The purpose of this paper is to extend classical modal analysis to decouple all damped linear systems in oscillatory free vibration. Based upon the solution of the quadratic eigenvalue problem associated with the damped system, a process of phase synchronization is developed. This process generates a real time-shifting transformation that decouples any damped system in the configuration space. The decoupling procedure reduces to classical modal analysis for systems that are undamped or classically damped.
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