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Some estimates on vibrations in thermoelasticity of dipolar bodies. (English) Zbl 1269.74096

Summary: We consider a right cylinder composed of a physically dipolar thermoelastic material for which one plane end is subjected to an excitation which is harmonic in time. By using a measure of Toupin type associated with the corresponding steady-state vibration and assuming that the exciting frequency is lower than a certain critical frequency, we obtain a spatial decay estimate, similar to that of Saint-Venant type.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74A35 Polar materials
74F05 Thermal effects in solid mechanics
35Q74 PDEs in connection with mechanics of deformable solids
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References:

[1] Fichera, G., Handbuch der Physik 2 (1972)
[2] Flavin, J.N., Journal of Elasticity 17 pp 249– (1987) · Zbl 0624.73012 · doi:10.1007/BF00049455
[3] Marin, M., Journal of Applied Mathematics (2007) · Zbl 1141.74007
[4] Marin, M., Nonlinear Analysis: RWA 10 pp 1572– · Zbl 1160.74002 · doi:10.1016/j.nonrwa.2008.02.001
[5] Toupin, R.A., Archive for Rational Mechanics and Analysis 18 pp 83– (1965) · Zbl 0203.26803 · doi:10.1007/BF00282253
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