On the validity of Hertz contact law for granular material acoustics

Coste, Christophe; Gilles, B.

doi:10.1007/s100510050598

Cited by 138 publications

(123 citation statements)

References 2 publications

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“…where C (1) and C (2) are diagonal matrices with ( j, j) entries sin ω j τ and cos ω j τ , respectively. The vectors a (1) and a (2) are determined from the initial conditions of the displacement u(0) = u o and velocityu(0) = v o .…”

Section: Linear Model: Analysismentioning

confidence: 99%

“…The vectors a (1) and a (2) are determined from the initial conditions of the displacement u(0) = u o and velocityu(0) = v o . Vector c has j th entry…”

Section: Linear Model: Analysismentioning

confidence: 99%

“…The introduction of nonlinear (e.g., Hertzian) particle interactions resembles most experiments with granular chains of pre-stressed elastic spheres and leads to novel behavior such as soliton-like nonlinear waves [2,17,[28][29][30]37,44]. Sen et al [43] provide a detailed account of prior studies concerning solitary waves in granular chains.…”

Section: Introductionmentioning

confidence: 99%

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Frequency filtering in disordered granular chains

Lawney¹,

Luding²

2014

Acta Mech

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The study of disorder-induced frequency filtering is presented for one-dimensional systems composed of random, pre-stressed masses interacting through both linear and nonlinear (Hertzian) repulsive forces. An ensemble of such systems is driven at a specified frequency, and the spectral content of the propagated disturbance is examined as a function of distance from the source. It is shown that the transmitted signal contains only low-frequency components, and the attenuation is dependent on the magnitude of disorder, the input frequency, and the contact model. It is found that increased disorder leads to a narrower bandwidth of transmitted frequencies at a given distance from the source and that lower input frequencies exhibit less sensitivity to the arrangement of the masses. Comparison of the nonlinear and linear contact models reveals qualitatively similar filtering behavior; however, it is observed that the nonlinear chain produces transmission spectrums with a greater density at the lowest frequencies. In addition, it is shown that random masses sampled from normal, uniform, and binary distributions produce quantitatively indistinguishable filtering behavior, suggesting that knowledge of only the distribution's first two moments is sufficient to characterize the bulk signal transmission behavior. Finally, we examine the wave number evolution of random chains constrained to move between fixed end-particles and present a transfer matrix theory in wave number space, and an argument for the observed filtering based on the spatial localization of the higher-frequency normal modes.

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Section: Linear Model: Analysismentioning

confidence: 99%

“…The vectors a (1) and a (2) are determined from the initial conditions of the displacement u(0) = u o and velocityu(0) = v o . Vector c has j th entry…”

Section: Linear Model: Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Frequency filtering in disordered granular chains

Lawney¹,

Luding²

2014

Acta Mech

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“…The operation is conducted by manually lifting and then releasing the striker. To add precompression to a chain of spherical particles Coste et al 4 applied a contact static force, which had the disadvantage of changing the boundary conditions. Daraio et al 13 instead used a permanent circular magnet.…”

Section: Introductionmentioning

confidence: 99%

Actuators for the generation of highly nonlinear solitary waves

Rizzo

Daraio

2011

Review of Scientific Instruments

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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.

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“…Granular chains represent one of the most studied examples of highly nonlinear systems exhibiting a very unique wave behavior in one dimension [1][2][3]. Recently, the study of the highly nonlinear behavior at the interface between two highly nonlinear media has received increasing attention due to the discovery of interesting new dynamical aspects arising from the selforganization of the granules in close proximity to the interface [4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Propagation of Highly Nonlinear Signals in a Two Dimensional Network of Granular Chains

Daraio¹,

Nesterenko²

2008

AIP Conference Proceedings

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Abstract.We report the first experimental observation of highly nonlinear signals propagating in a two dimensional system composed of granular chains. In this system one of the chains contacts two others to allow splitting and redirecting the solitary-like signal formed in the first chain. The system consists of a double Y-shaped guide in which high-and low-modulus chains of spheres are arranged in various geometries. We observed fast splitting of the initial pulse, rapid chaotization of the signal and sharp bending of the propagating acoustic information. Pulse and energy trapping was also observed in composite systems assembled from hard-and soft-particles in the branches.

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On the validity of Hertz contact law for granular material acoustics

Cited by 138 publications

References 2 publications

Frequency filtering in disordered granular chains

Frequency filtering in disordered granular chains

Actuators for the generation of highly nonlinear solitary waves

Propagation of Highly Nonlinear Signals in a Two Dimensional Network of Granular Chains

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