The problem of wave propagation in an infinite, homogeneous, transversely isotropic polygonal cross-sectional cylinder is studied using Fourier expansion collocation method, within the framework of linearized, three dimensional theory of thermoelasticity. Three displacement potential functions are introduced, to uncouple the equations of motion and the heat conduction. The frequency equations are obtained for longitudinal and flexural (symmetric and antisymmetric) modes of vibration and are studied numerically for triangular, square, pentagonal and hexagonal cross-sectional Zinc cylinders. To study the convergence, the non-dimensional wave numbers are obtained by Fourier Expansion Collocation Method and Finite Element Method and they are compared. The computed non-dimensional wave numbers are presented in the form of dispersion curves.
Antia, H.M., 2000, Numerical Methods for Scientists and Engineers, Hindustan Book Agency, New Delhi.
2.
Berliner, M.J. and Solecki, R., 1996, "Wave propagation in fluid-loaded transversely isotropic cylinders. Part 1 analytical formulation, Part II, numerical results" Journal of Acoustical Society of America99, 1841-1853.
3.
Biot, M.A., 1956, "Thermoelasticity and irreversible thermodynamics," Journal of Applied Physics27(3), 240-253.
Chen, W.Q., Ying, J., and Yang, Q.D., 1998a, "Free vibrations of transversely isotropic cylinders and cylindrical shells," ASME Journal of Pressure Vessel Technology120(4), 321-324.
6.
Chen, W.Q., Ding, H., and Xu, R., 1998b, "On exact analysis of free vibrations of embedded transversely isotropic cylindrical shells," International Journal of Pressure Vessels and Piping75(13), 961-996.
7.
Chen, W.Q., Lim, C.W., and Ding, H.J., 2005, "Point temperature solution for a penny-shaped crack in an infinite transversely isotropic thermo-piezo-elastic medium," Engineering Analysis with Boundary Elements29, 524-532.
8.
Erbay, S. and Suhubi, E.S., 1986, "Longitudinal wave propagation in a generalized thermoelastic cylinder," Journal of Thermal Stresses9, 279-295.
9.
Green, A.E. and Naghdi, P.M.,. 1993, "Thermoelasticity without energy dissipation," Journal of Elasticity31,189- 208.
10.
Honarvar, F. and Sinclair, A.N., 1996, "Acoustic wave scattering from transversely isotropic cylinders," Journal of Acoustical Society of America100, 57-63.
11.
Honarvar, F., Enjilela, E., Sinclair, A.N., and Mirnezami, S.A., 2007, "Wave propagation in a transversely isotropic cylinders ," International Journal of Solid and Structure44, 5236-5246.
12.
Kardomateas, G.A., 1989, "Transient thermal stresses in cylindrically orthotropic composite tubes," Journal of Applied Mechanics56, 411-417.
13.
Kumar, A.B., 1989, "Thermoelastic waves from suddenly punched hole in stretched elastic plate," Indian Journal of Pure and Applied Math20(2), 181-188.
14.
Lin-xiang, W. and Melnik, R.V.N., 2006, "Differential-algebraic approach to coupled problems of dynamic thermoelasticity," Applied Mathematics and Mechanics27(9), 1185-1196.
15.
Mirsky, I., 1964, "Wave propagation in a transversely isotropic circular cylinders Part I: Theory; Part II: Numerical results," Journal of Acoustical Society of America37(6), 1016-1026.
16.
Nagaya, K., 1981, "Dispersion of elastic waves in bar with polygonal cross-section ," Journal of Acoustical Society of America70(3), 763-770.
17.
Pan, Y., Rossignol, C., and Audoin, B., 2004, "Acoustic waves generated by a laser point source in an isotropic cylinder", Journal of Acoustical Society of America116(2), 814-820.
18.
Sharma, J.N. and Sharma, P.K., 2002, "Free vibration analysis of homogeneous transversely isotropic thermoelastic cylindrical panel," Journal of Thermal Stresses25, 169-182.
19.
Singh, H. and Sharma, J.N., 1985, "Generalized thermoelastic waves in transversely isotropic media," Journal of Acoustical Society of America77(3), 1046-1053.
20.
Suhubi, E.S., 1964, "Longitudinal vibrations of a circular cylindrical coupled with a thermal field," Journal of the Mechanics and Physics of Solids12, 69-75.
21.
Yee, K.C. and Moon, T.J., 2002, "Plane thermal stress analysis of an orthotropic cylinder subjected to an arbitrary, transient, asymmetric temperature distribution ," Journal of Trans ASME69, 632-640.
22.
Venkatesan, M. and Ponnusamy, P., 2002, "Wave propagation in a solid cylinder of arbitrary cross-section immersed in a fluid," Journal of Acoustical Society of America112, 936-942.
23.
Venkatesan, M. and Ponnusamy, P., 2003, "Wave propagation in a solid cylinder of polygonal cross-section immersed in a fluid," Indian Journal of Pure and Applied Math34(9), 1381-1391.
24.
Youssef, H.M. and El-Bary, A.A., 2006, "Mathematical model for thermal shock problem of a generalized thermoelastic layered composite material with variable thermal conductivity ," Computational Methods in Science and Technology12(2), 165-171.
25.
Youssef, H.M. and Abbas, I.A., 2007, "Thermal shock problem of a generalized thermoelasticity of an infinitely long annular cylinder with variable thermal conductivity ," Computational Methods in Science and Technology13(2), 95-100.
