Nature of coupling in non-conservative distributed parameter systems attached to external damping sources

Abstract

Non-conservative distributed parameter systems connected to external damping sources and possessing non-normal modes are analyzed in this work. The mathematical model of such systems is presented and real valued modal analysis is used to obtain the coupled modal equations of motion. A decoupling technique is developed using Fourier expansion, fictitious damping ratios, modal coupling parameters and pseudo forces. The method is applicable to all types of excitation. A normal mode criterion in the form of non-proportionality indices is also provided. The theoretical predictions are verified through application to a non-conservative Euler–Bernoulli beam with non-proportional damping configuration and various types of boundary conditions. Numerical examples emphasize the response errors associated with the proportional damping assumption and reveal the advantages of the proposed approach over the exact method.