus wave number in thermoelastic plate for α=75 deg

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Figure 11

Normalized phase velocity (V5) and attenuation coefficient (Q5) of extensional motion versus wave number in thermoelastic plate for α=75 deg

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Figure 12

Variations of phase velocity (V6) and attenuation coefficient (Q6) of extensional modes versus wave number in thermoelastic plate for α=75 deg

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