Investigation of co-travelling solitary wave collisions in a granular chain

We present investigations into the collision of co-travelling solitary waves in a granular chain. Impulses are injected into the system by means of a piezo stack and the results are compared to a numerical model of discrete masses connected by non-linear springs. Similar to other solitary wave-carrying systems, a phase shift in both interacting solitary waves is observed due to their collision. Additionally, the formation of small secondary waves is observed in both numerical and experimental results. Insight into solitary wave interactions will be important for high-frequency excitation of a granular crystal, which may allow for improved Non-Destructive Evaluation (NDE) and Structural Health Monitoring (SHM) methods

Stationary shocks in periodic highly nonlinear granular chains

We study the existence of stationary shock waves in uniform and periodic heterogeneous highly nonlinear granular chains governed by a power-law contact interaction, comparing discrete and continuum approaches, as well as experiments. We report the presence of quasisteady shock fronts without the need for dissipative effects. When viscous effects are neglected, the structure of the leading front appears to be solely the result of dispersive effects related to the lattice wave dispersion and, for heterogeneous bead chains, to the impedance mismatch between material domains. We report analytically and numerically the shock-width scaling with the variation in the particles periodicity (cell size) and compare the obtained results with experiments. We check the state (−) behind the shock front via quasistatic compression analysis and report a very good agreement between theory and numerical data

Complete Delocalization in a Defective Periodic Structure

We report on the existence of stable, completely delocalized response regimes in a nonlinear defective periodic structure. In this state of complete delocalization, despite the presence of the defect, the system exhibits in-phase oscillation of all units with the same amplitude. This elimination of defect-borne localization may occur in both the free and forced responses of the system. In the absence of external driving, the localized defect mode becomes completely delocalized at a certain energy level. In the case of a damped-driven system, complete delocalization may be realized if the driving amplitude is beyond a certain threshold. We demonstrate this phenomenon numerically in a linear periodic structure with one and two defective units possessing a nonlinear restoring force. We derive closed-form analytical expressions for the onset of complete delocalization and discuss the necessary conditions for its occurrence

Subwavelength edge detection through trapped resonances in waveguides

Lenses that can collect the perfect image of an object must restore propagative and evanescent waves. However, for efficient information transfer, e.g., in compressed sensing, it is often desirable to detect only the fast spatial variations of the wave field (carried by evanescent waves), as the one created by edges or small details. Image processing edge detection algorithms perform such operation but they add time and complexity to the imaging process. Here, we present a new subwavelength approach that generates an image of only those components of the acoustic field that are equal to or smaller than the operating wavelength. The proposed technique converts evanescent waves into propagative waves exciting trapped resonances in a waveguide, and it uses periodicity to attenuate the propagative components. This approach achieves resolutions about an order of magnitude smaller than the operating wavelength and makes it possible to visualize independently edges aligned along different directions

Generation of Sound Bullets with a Nonlinear Acoustic Lens

Acoustic lenses are employed in a variety of applications, from biomedical imaging and surgery, to defense systems, but their performance is limited by their linear operational envelope and complexity. Here we show a dramatic focusing effect and the generation of large amplitude, compact acoustic pulses (sound bullets) in solid and fluid media, enabled by a tunable, highly nonlinear acoustic lens. The lens consists of ordered arrays of granular chains. The amplitude, size and location of the sound bullets can be controlled by varying static pre-compression on the chains. We support our findings with theory, numerical simulations, and corroborate the results experimentally with photoelasticity measurements. Our nonlinear lens makes possible a qualitatively new way of generating high-energy acoustic pulses, enabling, for example, surgical control of acoustic energy.Comment: 19 pages, 7 figures, includes supplementary informatio

Wave mitigation in ordered networks of granular chains

We study the propagation of stress waves through ordered 2D networks of granular chains. The quasi-particle continuum theory employed captures the acoustic pulse splitting, bending, and recombination through the network and is used to derive its effective acoustic properties. The strong wave mitigation properties of the network predicted theoretically are confirmed through both numerical simulations and experimental tests. In particular, the leading pulse amplitude propagating through the system is shown to decay exponentially with the propagation distance and the spatial structure of the transmitted wave shows an exponential localization along the direction of the incident wave. The length scales that characterized these exponential decays are studied and determined as a function of the geometrical properties of the network. These results open avenues for the design of efficient impact mitigating structures and provide new insights into the mechanisms of wave propagation in granular matter.Comment: submitted to Journal of the Mechanics and Physics of Solid

