The decoupling of damped linear systems in oscillatory free vibration

The purpose of this paper is to extend classical modal analysis to decouple any viscously damped linear system in oscillatory free vibration. Based upon an exposition of how viscous damping causes phase drifts in the components of a linear system, the concept of non-classically damped modes of vibration is introduced. These damped modes are real and physically excitable. By synchronizing the phase angles in each damped mode, a time-varying transformation is constructed to decouple damped oscillatory free vibration. The decoupling procedure devised herein reduces to classical modal analysis for systems that are undamped or classically damped. This paper constitutes the first part of a solution to the “classical decoupling problem” of linear systems.