软粘弹性固体的声弹性分析及其在预应力声子晶体中的应用
Acoustoelastic analysis of soft viscoelastic solids with application to pre-stressed phononic crystals
摘要：
橡胶类材料的特定周期性结构的有效动态特性可以通过预应变来调节，从而便于定制声滤波器的设计。虽然非线性粘弹性行为是软固体的主要特征之一，但很少将其纳入此类声子介质的研究中。在这里，我们研究的动态响应的非线性粘弹性固体内的“小对大”声弹性框架，也就是说，我们认为小振幅波的传播叠加在一个大的静态变形。不可压缩软固体的行为所描述的Fung-Simo准线性粘弹性理论（QLV）被认为是。我们推导出的增量方程使用应力样的记忆变量由线性演化方程。因此，我们表明，波色散遵循应变相关的广义麦克斯韦流变学。插图涵盖了均匀拉伸应变下的平面波在QLV Mooney-Rivlin固体中的传播。声弹性理论，然后应用到声子晶体涉及的晶格的空心圆柱体，通过使用一个专用的微扰方法。特别是，结果突出的粘弹性耗散的第一带隙的位置上的影响。我们发现，耗散移动的带隙频率，同时增加了带隙宽度。这些结果对粘弹性软固体在静预应力作用下的实际应用具有指导意义。
英文摘要：
The effective dynamic properties of specific periodic structures involving rubber-like materials can be adjusted by pre-strain, thus facilitating the design of custom acoustic filters. While nonlinear viscoelastic behaviour is one of the main features of soft solids, it has been rarely incorporated in the study of such phononic media. Here, we study the dynamic response of nonlinear viscoelastic solids within a 'small-on-large' acoustoelasticity framework, that is we consider the propagation of small amplitude waves superimposed on a large static deformation. Incompressible soft solids whose behaviour is described by the Fung-Simo quasi-linear viscoelasticy theory (QLV) are considered. We derive the incremental equations using stress-like memory variables governed by linear evolution equations. Thus, we show that wave dispersion follows a strain-dependent generalised Maxwell rheology. Illustrations cover the propagation of plane waves under homogeneous tensile strain in a QLV Mooney-Rivlin solid. The acoustoelasticity theory is then applied to phononic crystals involving a lattice of hollow cylinders, by making use of a dedicated perturbation approach. In particular, results highlight the influence of viscoelastic dissipation on the location of the first band gap. We show that dissipation shifts the band gap frequencies, simultaneously increasing the band gap width. These results are relevant to practical applications of soft viscoelastic solids subject to static pre-stress.
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