Actuators for the generation of highly nonlinear solitary waves

In this paper we present the design of two actuators for the generation of highly nonlinear solitary waves (HNSWs), which are mechanical waves that can form and travel in highly nonlinear systems. These waves are characterized by a constant spatial wavelength and by a tunable propagation speed, dependent on the wave amplitude. To date, the simplest and widely adopted method to generate HNSWs is by impacting a striker onto a chain of beads of equal size and mass. This operation is conducted manually and it might be impracticable if repetition rates higher than 0.1 Hz are necessary. It is known that the HNSWs’ properties, such as amplitude, duration, and speed can be modified by changing the size or the material of the particles, the velocity of the striker, and/or the precompression on the chain. To address the limitations associated with the manual generation of HNSWs we designed, built, and tested two actuators. The first actuator consists of a chain of particles wrapped by an electromagnet that induces static precompression on the chain. This design allows for the generation of solitary waves with controlled properties. The second actuator consists of a chain surmounted by an electromagnet that lifts and releases a striker. This actuator permits the remote and noncontact generation of solitary waves. The performance of both actuators is evaluated by comparing the experimental HNSWs to theoretical predictions, based on the long wavelength approximation

Nonlinear repulsive force between two solids with axial symmetry

We modify the formulation of Hertz contact theory between two elastic half-solids with axial symmetry and show that these modifications to Hertz’s original framework allow the development of force laws of the form F∝z^n, 10 to describe any aspect ratio in the two bodies, all being valid near the contact surface. We let the x-y plane be the contact surface with an averaged pressure across the same as opposed to a pressure profile that depends on the contact area of a nonconformal contact as originally used by Hertz. We let the z axis connect the centers of the masses and define z_(1,2) = x^(α)/R_(1,2)^(α-1) + y^(α)/(mR_(1,2))^(α-1), where z_(1,2)≥0 refers to the compression of bodies 1, 2, α>1, m>0, x,y≥0. The full cross section can be generated by appropriate reflections using the first quadrant part of the area. We show that the nonlinear repulsive force is F=az^n, where n≡1+(1/α), and z≡z_1 + z_2 is the overlap and we present an expression for a=f(E,σ,m,α,R_(1),R_(2)) with E and σ as Young’s modulus and the Poisson ratio, respectively. For α=2,∞, to similar geometry-dependent constants, we recover Hertz’s law and the linear law, describing the repulsion between compressed spheres and disks, respectively. The work provides a connection between the contact geometry and the nonlinear repulsive law via α and m

Highly nonlinear solitary waves in chains of ellipsoidal particles

We study the dynamic response of a one-dimensional chain of ellipsoidal particles excited by a single compressive impulse. We detail the Hertzian contact theory describing the interaction between two ellipsoidal particles under compression, and use it to model the dynamic response of the system. We observe the formation of highly nonlinear solitary waves in the chain, and we also study their propagation properties. We measure experimentally the traveling pulse amplitude (force), the solitary wave speed, and the solitary wave width. We compare these results with theoretical predictions in the long wavelength approximation, and with numerical results obtained with a discrete particle model and with finite element simulations. We also study the propagation of highly nonlinear solitary waves in the chain with particles arranged in different configurations to show the effects of the particle's geometry on the wave propagation characteristics and dissipation. We find very good agreement between experiment, theory, and simulations for all the ranges of impact velocity and particle arrangements investigated

Hydrogen Evolution on Hydrophobic Aligned Carbon Nanotube Arrays

We investigate for the first time hydrophobic carbon nanotube-based electrochemical cells as an alternative solution to hydrogen sorting. We show that the electrically conducting surface of the nanotube arrays can be used as a cathode for hydrogen generation and absorption by electrolyzing water. We support our findings with Raman and gas chromatography measurements. These results suggest that carbon nanotube forests, presenting a unique combination of hydrophobicity and conductivity, are suitable for application in fuel cells and microelectromechanical devices