Free viscously damped vibrations of linear discrete systems are studied. The amount of damping varies among the various elements of the system resulting in several critical damping possibilities. A general method is developed for determining the “critical damping surfaces” of a system. These surfaces represent the loci of combinations of damping values corresponding to critically damped motions, and thus separate regions of partial or complete underdamping from those of overdamping. The dimension of a critical damping surface is equal to the number of independent amounts of damping present in the system. Three examples presented in detail illustrate the proposed technique and some of the important characteristics of critical damping surfaces.

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