Homogenization of a micro-periodic helix with parabolic or hyperbolic heat conduction

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 one-dimensional 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.