A modified modal analysis method for damped multi-degree-of-freedom-systems in structural mechanics

摘要

A general method for the modal decomposition of the equations of motion of damped multi-degree-of-freedom-systems is presented. The first variant of the presented method in earlier publications of the author, including the complex right eigenvectors, is briefly reviewed first. The second presented variant is also based on the corresponding eigenvalue problem of the damped structure including the complex left and right eigenvectors. After initial partitioning of the equations of motion a real modal transformation matrix is built by a combination of two complex transformations. For the general case of damped structures with non-modal symmetric damping matrix a modal analysis can be performed in real arithmetic. Two numerical examples with 3 and 10 DOF's demonstrate the accuracy and the advantages of the presented modal solution method. (C) 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim