Explicit Construction of Rods and Beams with Given Natural Frequencies

In this paper we present a new method for constructing one-dimensional vibrating systems having prescribed values of the first N natural frequencies, under a given set of boundary conditions. In the case of axially vibrating rods, the analysis is based on the determination of the so-called quasi-isospectral rods, that is rods which have the same spectrum as a given rod, with the exception of a single eigenvalue which is free to move in a prescribed interval. The reconstruction procedure needs the specification of an initial rod whose eigenvalues must be close to the assigned eigenvalues. The rods and their normal modes can be constructed explicitly by means of closed-form expressions. The results can be extended to strings and to some special classes of beams in bending vibration. © The Society for Experimental Mechanics 2014.