Decay estimates for micropolar elastic cylinders

Abstract

This paper is concerned with the deformation of cylinders in the context of linear theory of micropolar elasticity. First we consider the equilibrium theory and study the decay and growth behaviour for the solutions measured by the cross-sectional work function. We use the method introduced by Flavin et al., Q. Appl. Math. 47, 325–350 (1989) to show that this measure either decays faster than a certain decreasing exponential function or grows faster than a growing exponential function. Then, we use the approach in the paper by Flavin and Knops, J. Elast. 17, 249–264 (1987), in order to establish a spatial decay estimate in the theory of steady vibrations.