On the Frequency Equations of Combined Systems

Abstract

Summary: Two primary systems are considered: An \(n\)-mass oscillator and a one-dimensional continuous structure the displacements of which are discretized by its first \(n\) eigenfunctions. If to each of these systems the same spring-mass system is attached for example at their free ends, it may be expected intuitively that the frequency equations of the resulting combined systems with \(n + 1\) degrees of freedom reveal similar forms. The aim of this communication is to explore the correspondences between these two equations.