Interaction and multiscale mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Wave propagation in a generalized thermo elastic plate embedded in elastic medium

  • Ponnusamy, P. (Department of Mathematics, Government Arts College (Autonomous)) ;
  • Selvamani, R. (Department of Mathematics, Karunya University)
  • Received : 2012.01.30
  • Accepted : 2012.02.08
  • Published : 2012.03.25
⟨ Previous Next ⟩

Abstract

In this paper, the wave propagation in a generalized thermo elastic plate embedded in an elastic medium (Winkler model) is studied based on the Lord-Schulman (LS) and Green-Lindsay (GL) generalized two dimensional theory of thermo elasticity. Two displacement potential functions are introduced to uncouple the equations of motion. The frequency equations that include the interaction between the plate and foundation are obtained by the traction free boundary conditions using the Bessel function solutions. The numerical calculations are carried out for the material Zinc and the computed non-dimensional frequency and attenuation coefficient are plotted as the dispersion curves for the plate with thermally insulated and isothermal boundaries. The wave characteristics are found to be more stable and realistic in the presence of thermal relaxation times and the foundation parameter. A comparison of the results for the case with no thermal effects shows well agreement with those by the membrane theory.

Keywords

References

  1. Ashida, F. and Tauchert, T.R. (2001), "A general plane-stress solution in cylindrical coordinates for a piezoelectric plate", Int. J. Solids Struct., 38(28-29), 4969-4985. https://doi.org/10.1016/S0020-7683(00)00321-8
  2. Ashida, F. (2003), "Thermally-induced wave propagation in piezoelectric plate", Acta. Mech., 161(1-2), 1-16. https://doi.org/10.1007/s00707-002-0986-x
  3. Benhard, K., Howard, A.L. and Waldemar, V. (1999), "Buckling eigen values for a clamped plate embedded in an elastic medium and related questions", SIAM J. Math. Anal., 24(2), 327-340.
  4. Chandrasekharaiah, D.S. (1986), "Thermo elasticity with second sound - a review", Appl. Mech. Rev., 39(3), 355-376. https://doi.org/10.1115/1.3143705
  5. Dhaliwal, R.S. and Sherief, H.H. (1980), "Generalized thermo elasticity for anisotropic media", Appl. Math. Model, 8(1), 1-8.
  6. Erbay, E.S. and Suhubi, E.S. (1986), "Longitudinal wave propagation thermo elastic cylinder", J. Thermal Stresses, 9, 279-295. https://doi.org/10.1080/01495738608961904
  7. Gaikwad, M.K. and Desmukh, K.C. (2005), "Thermal deflection of an inverse thermo elastic problem in a thin isotropic circular plate", Appl. Math. Model, 29(9), 797-804. https://doi.org/10.1016/j.apm.2004.10.012
  8. Green, A.E. and Lindsay K.A. (1972), "Thermo elasticity", J. Elasticity, 2(1), 1-7. https://doi.org/10.1007/BF00045689
  9. Green, A.E. and Laws, N. (1972), "On the entropy production inequality", Arch. Ration. Mech. An., 45(1), 47-53.
  10. Heyliger, P.R. and Ramirez, G. (2000), "Free vibration of laminated circular piezoelectric plates and disc", J. Sound Vib., 229(4), 935-956. https://doi.org/10.1006/jsvi.1999.2520
  11. Kamal, K. and Duruvasula, S. (1983), "Bending of circular plate on elastic foundation", J. Eng. Mech.-ASCE, 109(5), 1293-1298. https://doi.org/10.1061/(ASCE)0733-9399(1983)109:5(1293)
  12. Lessia, A.W. (1981), "Plate vibration research: complicating effects", Shock. Vib., 13(10), 19-36.
  13. Lord, H.W. and Shulman, V. (1967), "A generalized dynamical theory of thermo elasticity", J. Mech. Phys. Solids, 15(5), 299-309. https://doi.org/10.1016/0022-5096(67)90024-5
  14. Paliwal, D.N., Pandey, R.K. and Nath, T. (1996) "Free vibrations of circular cylindrical shell on winkler and pasternak foundations", Int. J. Pres. Ves. Pip., 69(1), 79-89. https://doi.org/10.1016/0308-0161(95)00010-0
  15. Ponnusamy, P. (2007), "Wave propagations in a generalized thermo elastic solid cylinder of arbitrary cross section", Int. J. Solids Struct., 44(16), 5336-5348. https://doi.org/10.1016/j.ijsolstr.2007.01.003
  16. Ponnusamy, P. and Selvamani, R. (2011), "Wave propagation in a homogeneous isotropic thermo elastic cylindrical panel embedded on elastic medium", Int. J. Appl. Math. Mech., 7(19), 83-96.
  17. Selvadurai, A.P.S. (1979), "Elastic analysis of soil foundation interaction", New York, Elsevier Scientific Publishing Co.
  18. Sharma, J.N. and Pathania, V. (2005), "Generalized thermo elastic wave propagation in circumferential direction of transversely isotropic cylindrical curved plate", J. Sound Vib., 281(3-5), 1117-1131. https://doi.org/10.1016/j.jsv.2004.02.010
  19. Sharma, J.N. and Kaur, D. (2010), "Modeling of circumferential waves in cylindrical thermo elastic plates with voids", Appl. Math. Model, 34(2), 254-265. https://doi.org/10.1016/j.apm.2009.04.003
  20. Suhubi, E.S. (1975), "Thermo elastic solids in Eringen, AC (ed), continuum physics", Vol. II, Chapter 2. New York, Academic.
  21. Tso, Y.K. and Hansen, C.H. (1995), "Wave propagation through cylinder/plate junctions", J. Sound Vib. 186(3) 447-461. https://doi.org/10.1006/jsvi.1995.0460
  22. Wang, C.M. (2005), "Fundamental frequencies of a circular plate supported by a partial elastic foundation", J. Sound Vib., 285(4-5), 1203-1209. https://doi.org/10.1016/j.jsv.2004.11.018

