Experimental and theoretical analysis of the nonlinear dynamics and acoustics of a rattling plate

Abstract

Rattle has become an important issue in the motive and aerospace industries. Design for the prevention and reduction of rattle noise requires that the underlying mechanisms be understood and powerful, flexible numerical tools be developed. In this paper, the focus is on the former, developing a basic theoretical and experimental foundation for determining the vibroacoustic behavior arising from the nonlinear dynamics associated with the rattle process. In order to understand the fundamental mechanics of rattle, a model problem was formulated involving a hinged plate rattling against a stiff contact point excited by base motion. The plate was modeled as a flexible beam and the resulting equations of motion were solved explicitly. It was found that the calculated accelerations at the tip of the beam quantitatively agree with those measured from an experimental test stand. In addition, the predicted and measured sound pressure levels (SPL) at various points were found to agree qualitatively. Finally, the closed form flexible body solutions were analyzed with regard to stability to predict transitions from periodic to chaotic rattling behavior. In particular, the sensitivity of the transition region to chaos on the base motion amplitude and frequency are investigated experimentally and theoretically.