Dynamics and control of band gaps in a mass-in mass metamaterial model with an extra attached mass

IF 1.9 4区工程技术 Q3 MECHANICS

Continuum Mechanics and Thermodynamics Pub Date : 2023-08-12 DOI:10.1007/s00161-023-01250-8

A. V. Porubov

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Abstract

It is shown that the continuum limit of the metamaterial mass-in-mass model with additional attached mass describes not only the appearance of the additional band gap but also variations in the width and the position of the band gaps. These variations are governed by the key parameter—the stiffness ratio of the attached masses. Numerical study of periodic boundary excitation of the harmonic waves reveals suppression of the harmonic waves for the frequencies lying inside the both band gap areas. Also it is found that harmonic waves recover differently for the frequencies below and above the band gap values. The control mechanism is developed based on the abrupt variation of the stiffness ratio. It gives rise to the arising of phase shift of the wave, its suppression or recovery of the previously suppressed harmonic wave. Nonlinear long wavelength generalization of the model results in obtaining the model equation whose coefficients differ from those of the usual nonlinear mass-in-mass model. It gives rise to propagation of the localized wave with another amplitude and velocity.

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具有附加质量的质量中质量超材料模型中带隙的动力学和控制

研究表明，具有附加质量的超材料质量-质量模型的连续极限不仅描述了附加带隙的出现，还描述了带隙宽度和位置的变化。这些变化是由关键参数决定的——附着质量的刚度比。对谐波周期边界激励的数值研究揭示了谐波对两个带隙区域内频率的抑制。还发现，对于带隙值以下和以上的频率，谐波的恢复是不同的。该控制机构是基于刚度比的突然变化而开发的。它引起了波的相移的产生，它对先前被抑制的谐波的抑制或恢复。对模型进行非线性长波长推广，得到了与质量模型中常见的非线性质量系数不同的模型方程。它产生了具有另一振幅和速度的局域化波的传播。

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来源期刊

Continuum Mechanics and Thermodynamics 物理-力学

CiteScore

5.30

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： This interdisciplinary journal provides a forum for presenting new ideas in continuum and quasi-continuum modeling of systems with a large number of degrees of freedom and sufficient complexity to require thermodynamic closure. Major emphasis is placed on papers attempting to bridge the gap between discrete and continuum approaches as well as micro- and macro-scales, by means of homogenization, statistical averaging and other mathematical tools aimed at the judicial elimination of small time and length scales. The journal is particularly interested in contributions focusing on a simultaneous description of complex systems at several disparate scales. Papers presenting and explaining new experimental findings are highly encouraged. The journal welcomes numerical studies aimed at understanding the physical nature of the phenomena. Potential subjects range from boiling and turbulence to plasticity and earthquakes. Studies of fluids and solids with nonlinear and non-local interactions, multiple fields and multi-scale responses, nontrivial dissipative properties and complex dynamics are expected to have a strong presence in the pages of the journal. An incomplete list of featured topics includes: active solids and liquids, nano-scale effects and molecular structure of materials, singularities in fluid and solid mechanics, polymers, elastomers and liquid crystals, rheology, cavitation and fracture, hysteresis and friction, mechanics of solid and liquid phase transformations, composite, porous and granular media, scaling in statics and dynamics, large scale processes and geomechanics, stochastic aspects of mechanics. The journal would also like to attract papers addressing the very foundations of thermodynamics and kinetics of continuum processes. Of special interest are contributions to the emerging areas of biophysics and biomechanics of cells, bones and tissues leading to new continuum and thermodynamical models.