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Characterization of damped linear dynamical systems in free motion

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  • It is well known that the free motion of a single-degree-of-freedom damped linear dynamical system can be characterized as overdamped, underdamped, or critically damped. Using the methodology of phase synchronization, which transforms any system of linear second-order differential equations into independent second-order equations, this characterization of free motion is generalized to multi-degree-of-freedom damped linear systems. A real scalar function, termed the viscous damping function, is introduced as an extension of the classical damping ratio. It is demonstrated that the free motion of a multi-degree-of-freedom system is characterized by its viscous damping function, and sometimes the characterization may be conducted with ease by examining the extrema of the viscous damping function.
    Mathematics Subject Classification: Primary: 70J30; Secondary: 34A30.


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