Tunable magneto-granular phononic crystals

Abstract

This paper reports on the study of the dynamics of 1D magneto-granular phononic crystals composed of a chain of spherical steel beads inside a properly designed magnetic field. This field is induced by an array of permanent magnets, located in a holder at a given distance from the chain. The theoretical and experimental results of the band gap structure are displayed, including all six degrees of freedom for the beads, i.e. three translations and three rotations. Experimental evidence of transverse-rotational modes of propagation is presented; moreover, by changing the strength of the magnetic field, the dynamic response of the granular chain is tuned. The combination of non-contact tunability with the potentially strong nonlinear behavior of granular systems ensures the suitability of magneto-granular phononic crystals as nonlinear, tunable mechanical metamaterials for use in controlling elastic wave propagation.The ability to control the propagation of elastic waves has been widely investigated in phononic crystals, which are a class of engineered media composed of periodic arrays of scattering inclusions in a homogeneous host material 1 . The propagation of sound in phononic crystals is driven by the interference between Bragg scattered waves. Similar to the electronic band structure of semiconductors and the electromagnetic band structure of photonic crystals, the phononic crystal structure does not allow certain frequency ranges to propagate within it. The existence of these forbidden bands makes phononic crystals suitable for direct applications, such as mechanical frequency filtering and sound insulation. In addition, the removal of inclusions along some pathways produces acoustic waveguides, demultiplexers and other elastic wave devices. To foresee the next generation of elastic devices, it would be necessary to introduce a certain degree of frequency tunability in the phononic properties. Greater interest has been shown along these lines over the last few years, and many solutions have been proposed by a number of authors; these include geometric changes to the structure by applying external stresses 2 and changes to the elastic characteristics of the constitutive materials through application of external stimuli, like an electric field 3 , temperature changes 4 or a magnetic field 5 . Among the various proposed phononic crystals, granular crystals 6 , which are closely-packed ordered arrangements of elastic particles (mainly spheres) in contact, have been the topic of a large body of recent work. Due to the Hertzian contact interaction between particles 7 , the dynamic vibration response of these structures may be nonlinear and tunable. These features make granular chains a perfect medium for studying fundamental wave structures, including solitary waves with a highly localized waveform 8,9 or discrete breathers 10 , as well as in engineering applications, e.g. tunable vibration filters 11 , impulse energy protectors 12 , acoustic lenses 13 , acoustic rectifiers 14 , tunable functional switches 15 . Pr...

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

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