Boundary damping of flexural vibrations in beams and plates

Abstract

The damping of resonantly enhanced flexurally vibrating beams and plates is typically accomplished with surface treatments, viz. constrained or unconstrained damping layers. Alternatively, damping may be achieved at boundaries. In some sense this is a more fundamental approach in that for homogeneous plates, it is the boundaries that are solely responsible for resonant behavior. The theoretical performance of boundary treatments is unbounded, provided the treatment is full, that is continuous along the extent of the boundary. This is not the case however with partial coverage, where a portion of the boundary is left bare. The bounds for such treatments are explored in this paper. The treatment itself is defined in terms of a single bounce reflection coefficient (RC). It is found that for boundary damping in one dimension, viz., beams, the effective loss factor for individual modes is frequently invariant with either one or both ends treated, assuming RC constant. This is in contrast to the two-dimensional case, viz., thin plates, where analogous loss factor values are frequency dependent. Illustrative examples are presented and analyzed. [Work partially performed at CAA/Anteon Corp. and supported by NSWCCD and NSSC, Code 93R.]