Second-law analysis of thermoelastic damping II. A laminated beam and a spherical inclusion
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In a classic paper Clarence Zener (1938) considered transverse vibrations of an isotropic, homogenous, 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. Passive damping is a critically important property from the viewpoint of vibration suppression in large, flexible space structures, and metal-matrix composites are materials of choice for these structures. Unfortunately, Zener's model cannot be extended to calculate damping in heterogeneous materials; therefore, in this paper a more fundamental approach is taken. The Second Law of Thermodynamics is taken as the starting point, and the thermoelastic damping is calculated from the entropy created by the irreversible heat transfer in the medium. As a first step toward constructing a general theory for thermoelastic damping in composite materials, we solve three problems: a three-layer beam subjected to uniaxial tension and pure flexure, and a spherical inclusion in an unbounded matrix subjected to a far field hydrostatic stress.
