Eigenvalue curve veering in stressed structures: An experimental study

Abstract

There have been extensive research works on the veering phenomenon in dynamic systems. As eigenvalues change under parametric variation, converging loci are commonly seen to veer away suddenly in a small region of the graph such that the modes swap trajectories. All of the modal properties are swapped in the process, leading to some curious behaviour in the transition zone. Theoretical studies of this behaviour have been reported for half a century but despite this heritage, explicit references to experimental results are scarce. In this paper detailed experimental and numerical investigations on veering are reported. The parameter varied is the internal pre-load of a redundant frame. An FE model is presented and stress stiffening approximations are employed to obtain a tangent stiffness for a nonlinear static solution, which is then used in a linear dynamic analysis. Experimental results are given and the behaviour is found to correspond well with the analytical results. In particular the mode shape variation is found to be consistent, and the implications of this finding with regard to modal correlation and model validation are noted. Analyses of the mode shapes in terms of eigenvector rotations are presented and are found to form a valuable tool for the interpretation of experimental results.