In the last decade there has been an increasing interest in the use of highly- and weakly- nonlinear solitary waves in engineering and physics. Nonlinear solitary waves can form and travel in nonlinear systems such as one-dimensional chains of particles, where they are conventionally generated by the mechanical impact of a striker and are measured either by using thin transducers embedded in between two half-particles or by a force sensor placed at the chain’s base. These waves have a constant spatial wavelength and their speed, amplitude, and duration can be tuned by modifying the particles’ material or size, or the velocity of the striker. In this paper we propose two alternative sensing configurations for the measurements of solitary waves propagating in a chain of spherical particles. One configuration uses piezo rods placed in the chain while the other exploits the magnetostrictive property of ferromagnetic materials. The accuracy of these two sensing systems on the measurement of the solitary wave’s characteristics is assessed by comparing experimental data to the numerical prediction of a discrete particle model and to the experimental measurements obtained by means of a conventional transducer. The results show very good agreement and the advantages and limitations of the new sensors are discussed.
References
[1]
Nesterenko, V.F. Propagation of nonlinear compression pulses in granular media. J. Appl. Mech. Tech. Phys. 1983, 24, 733–743.
[2]
Lazaridi, A.N.; Nesterenko, V.F. Observation of a new type of solitary waves in one-dimensional granular medium. J. Appl. Mech. Tech. Phys. 1985, 26, 405–408.
[3]
Nesterenko, V.F.; Lazaridi, A.N.; Sibiryakov, E.B. The decay of soliton at the contact of two “acoustic vacuums”. J. Appl. Mech. Tech. Phys. 1995, 36, 166–168.
[4]
Coste, C.; Falcon, E.; Fauve, S. Solitary waves in a chain of beads under Hertz contact. Phys. Rev. E 1997, 56, 6104–6117.
[5]
Coste, C.; Gilles, B. On the validity of Hertz contact law for granular material acoustics. Eur. Phys. J. B 1999, 7, 155–168.
[6]
Daraio, C.; Nesterenko, V.F.; Herbold, E.B.; Jin, S. Strongly nonlinear waves in a chain of Teflon beads. Phys. Rev. E 2005, 72, 016603:1–016603:9.
[7]
Daraio, C.; Nesterenko, V.F.; Herbold, E.B.; Jin, S. Tunability of solitary wave properties in one-dimensional strongly nonlinear phononic crystals. Phys. Rev. E 2006, 73, 026610:1–026610:10.
[8]
Job, S.; Melo, F.; Sokolow, A.; Sen, S. How Hertzian solitary waves interact with boundaries in a 1D granular medium. Phys. Rev. Lett. 2005, 94, 178002:1–178002:4.
[9]
Job, S.; Melo, F.; Sokolow, A.; Sen, S. Solitary wave trains in granular chains- experiments, theory and simulations. Granul. Matter 2007, 10, 13–20.
[10]
Nesterenko, V.F.; Daraio, C.; Herbold, E.B.; Jin, S. Anomalous wave reflection at the interface of two strongly nonlinear granular media. Phys. Rev. Lett. 2005, 95, 158702:1–158702:4.
[11]
Yang, J.; Silvestro, C.; Khatri, D.; De Nardo, L.; Daraio, C. Interaction of highly nonlinear solitary waves with linear elastic media. Phys. Rev. E 2011, 83, 046606:1–046606:12.
[12]
Carretero-González, R.; Khatri, D.; Porter, M.A.; Kevrekidis, P.G.; Daraio, C. Dissipative solitary waves in granular crystals. Phys. Rev. Lett. 2009, 102, 024102:1–024102:4.
[13]
Ni, X.; Rizzo, P.; Daraio, C. Laser-based excitation of nonlinear solitary waves in a chain of particles. Phys. Rev. E 2011, 84, 026601:1–026601:5.
[14]
Ni, X.; Rizzo, P.; Daraio, C. Actuators for the generation of highly nonlinear solitary waves. Rev. Sci. Instrum. 2011, 82, 034902:1–034902:6.
[15]
Sen, S.; Manciu, M.; Wright, J.D. Solitonlike pulses in perturbed and driven Hertzian chains and their possible applications in detecting buried impurities. Phys. Rev. E 1998, 57, 2386–2397.
[16]
Chatterjee, A. Asymptotic solution for solitary waves in a chain of elastic spheres. Phys. Rev. E 1999, 59, 5912–5919.
[17]
Manciu, F.S.; Sen, S. Secondary solitary wave formation in systems with generalized Hertz interactions. Phys. Rev. E 2002, 66, 016616:1–016616:11.
[18]
Hong, J. Universal power-law decay of the impulse energy in granular protectors. Phys. Rev. Lett. 2005, 94, 108001:1–108001:4.
