Abstract:
The present paper considers a sequence of modeling problems involving idealized mechanical attachments that are connected to an external elastic structure at either a single point or a number of points. Previous analyses for cases when the attachments were rods and beams are reviewed along with the fuzzy-structure idealization that considers the mass per unit natural frequency to be continuous, and in which the asymptotic high-frequency limit is taken. Although the first approximation to this limit leads to a divergent integral for the frequency-dependent effective mass contributed by the internal structure, it is possible to obtain realistic high-frequency limits with incorporation of the knowledge of the total mass of the appendage. The remainder of the paper concentrates on two-dimensional elastic bodies, especially plates, that are connected to the master structure at one or more places, and explores the asymptotic tendencies of the elements of the modal mass matrix and the circumstances in which the number of attachments may be effectively blurred as a continuous distribution of nonconnected one-dimensional fuzzy attachments. [Work supported by the Office of Naval Research.]