Spatial behaviour in a Mindlin-type thermoelastic plate
Authors:
Ciro D’Apice and Stan Chiriţă
Journal:
Quart. Appl. Math. 61 (2003), 783-796
MSC:
Primary 74F05; Secondary 35B45, 35Q72, 74H40, 74K20
DOI:
https://doi.org/10.1090/qam/2019623
MathSciNet review:
MR2019623
Full-text PDF Free Access
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Abstract: Spatial behaviour is studied for the transient solutions in the bending of a Mindlin-type thermoelastic plate. Some appropriate time-weighted line-integral measures are associated with the transient solutions and the spatial estimates are established for these measures describing spatial behaviour results of the Saint-Venant and Phragmén-Lindelöf type. A complete description of the spatial behaviour is obtained by combining the spatial estimates with time-independent and time-dependent decay and growth rates. For a thermoelastic plate whose middle surface is like a semi-infinite strip, it is shown, by means of the maximum principle, that at infinity a sharper spatial decay holds and it is dominated by the thermal characteristics only. Uniqueness results are also established.
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M. Abramowitz and I. A. Stegun (eds.), Handbook of mathematical functions, Dover, New York, 1965.
P. Schiavone and R. J. Tait, Thermal effects in Mindlin-type plates, Quart. J. Mech. App. Math. 46, 27-39 (1993).
P. Schiavone and R. J. Tait, Steady time-harmonic oscillations in a linear thermoelastic plate model, Quart. Appl. Math. LIII, 215-223 (1995).
C. O. Horgan, Recent developments concerning Saint-Venant’s principle: an update, Applied Mechanics Reviews, 42, 295-303 (1989).
C. O. Horgan, Recent developments concerning Saint-Venant’s principle: a second update, Applied Mechanics Reviews, 48, S101-S111 (1996).
M. M. Mehrabadi, S. C. Cowin, and C. O. Horgan, Strain energy density bounds for linear anisotropic elastic materials, J. Elasticity, 30, 191-196 (1993).
S. Chiriţ[ill] and M. Ciarletta, Time-weighted surface power function method for the study of spatial behaviour in dynamics of continua, Eur. J. Mech. A/Solids 18, 915-933 (1999).
R. Quintanilla, End effects in thermoelasticity, Math. Methods Appl. Sci., 24, 93-102 (2001).
C. O. Horgan, L. E. Payne, and L. T. Wheeler, Spatial decay estimates in transient heat conduction, Quart. Appl. Math., 42, 119-127 (1984).
C. O. Horgan and R. Quintanilla, Spatial decay of transient end effects in functionally graded heat conducting materials, Quart. Appl. Math., 59, 529-542 (2001).
M. H. Protter and H. F. Weinberger, Maximum principles in differential equations, Prentice-Hall, New Jersey, 1967.
M. Abramowitz and I. A. Stegun (eds.), Handbook of mathematical functions, Dover, New York, 1965.
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© Copyright 2003
American Mathematical Society