Asymptotic analysis of torsional and stretching modes of thin rods

H. Irago, N. Kerdid, J. M. Viaño
2000 Quarterly of Applied Mathematics  
In this article, we show that a class of high frequencies of the threedimensional linearized elasticity system in a thin rod and their associated eigenfunctions converge in a precise sense, as the area of the cross section of the rod goes to zero. The limit model is a coupled one-dimensional problem giving the classical equations for torsion and stretching modes in rods.
doi:10.1090/qam/1770651 fatcat:xz6fylifwveapiml2zjsshxxxq