The Inverse Problem for the String or Rod Clamped at Both Sides

Abstract

The infinitesimal free longitudinal or torsional vibrations of a thin straight rod, and the infinitesimal free transverse vibrations of a taut string are all governed by a Sturm-Liouville differential equation, and their discrete approximations by a second order difference scheme. The inverse procedure is presented for constructing the mass and stiffness parameters of the discrete model from a knowledge of the natural frequencies and the static displacement of the system.