Structural vibration damping using lightweight, low-wave-speed media

Abstract

Incorporation of a low-density, low-wave-speed medium (LWSM) into a structure yields significant damping if the speed of wave propagation in the medium is low enough for standing waves to arise in it. In this thesis, we characterize wave propagation in low-density granular media and foams for use as structural damping treatments and develop analytical and numerical techniques for prediction of the damping attained in structures that incorporate LWSM. Structural damping by incorporation of LWSM is attractive for hollow thin-walled structures. We develop analytical approximations for the loss-factor in the structural modes of cylindrical shells and Timoshenko beams and attain predictions in good agreement with measurements. For more complicated geometries, it is often necessary to employ a finite element model to predict the dynamics of structures. But inclusion of LWSM into a finite element model significantly increases the size of the model, introduces frequency-dependent material properties, and introduces a large number of modes that are dominated by deformation of the LWSM. Hence, the eigenvalue problem becomes significantly more difficult by addition of the LWSM.

(cont.) We develop an iterative approach based on the eigensolution of a structure without LWSM and the forced response of the LWSM to obtain approximations for the complex eigensolution. Damping by inclusion of LWSM is an attractive option for reduction of the sound radiated from vehicle driveshafts, which are typically thin-walled hollow cylinders with yokes welded at each end. The bending and ovaling modes of the driveshaft between 500 and 3000 Hz are efficient radiators of sound and are excited by gear transmission error in the rear differential. Filling the driveshaft with a. lossy, low-density foam adds significant damping to these modes and thus reduces the radiated sound.