The Dynamic Excitation of a Chain of Pre-Stressed Spheres for Biomedical Ultrasound Applications: Contact Mechanics Finite Element Analysis and Validation

There has been recent interest in the transmission of acoustic signals along a chain of spheres to produce waveforms of relevance to biomedical ultrasound applications. Effects which arise as a result of Hertzian contact between adjacent spheres can potentially change the nature of the signal as it propagates down the chain. The possibility thus exists of generating signals with a different harmonic content to the signal input into one end of the chain. This transduction mechanism has the potential to be of use in both diagnostic and therapeutic ultrasound applications, and is the object of the study presented here. The nonlinear dynamics of granular chains can be treated using discrete mechanics models. However, in cases where the underlying assumptions of these models no longer hold, and where geometries are more complex, a more comprehensive numerical solution must be sought. Contact mechanics problems can efficiently be treated using the finite element method. The latter was used to investigate the dynamics of a pre-stressed chain of six, 1 mm diameter stainless steel spheres excited at one end using a tone burst displacement signal with a fundamental frequency of 73 kHz. The final sphere of the chain was assumed to be in contact with a cylindrical matching layer radiating into a half-space of fluid with the properties of water. After addition of the fluid loading, radiated acoustic pressures in the medium were predicted. Comparison with experimental results suggests that finite element analysis is a suitable tool for investigating the design and performance of contact mechanics based transducers. Nevertheless, a better handle on the model input parameters as well as an improved experimental protocol are required to fully validate the model.