Enhanced material damping through thermoelasticity
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In a seminal text Clarence Zener (1948) considered transverse vibrations of an isotropic, homogeneous, and thermoelastic beam. He observed that the tensile side of such a vibrating beam cools while the compressional side heats up resulting in irreversible heat transfer. This observation led him to predict the existence of thermoelastic damping which he modeled as a simple, three-parameter standard anelastic solid. During the ensuing half-century, the predictions of Zener's model have been shown to agree remarkable well with a wide variety of experimental results. Unfortunately, Zener's model cannot be easily extended to calculate damping in heterogeneous materials; therefore, in this paper we take a more fundamental approach. We take the Second Law of Thermodynamics as our starting point and calculate the thermoelastic damping from the entropy created by the irreversible heat transfer in the medium. As illustrative examples we solve two boundary value problems. First, the problem treated by Zener is revisited. It is shown that our exact solution is suprisingly close to Zener's standard anelastic model. Second, as a first step toward constructing a theory for thermoelastic damping in composite materials, we consider longitudinal vibrations of two rods in welded contact. We report an exact solution for the tehrmoelastic damping of an interface.
American Society of Mechanical Engineers, Aerospace Division (Publication) AD
author list (cited authors)
Kinra, V. K., & Milligan, K. B.
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