Structural Dynamics with Coincident Eigenvalues: Modelling and Testing

Abstract

Theory of curve crossing and curve veering phenomena is well known in structural dynamics, but only few papers have used test bench to demonstrate and validate this eigenvalues behaviour. The aim of this paper is to present a theoretical and experimental analysis on a nonsymmetric experimental structure with eigenvalues curve veering and crossing phenomena. Starting from literature examples, detailed numerical models on lumped parameters systems and continuous systems with coincident and/or close eigenvalues are examined in order to developed a numerical FE model suitable to describe a tunable and simple test rig with coincident eigenvalues and curve veering phenomena without symmetric properties or completely uncoupled dynamic systems. The test bench is made of simple beams and masses properly linked together. The angle of an intermediate beam is used as tunable physical parameter to vary the eigenvalues of the system and to couple two bending modes or bending and torsional modes. Numerical and experimental results are compared, and sensitivity of mode shapes to variation of system parameters is discussed.