A New Method for Finding Symmetric Form of Asymmetric Finite-Dimensional Dynamic Systems

A subclass of general lumped-parameter dynamic systems which can be transformed into an equivalent symmetric form is considered here. For the purpose of the present study, these systems are divided into two categories: those without velocity dependent forces (pseudo-conservative systems) and those with velocity dependent forces (pseudo-symmetric systems). For each category, the results on symmetrizability of matrices are used to develop an effective, systematic technique for computing the coordinate system in which the system is symmetric. The primary advantages of the technique presented in this study are twofold. First, it is computationally efficient and stable. Second, it can effectively handle systems with many degrees-of-freedom, unlike the trial and error approach suggested in previous studies.