Enhanced meta-modelling technique for analysis of mode crossing, mode veering and mode coalescence in structural dynamics

In this paper, an enhanced meta-modelling procedure for the approximation of structural eigenfrequencies and eigenvectors is introduced. The procedure allows for correct prediction of the modal parameters in case of mode crossing, veering, and coalescence phenomena that can be observed when variations of the structural parameters occur. The procedure overcomes the erroneous approximation of these phenomena which results from a direct approximation of the modal parameters. The methodology is based on the response surface approximation of the structural matrices and on the concept of modal reduction. A comparison with a direct response surface approximation of the eigenfrequencies shows a considerable improvement in the accuracy as it is presented for a finite element frame structure.