Spatial behaviour in a Mindlin-type thermoelastic plate

D’Apice, Ciro; Chiriţă, Stan

doi:10.1090/qam/2019623

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
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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.

Peter Schiavone and R. J. Tait, Thermal effects in Mindlin-type plates, Quart. J. Mech. Appl. Math. 46 (1993), no. 1, 27–39. MR 1222379, DOI https://doi.org/10.1093/qjmam/46.1.27
Peter Schiavone and R. J. Tait, Steady time-harmonic oscillations in a linear thermoelastic plate model, Quart. Appl. Math. 53 (1995), no. 2, 215–223. MR 1330649, DOI https://doi.org/10.1090/qam/1330649
Cornelius O. Horgan, Recent developments concerning Saint-Venant’s principle: an update, AMR 42 (1989), no. 11, 295–303. MR 1021553, DOI https://doi.org/10.1115/1.3152414

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 (1993), no. 2, 191–196. MR 1216738, DOI https://doi.org/10.1007/BF00041853
Stan Chiriţă and Michele Ciarletta, Time-weighted surface power function method for the study of spatial behaviour in dynamics of continua, Eur. J. Mech. A Solids 18 (1999), no. 5, 915–933. MR 1723228, DOI https://doi.org/10.1016/S0997-7538%2899%2900121-7
R. Quintanilla, End effects in thermoelasticity, Math. Methods Appl. Sci. 24 (2001), no. 2, 93–102. MR 1808685, DOI https://doi.org/10.1002/1099-1476%2820010125%2924%3A2%3C93%3A%3AAID-MMA199%3E3.0.CO%3B2-N
C. O. Horgan, L. E. Payne, and L. T. Wheeler, Spatial decay estimates in transient heat conduction, Quart. Appl. Math. 42 (1984), no. 1, 119–127. MR 736512, DOI https://doi.org/10.1090/S0033-569X-1984-0736512-8
C. O. Horgan and R. Quintanilla, Spatial decay of transient end effects in functionally graded heat conducting materials, Quart. Appl. Math. 59 (2001), no. 3, 529–542. MR 1848533, DOI https://doi.org/10.1090/qam/1848533
Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219861

M. Abramowitz and I. A. Stegun (eds.), Handbook of mathematical functions, Dover, New York, 1965.