Abstract:
It is by now well known that the resistive part of the combined driving-point impedance of a collection of sprung masses with closely spaced frequencies of antiresonance can be expressed by the simple relation R=1/2(pi)[sup 2]f[sup 2]m[inf 0], where m[inf 0] is the resonant mass density, defined so that m[inf 0]df is the combined mass of the sprung masses in antiresonance in a differential frequency band of width df centered at the cyclic driving frequency f. To apply this relation to a continuous or complicated structure, it is necessary to determine how the value of m[inf 0] varies with frequency for a set of sprung masses duplicating the driving-point impedance of the structure. The procedure is illustrated by calculating m[inf 0] for several simple continuous structures, including a long uniform rod in axial vibration, and a long uniform beam or large thin plate in flexural vibration. The values of resistance obtained by treating these systems as fuzzy structures agree with well-known values.