超材料中非线性调制弯曲应变波的边界激励

IF 2.8 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics Pub Date : 2024-10-09 DOI:10.1016/j.ijnonlinmec.2024.104922

A.V. Porubov, N.M. Bessonov

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引用次数: 0

摘要

研究了超材料质中质晶格模型中弯曲波的非线性调制。利用谐波边界激励获得了各种非线性波调制。研究表明，这些波可以用运动方程的渐近简化来描述，从而得到一个位移的非线性调制方程。该方程的精确周期性行波解显示了方程系数或原始模型弹性参数的符号依赖性。作为波数与频率的函数，获得了该方程载波部分的频散关系，并发现了其解与声学和光学分支以及带隙之间的关系。这种形式的色散关系被进一步用于描述谐波边界激励对波的调制的数值结果。

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Boundary excitation of nonlinearly modulated bending strain waves in a metamaterial

A non-linear modulation of bending waves in a metamaterial mass-in-mass lattice model is studied. Various kinds of non-linear wave modulation are obtained using a harmonic boundary excitation. It is shown, that these waves can be described by an asymptotic simplification of the equations of motion resulting in a non-linear modulation equation for the displacements. Exact periodic traveling wave solutions to the equation demonstrate a dependence on the sign of the equation coefficients or the elastic parameters of the original model. Dispersion relation for the carrier part of the solution is obtained as a function of wave number versus frequency, it is found how its solutions relate to the acoustic and optic branches and the band gap. This form of the dispersion relation is further used for a description of numerical results on the wave modulation by a harmonic boundary excitation.

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来源期刊

International Journal of Non-Linear Mechanics 物理-力学

CiteScore

5.50

自引率

9.40%

发文量

192

审稿时长

67 days

期刊介绍： The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear. The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas. Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.