The Effect of Boundary Conditions on Resonant Ultrasonic Spherical Chains.

O Akanji,Steven Freear,Nader Saffari,Jia Yang,Peter J Thomas,Lee A J Davis,Sevan Harput,Pierre N Gelat,David Hutchins

doi:10.1109/tuffc.2016.2576563

Abstract

The response of a resonant chain of spheres to changes in holder material and precompression is studied at ultrasonic frequencies. The system is found to be very sensitive to these parameters, with the creation of impulsive waveforms from a narrow bandwidth input seen only for certain chain lengths and holder materials. In addition, careful experiments were performed using known amounts of precompression force, using a calibrated stylus arrangement. At negligible precompression levels, impulses were generated within the chain, which were then suppressed by increased precompression. This was accompanied by large changes in the propagation velocity as the system gradually changes from being strongly nonlinear to being more linear. Simulations using a discrete model for the motion of each sphere agree well with the experimental data.

Highlights

Acoustic propagation along granular chains has been the subject of increased interest, because of their non-linear acoustic properties caused by Hertzian contact between the spheres, and this allows such systems to support a range of properties, depending on the amount of non-linearity present [1,2,3,4,5,6]
Such behaviour has been observed in different types of material that can be used in granular chains [7,8]
The work in this paper adds to our previous results [13,14] by considering both the effect of chain length for a fixed input frequency, the use of different holder materials, and investigates in detail the effect of precompression on these resonant systems, where the response varies from being highly non)linear in the case of negligible pre)compression (F0) to being almost linear at higher values of F0

Summary

INTRODUCTION

Acoustic propagation along granular chains has been the subject of increased interest, because of their non-linear acoustic properties caused by Hertzian contact between the spheres, and this allows such systems to support a range of properties, depending on the amount of non-linearity present [1,2,3,4,5,6]. Previous work by the present authors [13,14] has demonstrated that a train of impulses can be generated within chains of spheres at ultrasonic frequencies because of this effect, provided a negligible amount of pre-compression force F0 was applied. These studies used high amplitude, narrowbandwidth inputs at 73 kHz from an ultrasonic horn, with a chain containing small spheres (typically 1 mm diameter) of different types of material held within an acrylic holder.

APPARATUS AND METHODS

THEORY

RESULTS