On Symmetrizable Systems of Second Kind

Abstract

We discuss under what conditions multiple-parameter asymmetric linear dynamical systems can be transformed into equivalent symmetric systems by nonsingular linear transformations. So far, in structural dynamics literature this problem has been addressed in the context of the original work by Taussky. Taussky’s approach of symmetrization was based on similarity transformation. In this paper an approach is proposed to transform asymmetric systems into symmetric systems by equivalence transformation. We call Taussky’s approach of symmetrization by similarity transformation “first kind” and proposed approach by equivalence transformation “second kind.” Since equivalence transformations are most general nonsingular linear transformations, conditions of symmetrizability obtained here are more “liberal” than the first kind and numerical calculations also become more straightforward. Several examples are provided to illustrate the new approach. [S0021-8936(00)00504-3]