Structural Dynamic Analysis with Generalized Damping Models: Analysis

AppendixSymmetrizable Damped Systems

Theory of dynamics of multiple-degrees-of-freedom symmetric systems has been studied in this book so far. However, dynamical behavior of some systems encountered in practice cannot be expressed in terms of symmetric coefficient matrices or self-adjoint linear operators. Some examples are gyroscopic and circulatory systems [HUS 73], aircraft flutter [FAW 77b], ship motion in sea water [BIS 79], contact problems [SOO 83] and many actively controlled systems [CAU 93]. The aim of this appendix is to propose methods by which asymmetric dynamic systems can be transformed into symmetric systems. In this way, methods proposed in the book can, in turn, be applied to asymmetric systems as well.

Few authors have considered such general asymmetric dynamical systems. Fawzy and Bishop [FAW 76] presented several relationships satisfied by the eigenvectors and “eigenrows” of a damped asymmetric system and also presented a method to normalize them. Caughey and Ma [CAU 93] have derived conditions under which such systems can be diagonalized by a similarity transformation. In a subsequent chapter, Ma and Caughey [MA 95] utilized equivalence transformation to analyze asymmetric non-conservative systems and gave the condition under which they can be diagonalized. Adhikari [ADH 99a] proposed a method to obtain (complex) eigensolutions of general asymmetric non-conservative systems without converting the equations of motion into the first-order form.

The above-mentioned ...