有限磁变形下软弹性层合板的非线性色散波

IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY
Harold Berjamin, Stephan Rudykh
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引用次数: 0

摘要

层状介质可以用作声波过滤器,只允许某些频率的波传播。在软磁有源层合板中,可以利用磁弹性耦合在制作后调节剪切波带隙(即剪切波不能传播的频率间隔)。在本研究中,利用均匀化理论重新研究了磁活性层状介质中剪切波传播的控制,并将其推广到中等振幅的非线性波。在早期工作的基础上,通过修正的硬磁材料理论对这些层进行建模,其中总柯西应力是对称的,不可压缩弹性响应是广义的新hookean类型(包括Yeoh, Fung-Demiray和Gent材料)。在一定的简化假设下,利用渐近均匀化,导出了具有三次非线性的非线性色散波动方程。同时,得到了描述这种层合板的有效应变能函数。非线性和波色散的综合作用有助于孤波的形成,使用均匀波动方程和后者的改进Korteweg-de Vries (mKdV)近似来分析孤波。将mKdV方程与撞击问题的直接数值模拟进行了比较,并探讨了这些结果的各种后果。特别地,我们证明了孤波速度的上限可以通过改变外加磁场或通过改变微观结构的性质来调整。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Nonlinear dispersive waves in soft elastic laminates under finite magneto–deformations
Layered media can be used as acoustic filters, allowing only waves of certain frequencies to propagate. In soft magneto-active laminates, the shear wave band gaps (i.e., the frequency intervals for which shear waves cannot propagate) can be adjusted after fabrication by exploiting the magneto-elastic coupling. In the present study, the control of shear wave propagation in magneto-active stratified media is revisited by means of homogenisation theory, and extended to nonlinear waves of moderate amplitude. Building upon earlier works, the layers are modelled by means of a revised hard-magnetic material theory for which the total Cauchy stress is symmetric, and the incompressible elastic response is of generalised neo-Hookean type (encompassing Yeoh, Fung-Demiray, and Gent materials). Using asymptotic homogenisation, a nonlinear dispersive wave equation with cubic nonlinearity is derived, under certain simplifying assumptions. In passing, an effective strain energy function describing such laminates is obtained. The combined effects of nonlinearity and wave dispersion contribute to the formation of solitary waves, which are analysed using the homogenised wave equation and a modified Korteweg–de Vries (mKdV) approximation of the latter. The mKdV equation is compared to direct numerical simulations of the impact problem, and various consequences of these results are explored. In particular, we show that an upper bound for the speed of solitary waves can be adjusted by varying the applied magnetic field, or by modifying the properties of the microstructure.
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来源期刊
International Journal of Engineering Science
International Journal of Engineering Science 工程技术-工程:综合
CiteScore
11.80
自引率
16.70%
发文量
86
审稿时长
45 days
期刊介绍: The International Journal of Engineering Science is not limited to a specific aspect of science and engineering but is instead devoted to a wide range of subfields in the engineering sciences. While it encourages a broad spectrum of contribution in the engineering sciences, its core interest lies in issues concerning material modeling and response. Articles of interdisciplinary nature are particularly welcome. The primary goal of the new editors is to maintain high quality of publications. There will be a commitment to expediting the time taken for the publication of the papers. The articles that are sent for reviews will have names of the authors deleted with a view towards enhancing the objectivity and fairness of the review process. Articles that are devoted to the purely mathematical aspects without a discussion of the physical implications of the results or the consideration of specific examples are discouraged. Articles concerning material science should not be limited merely to a description and recording of observations but should contain theoretical or quantitative discussion of the results.
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