Abstract:
The fuzzy structure theory concept of modal mass per unit natural frequency is explored for an elastic substructure attached to a master structure. The passive influence on the master structure vibration is specified by the driving point impedance of the substructure, which in turn is expressed as a sum over terms, each corresponding to a natural mode. Term parameters are a modal mass in the numerator and the natural frequency. The fuzzy structure idealization replaces the sum by a derivative term (dissipative part) plus an integral (reactive part), both involving modal mass per unit frequency. Generic continuum models of the attachment are inhomogeneous rods, beams, and plates. (In the latter cases, the impedance becomes a matrix, with generalized forces incorporated that correspond to torques, and generalized velocities that are angular velocities.) Asymptotic ideas analogous to those that yield modal density predictions yield predictions of the mass per unit natural frequency (and its generalizations) in the limit of high frequencies. [Work supported by ONR.]