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Structural Dynamic Analysis with Generalized Damping Models: Identification by Sondipon Adhikari

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Chapter 2

Identification of Viscous Damping

Modal analysis of generaly damped linear systems has been discussed in detail so far. The results based on these studies give a firm basis for further analysis, to use the details of the measured vibration data to learn more about the underlying damping mechanisms. It has been shown that non-viscously damped systems have two types of modes: (1) elastic modes and (2) non-viscous modes. The elastic modes correspond to the “modes of vibration” of a linear system. The non-viscous modes occur due to the non-viscous damping mechanism and they are not oscillatory in nature. For an underdamped system, that is a system whose modes are all vibrating, the elastic modes are complex (appear in complex conjugate pairs) and non-viscous modes are real. For N-degrees-of-freedom non-viscously damped systems, there are exactly N pairs of elastic modes. The number of non-viscous modes depends on the nature of the damping mechanisms. Conventional viscously damped systems are special cases of non-viscously damped systems when the damping kernel functions have no “memory”. Modes of viscously damped systems consist of only (complex) elastic modes as non-viscous modes do not appear in such systems. Elastic modes can be real only if the damping is proportional, that is only if Caughey and O’Kelly’s condition [CAU 65] given in theorem 2.1 of [ADH 14] is satisfied.

While the previous chapters give insights into the dynamics of damped systems, we have not discussed ...

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