Abstract:
This paper presents a new approach to the problem of coupled longitudinal
and transversal propagation of stress waves in an isotropic thick and
elastic rod, based on the Mindlin-Herrmann theory. The novelty is that, the
Hamilton vriational principle is used not only for derivation of the governing
equations and set of natural boundary conditions, but also for obtaining
the exact solution in terms Green functions directly from the Langrangian.
The success of this approach is based on the existence of multiple orthogonalities
of the eigenfuctions. The proposed method is much easier than the
standard approach of building Green functions. A numerical example illustrates
the method of finding eigenfrequencies and eigenfunctions for isotropic
Mindlin-Herrmann rod.
