Inverse eigenvalue problem for mass–spring–inerter systems

Abstract

This paper has solved the inverse eigenvalue problem for a “fixed–free” mass-chain system with inerters. It is well known that for a spring–mass system wherein the adjacent masses are linked through a spring, the natural frequency assignment can be achieved by choosing appropriate masses and spring stiffnesses if and only if the given positive eigenvalues are distinct. However, when we involve inerters, multiple eigenvalues in the assignment are allowed. In fact, for a set of arbitrarily given positive real numbers, we derive a necessary and sufficient condition on the multiplicities of these numbers, which are assigned as the natural frequencies of the concerned mass–spring–inerter system.