A Natural Modes Model and Modal Identities for Damped Linear Structures

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Abstract
A modal model is derived for a passive elastic structure with linear viscous damping, from a first-order state variable arrangement of the physical parameters model. The state variable form of the model is composed using the equations Kq˙ − Kq˙ = 0 and Mq¨ + Cq˙ + Kq = f. An attribute of the particular formulation is that it facilitates a straightforward derivation of mass-properties-related modal identities for the associated damped natural modes. Transfer functions and normalizations used in experimental modal parameter estimation are also given special attention.

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