Mathematical justification of stretching and torsional vibration models for elastic rods

摘要

Our goal in this work is to derive from the three-dimensional elasticity and using the asymptotic analysis, the one-dimensional evolution models for the stretching and the torsion of linearly elastic rods. More precisely, starting with the three-dimensional scaled dynamical problem and assuming the specific mass independent of the diameter ε of the transversal section of the rod, we obtain the classical stretching and torsional models in the zeroth and second-order terms of an asymptotic expansion of the (scaled) three- dimensional solution in powers of ε (small parameter).