Steady time-harmonic oscillations in a linear thermoelastic plate model
Authors:
Peter Schiavone and R. J. Tait
Journal:
Quart. Appl. Math. 53 (1995), 215-223
MSC:
Primary 35Q72; Secondary 73B30, 73D30, 73K10
DOI:
https://doi.org/10.1090/qam/1330649
MathSciNet review:
MR1330649
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Abstract: We examine the bending of a Mindlin-type thermoelastic plate when the source terms are time-harmonic with angular frequency $\omega$, and sufficient time has elapsed for the system to have reached a steady-state. We show that in an infinite plate the solution can be represented as the sum of five waves all but one of which exhibit damping. By formulating appropriate radiation conditions we prove uniqueness results for exterior boundary value problems subject to certain regularity assumptions and a condition on the angular frequency of oscillation.
A. C. Eringen and E. S. Suhubi, Elastodynamics, Volume II, Academic Press, New York, 1975
J. A. Hudson, The Excitation and Propagation of Elastic Waves, Cambridge University Press, Cambridge, 1980
D. Colton and R. Kress, Intregral Equation Methods in Scattering Theory, Wiley, New York, 1983
P. Schiavone and R. J. Tait, Thermal effects in Mindlin-type plates, Quart. J. Mech. Appl. Math. 46, 27–39 (1993)
V. D. Kupradze, T. G. Gegelia, M. O. Basheleǐshvili, and T. V. Burchuladze, Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity, North-Holland Publ. Co., Amsterdam, 1979
C. Constanda, A Mathematical Analysis of Bending of Plates with Transverse Shear Deformation, Pitman Research Notes in Mathematics Series, No. 215, 1990
C. Constanda and P. Schiavone, Flexural waves in Mindlin-type plates, ZAMM 74, 492–493 (1994)
P. Schiavone and C. Constanda, Oscillation problems in thin plates with transverse shear deformation, SIAM J. Appl. Math. 53, 1253–1263 (1993)
A. C. Eringen and E. S. Suhubi, Elastodynamics, Volume II, Academic Press, New York, 1975
J. A. Hudson, The Excitation and Propagation of Elastic Waves, Cambridge University Press, Cambridge, 1980
D. Colton and R. Kress, Intregral Equation Methods in Scattering Theory, Wiley, New York, 1983
P. Schiavone and R. J. Tait, Thermal effects in Mindlin-type plates, Quart. J. Mech. Appl. Math. 46, 27–39 (1993)
V. D. Kupradze, T. G. Gegelia, M. O. Basheleǐshvili, and T. V. Burchuladze, Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity, North-Holland Publ. Co., Amsterdam, 1979
C. Constanda, A Mathematical Analysis of Bending of Plates with Transverse Shear Deformation, Pitman Research Notes in Mathematics Series, No. 215, 1990
C. Constanda and P. Schiavone, Flexural waves in Mindlin-type plates, ZAMM 74, 492–493 (1994)
P. Schiavone and C. Constanda, Oscillation problems in thin plates with transverse shear deformation, SIAM J. Appl. Math. 53, 1253–1263 (1993)
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Article copyright:
© Copyright 1995
American Mathematical Society
