Spatial mapping of modal damping in vibrating plates.

Abstract

Effective design and placement of damping treatments for complex structures benefit greatly from a knowledge of where the vibrational energy is being dissipated. Previously, the authors presented a method for spatially mapping contributions to the modal loss factor of a viscously damped structure [McDaniel et al., J. Acoust. Soc. Am. 125, 2603 (2009)]. The method is based on an inverse approach that uses experimental data to construct a damping matrix as a summation over elemental dashpots that connect measurement points to each other and to ground. This is followed by an assumption that ignores coupling in the modally transformed damping matrix, resulting in an expression for the modal loss factor as a weighted sum of elemental dashpots. In the present work, the method is applied to a vibrating plate with spatially distributed damping. An experiment is numerically simulated in which vibrational responses are measured at a small number of points. From these measurements, contributions to the modal loss factor are computed and used to construct a spatial map of damping effectiveness. Issues such as measurement error and modal coupling are used to further understand the method’s potential. [Work supported by ONR under Grant No. N000140810531.]