Reconstruction of a mass-spring system from spectral data i: theory

Abstract

Ram and Caldwell [1] have recently devised an algorithm for the reconstruction of a system consisting of n masses vibrating in line and all connected by springs. The data needed for the reconstruction are the eigenvalues of the system, and those of the subsystems obtained by successively fixing 1,2,…,n−1 of the masses, starting from a free end. It is known that successive sets of eigenvalues must interlace, but a full set of sufficient conditions on the eigenvalues which will yield positive stiffnesses and masses is still not known. We provide such a set of conditions for the case n=3, and comment on the case n⩾ 4.

Keywords:

• Vibration
• inverse problems