Cited by

  1. Edge wave propagation in an Electro-Magneto-Thermoelastic homogeneous plate subjected to stress vol.53, pp.6, 2015, https://doi.org/10.12989/sem.2015.53.6.1201
  2. Buckling and vibration of laminated composite circular plate on winkler-type foundation vol.17, pp.1, 2014, https://doi.org/10.12989/scs.2014.17.1.001
  3. Exact solution for transverse bending analysis of embedded laminated Mindlin plate vol.49, pp.5, 2014, https://doi.org/10.12989/sem.2014.49.5.661
  4. Influence of impulsive line source and non-homogeneity on the propagation of SH-wave in an isotropic medium vol.6, pp.3, 2013, https://doi.org/10.12989/imm.2013.6.3.287
  5. Wave propagation in a generalized thermo elastic circular plate immersed in fluid vol.46, pp.6, 2013, https://doi.org/10.12989/sem.2013.46.6.827
  6. Wave propagation in a generalized thermoelastic plate using eigenvalue approach vol.39, pp.11, 2016, https://doi.org/10.1080/01495739.2016.1218229
  7. Nonlinear bending behavior of orthotropic Mindlin plate resting on orthotropic Pasternak foundation using GDQM vol.78, pp.3, 2014, https://doi.org/10.1007/s11071-014-1545-4
  8. Dispersion of elastic waves in a layer interacting with a Winkler foundation vol.144, pp.5, 2018, https://doi.org/10.1121/1.5079640
  9. Static response of 2-D functionally graded circular plate with gradient thickness and elastic foundations to compound loads vol.44, pp.2, 2012, https://doi.org/10.12989/sem.2012.44.2.139
  10. Analysis of elastic foundation plates with internal and perimetric stiffening beams on elastic foundations by using Finite Differences Method vol.45, pp.2, 2012, https://doi.org/10.12989/sem.2013.45.2.169
  11. Theoretical analysis of transient wave propagation in the band gap of phononic system vol.6, pp.1, 2013, https://doi.org/10.12989/imm.2013.6.1.015
  12. Study of viscoelastic model for harmonic waves in non-homogeneous viscoelastic filaments vol.6, pp.1, 2012, https://doi.org/10.12989/imm.2013.6.1.031