On the strength of mechanical and thermal damping in linear materials
Authors:
J. Bielak and R. C. MacCamy
Journal:
Quart. Appl. Math. 47 (1989), 555-570
MSC:
Primary 73F05; Secondary 73U05
DOI:
https://doi.org/10.1090/qam/1012279
MathSciNet review:
MR1012279
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Abstract: This paper gives a criterion for distinguishing between various types of linear models for elastic and thermoelastic behavior. The models are all dissipative and the steady-state periodic limit for periodic input can be defined. Associated with this limit is a scalar function of frequency which could be determined experimentally. Its behavior for large frequency determines the strength of the damping. Both fibers and one-dimensional bars are considered. The models include Kelvin—Voigt materials, viscoelastic models with regular and singular kernels as well as standard thermoelasticity. It is found that strength of damping increases the order of singularity in the viscoelastic models. Thermoelastic damping is shown to be weak and to be of the same order as for elastic models with smooth kernels.
C. W. Bert, Material damping, J. Sound and Vibration 29, 129–153 (1973)
M. A. Boit, Linear thermodynamics and the mechanics of solids, Proc. Third U.S. National Congress on Applied Mechanics (1958), pp. 1–18
- U Jin Choi and R. C. MacCamy, Fractional order Volterra equations with applications to elasticity, J. Math. Anal. Appl. 139 (1989), no. 2, 448–464. MR 996970, DOI https://doi.org/10.1016/0022-247X%2889%2990120-0
- Bernard D. Coleman, Thermodynamics of materials with memory, Arch. Rational Mech. Anal. 17 (1964), 1–46. MR 171419, DOI https://doi.org/10.1007/BF00283864
- W. J. Hrusa and M. Renardy, On wave propagation in linear viscoelasticity, Quart. Appl. Math. 43 (1985), no. 2, 237–254. MR 793532, DOI https://doi.org/10.1090/S0033-569X-1985-0793532-0
- R. C. MacCamy and J. S. W. Wong, Stability theorems for some functional equations, Trans. Amer. Math. Soc. 164 (1972), 1–37. MR 293355, DOI https://doi.org/10.1090/S0002-9947-1972-0293355-X
- M. Renardy, Some remarks on the propagation and nonpropagation of discontinuities in linearly viscoelastic liquids, Rheol. Acta 21 (1982), no. 3, 251–254. MR 669374, DOI https://doi.org/10.1007/BF01515713
C. W. Bert, Material damping, J. Sound and Vibration 29, 129–153 (1973)
M. A. Boit, Linear thermodynamics and the mechanics of solids, Proc. Third U.S. National Congress on Applied Mechanics (1958), pp. 1–18
U. J. Choi and R. C. MacCamy, A fractional order Volterra equation with applications to elasticity, J. Math. Anal. Appl. 132, 448–464 (1989)
B. D. Coleman, Thermodynamics of materials with memory, Archive for Rational Mechanics and Analysis, Vol. 17, (1964), pp. 1–46
W. J. Hrusa and M. Renardy, On wave propagation in linear viscoelasticity, Quart. Appl. Math. 43, 237–253 (1985)
R. C. MacCamy and J. S. W. Wong, Stability theorems for some functional equations, Trans. Amer. Math. Soc. 164, 1–37 (1972)
M. Renardy, Some remarks on the propagation and non-propagation of discontinuities in linearly viscoelastic liquids, Rheological Acta. 21, 251–254 (1982)
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Article copyright:
© Copyright 1989
American Mathematical Society