Coupling of a Granular Chain to an Acoustic Medium: Sensitivity Analyses of the Propagation of Ultrasonic Pulse Trains

Effects which arise as a result of Hertzian contact between adjacent spheres of a granular chain can potentially change the nature of a 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. Due to metrological challenges which arise when characterizing this transduction process, numerical models play a fundamental role in assisting the design of these novel devices. Previously, a finite element model was presented, which predicts the acoustic pressure generated by a sinusoidally excited granular chain coupled into an acoustic medium. The study described here exploits this model to carry out sensitivity analyses of the system to key input parameters, including excitation frequency and amplitude, sphere diameter and the number of spheres present in the chain. Granular chains were excited at one end using tone burst displacement signals with fundamental frequencies of 73 kHz and 100 kHz. The final sphere of the chain was assumed to be in contact with a cylindrical vitreous carbon layer, coupled to a half-space of water. Using the finite element method, it was possible to predict the acoustic pressure in the fluid, for a specific dynamic excitation of the first sphere of the granular chain. The sensitivity analyses demonstrated that, under tone burst excitation conditions, a train of impulses could be propagated into an acoustic medium. The sensitivity analyses also show that, due to inherent nonlinearities present in this type of system, the time and frequency domain characteristics of the signals are highly sensitive to input conditions.