Realization of mechanical systems from second-order models

Congruent coordinate transformations are used to convert second-order models to a form in which the mass, damping, and stiffness matrices can be interpreted as a passive mechanical system. For those systems which can be constructed from interconnected mass, stiffness, and damping elements, it is shown that the input–output preserving transformations can be parametrized by an orthogonal matrix whose dimension corresponds to the number of internal masses—those masses at which an input is not applied nor an output measured. Only a subset of these transformations results in mechanically realizable models. For models with a small number of internal masses, complete discrete mapping of the transformation space is possible, permitting enumeration of all mechanically realizable models sharing the original model’s input–output behavior. When the number of internal masses is large, a nonlinear search of transformation space can be employed to identify mechanically realizable models. Applications include scale model vibration testing of complicated structures and the design of electromechanical filters