Alternative Designs of Acoustic Lenses Based on Nonlinear Solitary Waves

In the last decade, there has been an increasing attention on the use of highly- and weakly-nonlinear solitary waves in engineering and physics. These waves can form and travel in nonlinear systems such as one-dimensional chains of particles. When compared to linear elastic waves, solitary waves are much slower, nondispersive, and their speed is amplitude-dependent. Moreover, they can be tuned by modifying the particles' material or size, or the chain's precompression. One interesting engineering application of solitary waves is the fabrication of acoustic lenses, which are employed in a variety of fields ranging from biomedical imaging and surgery to defense systems and damage detection in materials. In this paper, we propose the design of acoustic lenses composed by one-dimensional chains of spherical particles arranged to form a line or a circle array. We show, by means of numerical simulations and an experimental validation, that both the line and circle arrays allow the focusing of waves transmitted into a solid or liquid (the host media) and the generation of compact sound bullets of large amplitude. The advantages and limitations of these nonlinear lenses to attain accurate high-energy acoustic pulses with high signal-to-noise ratio are discussed.

[1]  Liuxian Zhao,et al.  Visualization of solitary waves via laser Doppler vibrometry for heavy impurity identification in a granular chain , 2013 .

[2]  Hertz On the Contact of Elastic Solids , 1882 .

[3]  V. Nesterenko,et al.  Observation of a new type of solitary waves in a one-dimensional granular medium , 1985 .

[4]  V. Nesterenko,et al.  The decay of soliton at the contact of two “acoustic vacuums” , 1995 .

[5]  Claudio Silvestro,et al.  Nondestructive evaluation of orthopaedic implant stability in THA using highly nonlinear solitary waves , 2011 .

[6]  Piervincenzo Rizzo,et al.  Highly Nonlinear Solitary Waves for the Inspection of Adhesive Joints , 2012 .

[7]  Xianglei Ni,et al.  Monitoring the hydration of cement using highly nonlinear solitary waves , 2012 .

[8]  Thomas Anderson Keller,et al.  Experimental realization of a nonlinear acoustic lens with a tunable focus , 2013, 1308.1483.

[9]  G. Theocharis,et al.  Bifurcation-based acoustic switching and rectification. , 2011, Nature materials.

[10]  S. Mallat A wavelet tour of signal processing , 1998 .

[11]  Adam Sokolow,et al.  Solitary wave trains in granular chains: experiments, theory and simulations , 2007, 0712.0006.

[12]  Alessandro Spadoni,et al.  Generation and control of sound bullets with a nonlinear acoustic lens , 2009, Proceedings of the National Academy of Sciences.

[13]  Mason A Porter,et al.  Dissipative solitary waves in granular crystals. , 2008, Physical review letters.

[14]  V. Nesterenko,et al.  Dynamics of Heterogeneous Materials , 2001 .

[15]  Piervincenzo Rizzo,et al.  Semi-analytical formulation for the guided waves-based reconstruction of elastic moduli , 2011 .

[16]  Aiguo Xu,et al.  Nondestructive identification of impurities in granular medium , 2002 .

[17]  C. Daraio,et al.  Strongly nonlinear waves in a chain of Teflon beads. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  C Daraio,et al.  Anomalous wave reflection at the interface of two strongly nonlinear granular media. , 2005, Physical review letters.

[19]  Bruno Gilles,et al.  On the validity of Hertz contact law for granular material acoustics , 1999 .

[20]  V. Nesterenko,et al.  Propagation of nonlinear compression pulses in granular media , 1984 .

[21]  Eric Falcon,et al.  Solitary waves in a chain of beads under Hertz contact , 1997 .

[22]  Adam Sokolow,et al.  How hertzian solitary waves interact with boundaries in a 1D granular medium. , 2005, Physical review letters.

[23]  Xianglei Ni,et al.  Use of Highly Nonlinear Solitary Waves in Nondestructive Testing , 2012 .

[24]  Fernando Fraternali,et al.  Optimal Design of Composite Granular Protectors , 2008, 0802.1451.

[25]  Xianglei Ni,et al.  Laser-based excitation of nonlinear solitary waves in a chain of particles. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Claudio Silvestro,et al.  Interaction of highly nonlinear solitary waves with linear elastic media. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Francesco Lanza di Scalea,et al.  Propagation of ultrasonic guided waves in lap-shear adhesive joints: case of incident a0 Lamb wave. , 2004 .

[28]  Xianglei Ni,et al.  Actuators for the generation of highly nonlinear solitary waves. , 2011, The Review of scientific instruments.

[29]  C. Daraio,et al.  Tunability of solitary wave properties in one-dimensional strongly nonlinear phononic crystals. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Surajit Sen,et al.  Solitonlike pulses in perturbed and driven Hertzian chains and their possible applications in detecting buried impurities , 1998 .

[31]  Fernando Fraternali,et al.  Solitary waves on tensegrity lattices , 2012 .