[19]
Vergara, L. Scattering of Solitary Waves from Interfaces in Granular Media. Phys. Rev. Lett. 2005, 95, 108002:1–108002:4.
[20]
Rosas, A.; Romero, A.H.; Nesterenko, V.F.; Lindenberg, K. Observation of two-wave structure in strongly nonlinear dissipative granular chains. Phys. Rev. Lett. 2007, 98, 164301:1–164301:4.
[21]
Spadoni, A.; Daraio, C. Generation and control of sound bullets with a nonlinear acoustic lens. Proc. Natl. Acad. Sci. USA 2010, 107, 7230–7234.
[22]
Fraternali, F.; Porter, M.A.; Daraio, C. Optimal design of composite granular protectors. Mech. Adv. Mater. Struct. 2009, 17, 1–19.
[23]
Hong, J.; Xu, A. Nondestructive identification of impurities in granular medium. Appl. Phys. Lett. 2002, 81, 4868–4870.
[24]
Boechler, N.; Theocharis, G.; Daraio, C. Bifurcation-based acoustic switching and rectification. Nat. Mater. 2011, 10, 665–668.
[25]
Ni, X.; Rizzo, P.; Yang, J.; Katri, D.; Daraio, C. Monitoring the hydration of cement using highly nonlinear solitary waves. NDT E Int. 2012, 52, 76–85.
[26]
Ni, X.; Rizzo, P. Use of highly nonlinear solitary waves in NDT. Mater. Eval. 2012, 70, 561–569.
[27]
Ni, X.; Rizzo, P. Highly Nonlinear Solitary Waves for the Inspection of Adhesive Joints. Exp. Mech. 2012, 52, 1493–1501.
[28]
Yang, J.; Silvestro, C.; Sangiorgio, S.N.; Borkowski, S.L.; Ebramzadeh, E.; De Nardo, L.; Daraio, C. Nondestructive evaluation of orthopaedic implant stability in THA using highly nonlinear solitary waves. Smart Mater. Struct. 2012, 21, 012002:1–012002:10.
[29]
Leonard, A.; Fraternali, F.; Daraio, C. Directional wave propagation in a highly nonlinear square packing of spheres. Exp. Mech. 2011, doi:10.1007/s11340-011-9544-6.
[30]
Leonard, A.; Daraio, C. Stress wave anisotropy in centered square highly nonlinear granular systems. Phys. Rev. Lett. 2012, 108, 214301:1–214301:4.
[31]
Zhu, Y.; Shukla, A.; Sadd, M.H. The effect of microstructural fabric on dynamic load transfer in two dimensional assemblies of elliptical particles. J. Mech. Phys. Solids 1996, 44, 1283–1303.
[32]
Geng, J.; Reydellet, G.; Clément, E.; Behringer, R.P. Green's function measurements of force transmission in 2D granular materials. Phys. D Nonlinear Phenom. 2003, 182, 274–303.
[33]
Calkins, F.T.; Flatau, A.B.; Dapino, M.J. Overview of magnetostrictive sensor technology. J. Intell. Mater. Syst. Struct. 2007, 18, 1057–1066.
[34]
Joule, J.P. On the effects of magnetism upon the dimensions of iron and steel bars. Philos. Mag. 1847, 30, 76–87.
[35]
Kleinke, D.K.; Uras, M.H. A magnetostrictive force sensor. Rev. Sci. Instrum. 1994, 65, 1699–1710.
Villari, E. Change of magnetization by tension and by electric current. Ann. Phys. Chem. 1865, 126, 87–122.
[39]
Lanza di Scalea, F.; Rizzo, P.; Seible, F. Stress measurement and defect detection in steel strands by guided stress waves. J. Mater. Civ. Eng. 2003, 15, 219–227.
[40]
Rizzo, P.; Lanza di Scalea, F. Monitoring in cable stays via guided wave magnetostrictive ultrasonics. Mater. Eval. 2004, 62, 1057–1065.
[41]
Rizzo, P.; Lanza di Scalea, F. Ultrasonic inspection of multi-wire steel strands with the aid of the wavelet transform. Smart Mater. Struct. 2005, 14, 685–695.
[42]
Rizzo, P.; Sorrivi, E.; Lanza di Scalea, F.; Viola, E. Wavelet-based outlier analysis for guided wave structural monitoring: application to multi-wire strands. J. Sound Vib. 2007, 307, 52–68.
[43]
Rizzo, P.; Bartoli, I.; Marzani, A.; Lanza di Scalea, F. Defect classification in pipes by neural networks using multiple guided ultrasonic wave features extracted after wavelet processing. J. Press. Vessel Tech. 2005, 127, 294–303.
[44]
Rizzo, P.; Lanza di Scalea, F. Feature extraction for defect detection in strands by guided ultrasonic waves. Struct. Health Monit. 2006, 5, 297–308.