Ultrasonic propagation in finite-length granular chains

Abstract

A narrowband ultrasound source has been used to generate solitary wave impulses in finite-length chains of spheres. Once the input signal is of sufficient amplitude, both harmonics and sub-harmonics of the input frequency can be generated as non-linear normal modes of the system, allowing a train of impulses to be established from a sinusoidal input. The characteristics of the response have been studied as a function of the physical properties of the chain, the input waveform and the level of static pre-compression. The results agree with the predictions of a theoretical model, based on a set of discrete dynamic equations for the spheres for finite-length chains. Impulses are only created for very small pre-compression forces of the order of 0.01N, where strongly non-linear behaviour is expected.

The dynamic excitation of a granular chain: Contact mechanics finite element analysis and experimental validation

“…9,10,11 Spadoni and Daraio 9 generated high-amplitude focused acoustic pulses using a one-dimensional array of granular chains. An investigation was conducted where the amplitude, size, and location of the focus could be controlled by varying the static pre-compression of the chains.…”

“…Yang et al employed granular chains to assess the structural integrity of orthopedic implants. 10 In the study described by Hutchins et al 11 , displacements of the order of 1 m were produced by a resonant 73 kHz ultrasonic source to drive a granular chain consisting of six 1 mm diameter chrome steel spheres. The final sphere of the chain was in contact with a fixed support.…”

“…This work was subsequently expanded upon to study the response of granular chains to a narrow band ultrasonic source, as a function of the static pre-compression of the chain, and of its properties. 12 A transduction mechanism based on the nonlinear dynamics of granular chains may in fact possess distinct features that could make it attractive to 6 both therapeutic high-intensity focused ultrasound applications and diagnostic applications. 11,12 Discrete mechanics models such as the one proposed by Lydon et al 13 , have been shown to replicate features of the experimentally observed dynamics of granular chains.…”

“…12 A transduction mechanism based on the nonlinear dynamics of granular chains may in fact possess distinct features that could make it attractive to 6 both therapeutic high-intensity focused ultrasound applications and diagnostic applications. 11,12 Discrete mechanics models such as the one proposed by Lydon et al 13 , have been shown to replicate features of the experimentally observed dynamics of granular chains. 5,6,11,12 Nevertheless, such models are likely to have limitations when it comes to designing, developing and optimizing application-specific transducers.…”

Generation of Ultrasound Pulses in Water Using Granular Chains with a Finite Matching Layer

“…A prototype device was developed based on this nonlinearity in a one-dimensional chain of spheres by Hutchins et al [18,[21][22][23]. The developed transducer is able to transform a narrow-band sinusoidal input force into a train of wideband impulses at ultrasonic frequencies.…”