Consider a cylinder made of a microstretch thermoelastic material for which one plane end is subjected to plane boundary data varying harmonically in time. On the lateral surface and other base, we have zero body force and heat supply. By using a Toupin type measure associated with the corresponding steady-state vibration, and by assuming that the angular frequency of oscillations is lower than a certain critical frequency, we show that the amplitude of the vibrations decays exponentially with the distance to the base. This decay estimate is similar to that of the Saint-Venant type.
Issue Section:
Technical Briefs
1.
Eringen
, A. C.
, 1972, “Theory of Micromorphic Materials With Memory
,” Int. J. Eng. Sci.
0020-7225, 10
, pp. 623
–641
.2.
Eringen
, A. C.
, 1990, “Theory of Thermo-Microstretch Elastic Solids
,” Int. J. Eng. Sci.
0020-7225, 28
, pp. 1291
–1301
.3.
Eringen
, A. C.
, 1999, Microcontinuum Field Theories
, Springer-Verlag
, New York
.4.
Flavin
, J. N.
, and Knops
, R. J.
, 1987, “Some Spatial Decay Estimates in Continuum Dynamics
,” J. Elast.
0374-3535, 17
, pp. 249
–264
.5.
Toupin
, R. A.
, 1965, “Saint-Venant’s Principle
,” Arch. Ration. Mech. Anal.
0003-9527, 18
, pp. 83
–96
.6.
Quintanilla
, R.
, 2008, “Polynomial and Exponential Spatial Decay Estimates in Elasticity
,” J. Elast.
0374-3535, 93
, pp. 279
–290
.7.
Marin
, M.
, 2007, “On the Nonlinear Theory of Micropolar Bodies With Voids
,” J. Appl. Math.
1110-757X, 2007
, pp. 1
–11
.8.
Marin
, M.
, 2009, “On the Minimum Principle for Dipolar Materials With Stretch
,” Nonlinear Anal.: Real World Appl.
1468-1218, 10
(3
), pp. 1572
–1578
.9.
Hlaváček
, I.
, and Necas
, J.
, 1970, “On Inequalities of Korn’s Type
,” Arch. Ration. Mech. Anal.
0003-9527, 36
, pp. 305
–311
.10.
Fichera
, G.
, 1972, “Existence Theorems in Elasticity
,” Handbuch der Physik
, Springer
, Berlin
.Copyright © 2010
by American Society of Mechanical Engineers
You do not currently have access to this content.
