Omololu Akanji

Evolution of ultrasonic impulses in chains of spheres using resonant excitation

It is demonstrated that broad-bandwidth ultrasonic signals containing frequency components in excess of 200 kHz can be created in spherical chains using harmonic excitation at 73 kHz. Multiple reflections created a periodic waveform containing both harmonics and sub-harmonics of the original forcing frequency, due to non-linear Hertzian contact. These discrete frequencies represented some of the many allowed non-linear normal modes of vibration of the whole chain. Excitation at a single fixed frequency could thus be used to produce wide-bandwidth impulses for different lengths of spherical chains. Experimental results were in good agreement with theoretical predictions.

The dynamic excitation of a granular chain for biomedical ultrasound applications: contact mechanics finite element analysis and validation

There has been recent interest in the transmission of acoustic signals along granular chains of spherical beads to produce waveforms of relevance to biomedical ultrasound applications. Hertzian contact between adjacent beads can introduce different harmonic content into the signal as it propagates. 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. Although discrete dynamics models of this behaviour exist, a more comprehensive solution must be sought if changes in shape and deformation of individual beads are to be considered. Thus, the finite element method was used to investigate the dynamics of a granular chain of six, 1 mm diameter chrome steel spherical beads excited at one end using a sinusoidal displacement signal at 73 kHz. Output from this model was compared with the solution provided by the discrete dynamics model, and good overall agreement obtained. In addition, it was able to resolve the complex dynamics of the granular chain, including the multiple collisions which occur. It was demonstrated that under dynamic excitation conditions, the inability of discrete mechanics models to account for elastic deformation of the beads when these lose contact, could lead to discrepancies with experimental observations.

Ultrasonic propagation in finite-length granular chains

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 study of chain-like materials for use in biomedical ultrasound

Wave propagation in chain-like materials has been studied previously at low frequencies. The present study has generated these waves at higher frequencies with components >200 kHz, using chains of 1 mm diameter spheres. Resonant ultrasonic horns at 73 kHz have been used as sources of narrowband excitation, which transform into a train of broadband impulses that have the characteristics of solitary waves. These have potential applications in biomedical ultrasound as high amplitude, wide bandwidth impulses.

Nonlinear generation of harmonic content within High Intensity Ultrasound signals using granular chains

Applications such as High Intensity Focused Ultrasound (HIFU) conventionally use narrowband signals of high amplitude, which are then focused to a known region within the body. It would be advantageous to be able to broaden the bandwidth, as this could lead to a more spatially-concentrated focal region. One way of increasing the bandwidth is to generate harmonics. The eventual aim of this study is to generate wideband ultrasonic signals with high amplitudes, primarily for therapeutic ultrasound and drug delivery applications. In this paper, a new ultrasonic transducer technology using a one-dimensional chain of spheres is presented to achieve this aim.

The generation of impulses from narrow bandwidth signals using resonant spherical chains

An ultrasonic horn operating at 73 kHz has been used to excite one end of a chain of steel spheres. The signal transmitted along the chain was measured at the far end using a laser vibrometer. Various chain lengths, ranging from 2-10 spheres, have been studied. It was found that a set of solitary wave impulses were generated when a high input amplitude and a minimal pre-compression force was used. Both harmonics and sub-harmonics of the input frequency could be observed. Theoretical models were developed, based on the relevant equations of motion, which modelled the end conditions properly, and their predictions confirmed the experimental observations. Solitary wave impulses were generated only when certain numbers of spheres were used, corresponding to the establishment of resonances in the form of nonlinear normal modes (NNMs). It was found that longer chains led to wider impulse bandwidths. Increased pre-compression tended to damp out this phenomenon, but gave a weakly non-linear state where the time delay of propagation along the chain changed with applied static force. It was thus established that a gated sinusoidal input could be transformed into a set of impulses, of interest in biomedical applications.

Coupling of wideband impulses generated by granular chains into liquids for biomedical applications

An ultrasonic transducer technology to generate wideband impulses using a one-dimensional chain of spheres was previously presented. The Hertzian contact between the spheres causes the nonlinearity of the system to increase, which transforms high amplitude narrowband sinusoidal input into a train of wideband impulses. Generation of short duration ultrasonic pulses is desirable both in diagnostic and therapeutic ultrasound. Nevertheless, the biggest challenge in terms of adaptation to biomedical ultrasound is the coupling of the ultrasonic energy into biological tissue. An analytical model was created to address the coupling issue. Effect of the matching layer was modelled as a flexible thin plate clamped from the edges. Model was verified against hydrophone measurements. Different coupling materials, such as glass, aluminium, acrylic, silicon rubber, and vitreous carbon, was analysed with this model. Results showed that soft matching layers such as acrylic and rubber inhibit the generation of higher order harmonics. Between the hard matching materials, vitreous carbon achieved the best results due to its acoustic impedance.

Analysis of solitary wave impulses in granular chains using ultrasonic excitation.

The propagation of broad bandwidth solitary wave impulses, generated within granular chains by narrow bandwidth ultrasonic excitation, is studied in detail. Theoretical predictions are compared to experimental results. It is demonstrated that the observed effects result from a sum of a solitary wave traveling out from the source with a wave that reflects from the far end of the chain. It is shown that this combination, when used with an excitation in the form of a long-duration tone burst, encourages the generation of multiple impulses with a characteristic periodicity. This study shows that the properties of the chain structure and the excitation can be adjusted so as to generate ultrasonic solitary wave impulses with a high amplitude and known frequency content, which are of interest in applications such as biomedical ultrasound.

The Effect of Boundary Conditions on Resonant Ultrasonic Spherical Chains

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.

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.