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首页> 外文期刊>The Journal of the Acoustical Society of America >Connecting the grain-shearing mechanism of wave propagation in marine sediments to fractional order wave equations
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Connecting the grain-shearing mechanism of wave propagation in marine sediments to fractional order wave equations

机译：将海洋沉积物中波传播的切变机制与分数阶波动方程联系起来

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摘要

The characteristic time-dependent viscosity of the intergranular pore-fluid in Buckingham's grain-shearing (GS) model [Buckingham, J. Acoust. Soc. Am. 108, 2796-2815 (2000)] is identified as the property of rheopecty. The property corresponds to a rare type of a non-Newtonian fluid in rheology which has largely remained unexplored. The material impulse response function from the GS model is found to be similar to the power-law memory kernel which is inherent in the framework of fractional calculus. The compressional wave equation and the shear wave equation derived from the GS model are shown to take the form of the Kelvin-Voigt fractional-derivative wave equation and the fractional diffusion-wave equation, respectively. Therefore, an analogy is drawn between the dispersion relations obtained from the fractional framework and those from the GS model to establish the equivalence of the respective wave equations. Further, a physical interpretation of the characteristic fractional order present in the wave equations is inferred from the GS model. The overall goal is to show that fractional calculus is not just a mathematical framework which can be used to curve-fit the complex behavior of materials. Rather, it can also be derived from real physical processes as illustrated in this work by the example of GS. (C) 2016 Acoustical Society of America.
机译：在白金汉的颗粒剪切（GS）模型中，颗粒间孔隙流体的特征随时间变化的粘度[Buckingham，J. Acoust。 Soc。上午。 108，2796-2815（2000）]被识别为流变仪的属性。该性质对应于流变学中非牛顿流体的稀有类型，至今仍未开发。 GS模型的物质冲激响应函数被发现类似于分数微积分框架中固有的幂律记忆核。 GS模型导出的压缩波方程和切变波方程分别采用开尔文-沃格分数阶导数波动方程和分数扩散波方程的形式表示。因此，在从分数框架获得的色散关系与从GS模型获得的色散关系之间进行类比，以建立各个波动方程的等价关系。此外，可以从GS模型推断出波动方程中存在的特征分数阶的物理解释。总体目标是证明分数演算不仅仅是可以用于曲线拟合材料复杂行为的数学框架。相反，它也可以从真实的物理过程中得出，如GS的示例所示。 （C）2016年美国声学学会。

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