Efficient methods for determining modal parameters of dynamic structures with large modifications

Abstract

The paper presents efficient methods for determining the modified modal parameters (natural frequencies and mode shapes) in a structural dynamic modification analysis when structural modifications are relatively large. Based on the developed theory that can provide an exact relationship between the modifications of structural parameters (stiffness and mass) and the associated modal parameters, an efficient iterative computational procedure is proposed for determining the modified eigenvalues and the corresponding eigenvectors for complex structural systems. A high order approximation approach is further presented from the exact relationship and compared with the existing first-order approximation approach and the proposed iterative procedure. From the results for the given numerical example, it is shown that even in the cases with a large modification of structural parameters the proposed iterative procedure can provide exact predictions of the modified modal parameters after only a few iterations, and the high order approximation approach can give excellent estimates. The computation of the modified modal parameters does not require the knowledge of the original or modified structural parameters, and only a limited knowledge of the original modal data may be sufficient in a dynamic reanalysis for complex structures.