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aThe University of Texas at Austin, Applied Research Laboratories, 10000 Burnet ... Keywords: acoustic metamaterial; homogenization; Willis-solid; bianisotropy.
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Journal of Thermal Stresses, 29: 467–483, 2006 Copyright # Taylor & Francis Group, LLC ISSN: 0149-5739 print/1521-074X online DOI: 10.1080/01495730500360609
HOMOGENIZATION OF A MICRO-PERIODIC HELIX WITH PARABOLIC OR HYPERBOLIC HEAT CONDUCTION J. M. Vivar-Perez, J. Bravo-Castillero, and R. Rodriguez-Ramos Facultad de Matematica y Computaci on, Universidad de La Habana, San Lazaro y L, Vedado, La Habana, Cuba
M. Ostoja-Starzewski Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA Based on a recent model for vibration of an elastic helix [6], a thermoelastic heterogeneous helix is studied by the asymptotic homogenization method. The objective of the study is the determination of the averaged equation of motion and of the effective coefficients of a onedimensional micro-periodic thermoelastic helix. The results are valid in the case of waves much longer than the length of the periodic unit cell, and for any finite number of phases for within that cell. Also perfect contact conditions between phases are considered. Generally, the constitutive coefficients are harmonic averages, while the mass density and polar moment of inertia are arithmetic averages. Keywords: Helix; Composite material; Homogenization; Generalized thermoelasticity
STATEMENT OF THE PROBLEM Let us consider a heterogeneous rod with a periodic structure. More precisely, it is a composite bar composed of two, or more, locally homogeneous materials distributed in periodic cells, and arranged sequentially as shown in Figure 1. The length of this periodic cell is assumed to be very small as compared with the unit length taken, and this is expressed by a parameter e
