标题： 软弹性层合板在有限磁变形下的非线性色散波 显示英文标题

标题： Nonlinear dispersive waves in soft elastic laminates under finite magneto-deformations

摘要： 层状介质可用作声学滤波器，仅允许特定频率的波传播。 在软磁活性层压板中，剪切波禁带（即剪切波无法传播的频率区间）可在制造后通过利用磁弹性耦合进行调整。 在本研究中，通过均质化理论重新研究了磁活性分层介质中剪切波传播的控制，并扩展到中等振幅的非线性波。 基于先前的研究，层压板通过一种修正的硬磁材料理论进行建模，该理论的总柯西应力是对称的，不可压缩弹性响应为广义neo-Hookean类型（包括Yeoh、Fung-Demiray和Gent材料）。 在某些简化假设下，使用渐近均质化方法推导出一个具有三次非线性的非线性色散波方程。 顺便提一下，得到了描述此类层压板的有效应变能函数。 非线性和波色散的综合效应导致孤波的形成，这些孤波通过均质化波方程和后者的一个修改的Korteweg-de Vries（mKdV）近似进行分析。 将mKdV方程与冲击问题的直接数值模拟进行比较，并探讨了这些结果的各种后果。 特别是，我们展示了孤波的速度上限可以通过改变施加的磁场或修改微结构的特性来调整。 显示英文摘要

摘要： 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.