Structural dynamic analysis with generalized damping models. Analysis (Q2873693)

The author presents a systematic study on the analysis and identification of damped discrete linear dynamic systems. The intended readers of the present book are primarily senior undergraduate students, graduate students and practicing engineers working in the field of vibrations. The book is divided into 6 chapters and an appendix.NEWLINENEWLINE First, the idea of classical damping or proportional damping is critically reviewed, and a generalized proportional damping is introduced. Then the author derives stationary properties of proportional damping and non-proportional damping for single- and multiple-degree-of-freedom systems. The traditional state-space approach, well-known for viscously damped systems, is extended to non-viscously damped systems using a set of interval variables. Two physically realistic cases are presented: when all the damping coefficient matrices are of full rank, and when the damping coefficient matrices have rank deficiency.NEWLINENEWLINE In Chapter 5, the author suggests a numerical method based on the Neumann series expansion for the calculation of eigenvectors. The concept of Rayleigh quotients is proposed, and their stationary properties are investigated.NEWLINENEWLINE The last chapter is devoted to reduced computational methods for damped dynamic systems. The used technique enables one to approximately calculate the eigenvalues of non-viscously damped systems by simple post-processing of undamped eigenvalues. Representative numerical examples are given to verify the accuracy of the derived expressions.