Gusev Vitalyi, Aleshin Vladislav
Laboratoire de Physique de l'Etat Condensé, UPRESA-CNRS 6087, Faculté des Sciences, Ecole Nationale Supérieure d'Ingénieurs du Mans, Université du Maine, 72085 Le Mans, France.
J Acoust Soc Am. 2002 Dec;112(6):2666-79. doi: 10.1121/1.1517252.
Nonlinear wave propagation in materials, where distribution function of mesoscopic mechanical elements has very different scales of variation along and normally to diagonal of Preisach-Mayergoyz space, is analyzed. An evolution equation for strain wave, which takes into account localization of element distribution near the diagonal and its slow variation along the diagonal, is proposed. The evolution equation provides opportunity to model propagation of elastic waves with strain amplitudes comparable to and even higher than characteristic scale of element localization near Preisach-Mayergoyz space diagonal. Analytical solutions of evolution equation predict nonmonotonous dependence of wave absorption on its amplitude in a particular regime. The regime of self-induced absorption for small-amplitude nonlinear waves is followed by the regime of self-induced transparency for high-amplitude waves. The developed theory might be useful in seismology, in high-pressure nonlinear acoustics, and in nonlinear acoustic diagnostics of damaged and fatigued materials.
分析了材料中的非线性波传播，其中介观力学元件的分布函数在Preisach-Mayergoyz空间的对角线方向及其垂直方向上具有非常不同的变化尺度。提出了一个应变波的演化方程，该方程考虑了元件分布在对角线附近的局部化及其沿对角线的缓慢变化。该演化方程为模拟应变幅度与Preisach-Mayergoyz空间对角线附近元件局部化特征尺度相当甚至更高的弹性波传播提供了机会。演化方程的解析解预测了在特定情况下波吸收对其幅度的非单调依赖性。小振幅非线性波的自感应吸收状态之后是高振幅波的自感应透明状态。所发展的理论可能在地震学、高压非线性声学以及受损和疲劳材料的非线性声学诊断中有用。
