A variational approach to vibrating frames

Abstract

This article deals with the use of calculus of variations, to derive the boundary and eigenvalue problems that describe the dynamical behaviour of frame structures with ends and intermediate points elastically restrained and with the determination of exact eigenfrequencies. It is the purpose of this article to present a rigorous procedure by introducing adequate functionals with a complete description of the corresponding domains. In each case, the stationary condition required by the Hamilton's principle is rigorously stated by defining the domain D of the action integral and the space Da of admissible directions. In addition, exact frequencies for the restrained frames with rotational and translational restraints at the ends and/or intermediate points are included.