超弹性和粘弹性框架中的非线性不可压缩剪切波模型及其在爱波中的应用

IF 2.1 3区 物理与天体物理 Q2 ACOUSTICS Wave Motion Pub Date : 2024-11-01 DOI:10.1016/j.wavemoti.2024.103434
Shawn Samuel Carl McAdam, Samuel Opoku Agyemang, Alexei Cheviakov
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引用次数: 0

摘要

本文提出了描述不可压缩超弹性材料剪切位移的一般方程,该方程适用于任意形式的应变能密度函数,并将其应用于描述在具有不同机械特性的材料之间的界面上传播的非线性洛夫型波。该模型适用于一大类超粘弹性材料。对于 Murnaghan 构成模型,剪切波方程包含三次和五次微分多项式项,其中包括粘弹性贡献,即包含材料位移混合导数 uxxt 的分散项。对波在双层固体体中传播进行了全 (2+1) 维数值模拟,并根据源位置和层的机械特性进行了分析。对界面非线性洛夫波和自由上表面剪切波进行了跟踪;结果表明,在全非线性情况下,界面波和表面波的可变波速一般满足线性洛夫波存在条件 c1<v<c2,同时在大时间内趋向于较大的材料波速 c1 或 c2。
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Nonlinear incompressible shear wave models in hyperelasticity and viscoelasticity frameworks, with applications to Love waves
General equations describing shear displacements in incompressible hyperelastic materials, holding for an arbitrary form of strain energy density function, are presented and applied to the description of nonlinear Love-type waves propagating on an interface between materials with different mechanical properties. The model is valid for a broad class of hyper-viscoelastic materials. For the Murnaghan constitutive model, shear wave equations contain cubic and quintic differential polynomial terms, including viscoelasticity contributions in terms of dispersion terms that include mixed derivatives uxxt of the material displacement. Full (2+1)-dimensional numerical simulations of waves propagating in the bulk of a two-layered solid are undertaken and analysed with respect to the source position and mechanical properties of the layers. Interfacial nonlinear Love waves and free upper surface shear waves are tracked; it is demonstrated that in the fully nonlinear case, the variable wave speed of interface and surface waves generally satisfies the linear Love wave existence condition c1<v<c2, while tending to the larger material wave speed c1 or c2 for large times.
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来源期刊
Wave Motion
Wave Motion 物理-力学
CiteScore
4.10
自引率
8.30%
发文量
118
审稿时长
3 months
期刊介绍: Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics. The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.
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