Universal design law of equivalent systems for Nesterenko solitary waves transmission

Zhang, Wen; Xu, Jun

doi:10.1007/s10035-020-1011-6

Cited by 8 publications

(3 citation statements)

References 66 publications

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“…The last term in Equation ( 51) represents the frequency-dependent damping (energy dissipation, not attenuation), characterized by the damping rate d (s) , which was zero in this research since the total energy in a chain was considered to be conserved. Given any matrix Q, the evolution of energy with time can be easily modeled/integrated using the master equation in Equation (51). Thanks to the reduced order modeling in a master equation approach that combines many eigenmodes in the frequency bands, this solution is very efficient and much faster than any numerical solution of the full model.…”

Section: Stochastic Modeling-energy Propagation In the Wavenumbermentioning

confidence: 99%

“…Complementing earlier studies on the transfer of energy between frequency bands [4], evolving in space [25,[47][48][49], this research focuses also on the transfer of energy across different wavenumbers, as the system evolves in time. A master equation is devised and utilized for analyzing the transfer energy across different wavenumbers, studied with the aid of a one-dimensional granular chain [4,42,50,51]. Using the ensembled spatio-spectral energy response from the granular chain, the transfer coefficients of a reduced-complexity, disorder-specific master equation are evaluated.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic Model for Energy Propagation in Disordered Granular Chains

2021

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Energy transfer is one of the essentials of mechanical wave propagation (along with momentum transport). Here, it is studied in disordered one-dimensional model systems mimicking force-chains in real systems. The pre-stressed random masses (other types of disorder lead to qualitatively similar behavior) interact through (linearized) Hertzian repulsive forces, which allows solving the deterministic problem analytically. The main goal, a simpler, faster stochastic model for energy propagation, is presented in the second part, after the basic equations are re-visited and the phenomenology of pulse propagation in disordered granular chains is reviewed. First, the propagation of energy in space is studied. With increasing disorder (quantified by the standard deviation of the random mass distribution), the attenuation of pulsed signals increases, transiting from ballistic propagation (in ordered systems) towards diffusive-like characteristics, due to energy localization at the source. Second, the evolution of energy in time by transfer across wavenumbers is examined, using the standing wave initial conditions of all wavenumbers. Again, the decay of energy (both the rate and amount) increases with disorder, as well as with the wavenumber. The dispersive ballistic transport in ordered systems transits to low-pass filtering, due to disorder, where localization of energy occurs at the lowest masses in the chain. Instead of dealing with the too many degrees of freedom or only with the lowest of all the many eigenmodes of the system, we propose a stochastic master equation approach with reduced complexity, where all frequencies/energies are grouped into bands. The mean field stochastic model, the matrix of energy-transfer probabilities between bands, is calibrated from the deterministic analytical solutions by ensemble averaging various band-to-band transfer situations for short times, as well as considering the basis energy levels (decaying with the wavenumber increasing) that are not transferred. Finally, the propagation of energy in the wavenumber space at transient times validates the stochastic model, suggesting applications in wave analysis for non-destructive testing, underground resource exploration, etc.

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Section: Stochastic Modeling-energy Propagation In the Wavenumbermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stochastic Model for Energy Propagation in Disordered Granular Chains

2021

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“…Daraio [ 38 ] experimentally captured weak separation pulses in the soft granule segments of the low elastic modulus in the multi-segment granular chain. Zhang and Xu [ 39 , 40 ] used experimental and numerical simulation methods to create staggered composite granular chains of materials to attenuate impact wave amplitudes and design equivalent waves [ 41 ]. Wang [ 42 ] studied the energy decay caused by the transitional behavior in the light granule region of a one-dimensional three-segment composite granular chain by means of the momentum conservation principle.…”

Section: Introductionmentioning

confidence: 99%

Impact Buffering Characteristics of One-Dimensional Elastic–Plastic Composite Granular Chain

Mao

Wang

et al. 2023

Materials

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Considering the elastic–plastic deformation, the wave propagations and energy transmissions of the one-dimensional three-segment composite granular chain are studied. The axial symmetry model for elastic-perfectly plastic materials is built by using the finite element method. Six materials with different yield strengths are selected for the adjustable segment. The results show that the repeated loading and unloading behaviors, as well as the wave propagations in the elastic–plastic granular chain, are complex and significantly different from those in the purely elastic granular chain. The yield strength of the granular materials in the adjustable segment has significant effects on energy dissipation and wave velocity, which could be used to design the impact buffer. The studies show that taking lower yield strength for the adjustable part than the non-adjustable part, the energy dissipation could be increased, and the wave velocity could be reduced, then the arrival time of the impact waves could be delayed. These characteristics of the elastic–plastic granular chain could be used to design metamaterials for impact absorbers in impact protection.

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Pulse mitigation in ordered granular structures: from granular chains to granular networks

Espinosa,

Calius,

Hall

et al. 2024

Nonlinear Dyn

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Ordered granular structures have garnered considerable attention across various fields due to their capacity to manipulate the transmission of mechanical energy and mitigate the adverse effects of impacts and vibrations. The ability to control wave propagation is crucial in the design of protective equipment, seismic isolation systems, aerospace vibroacoustic attenuation and shock-absorbing materials, among many other applications. Here, we delve into the myriad configurations of ordered granular systems: from one dimensional granular chains to granular chain networks, showcasing their significance for pulse mitigation. Given the unique behaviours that these granular structures can generate, they can be described as discrete or granular metamaterials. A detailed analysis of the wave behaviour in these structures is presented, encompassing the influence of heterogeneity, chain curvature, and dimensional complexity on energy dissipation. This discourse extends to encompass a comparison of analytical and numerical approaches used in the examination and application of these systems, along with an exploration of the implications of advances in manufacturing methods. Unlike other examinations, this comprehensive review underscores the multifaceted nature of our study, with a steadfast focus on their applicability to impact mitigation and wave control. We conclude with a summary on the current challenges and future outlook of engineered granular systems, emphasizing their transformative potential in safeguarding structures from dynamic forces and advancing the frontier of energy management technologies.

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Universal design law of equivalent systems for Nesterenko solitary waves transmission

Cited by 8 publications

References 66 publications

Stochastic Model for Energy Propagation in Disordered Granular Chains

Stochastic Model for Energy Propagation in Disordered Granular Chains

Impact Buffering Characteristics of One-Dimensional Elastic–Plastic Composite Granular Chain

Pulse mitigation in ordered granular structures: from granular chains to granular networks

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