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Published in:
2021 | OriginalPaper | Chapter
2. Phase Synchronization and the Physics of Damping
Authors : Rubens Gonçalves Salsa Junior, Fai Ma
Published in: Advances in the Theory of System Decoupling
Publisher: Springer International Publishing
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Abstract
A classically damped linear system possesses classical normal modes, which constitute a linear coordinate transformation that decouples the undamped system. This process of decoupling the equation of motion of a dynamical system is the time-honored procedure termed modal analysis. In general, damping is not classical and thus passive linear systems cannot be decoupled by modal analysis. This chapter shows how classical modal analysis can be extended to decouple damped linear systems in configuration space through a procedure called phase synchronization. Similar to modal analysis, decoupling by phase synchronization possesses ample physical insight based upon a consideration of the physics of damping. In this regard, phase angles are shifted in each non-classically damped mode of vibration so as to transform it into a classical mode. Eleven illustrative examples are provided.