The traditional integer order model cannot well describe the complex mechanical behavior of viscoelastic materials, so the fractional derivative is proposed to model the constitutive relationship of viscoelastic materials. The value of the fractional order of the fractional viscoelastic model is vital to the application. This paper proposes a guided wave technology for determining the fractional order of a viscoelastic multilayered cylinder by using the cement grouted resin anchor bolt as an example. The wave differential equation is derived in terms of the Weyl definition of fractional order derivatives and the Kelvin-Voigt viscoelastic theory. It is solved by virtue of the Legendre orthogonal polynomial method. The dispersion and attenuation curves of guided waves are obtained. Meanwhile, the influence of the fractional order on the dispersion curve is analyzed to provide theoretical guidance for the experiment. By comparing and correcting the experimental and theoretical results, the fractional order that makes the experimental attenuation coefficient equal to the theoretical one can be determined, which makes the guided wave attenuation characteristics of the viscoelastic material can be described theoretically more accurately.

中文翻译：

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利用导波技术确定水泥灌浆树脂锚栓中层状粘弹性材料的分数阶数


传统的整数阶模型不能很好地描述粘弹性材料复杂的力学行为，因此提出了分数阶导数来模拟粘弹性材料的本构关系。分数阶粘弹性模型的分数阶数值对于应用至关重要。本文以水泥灌浆树脂锚固螺栓为例，提出了一种用于确定粘弹性多层圆柱体分数阶数级的导波技术。波动微分方程是根据分数阶导数的 Weyl 定义和 Kelvin-Voigt 粘弹性理论推导的。它是通过 Legendre 正交多项式方法解决的。得到导波的色散和衰减曲线。同时，分析了分数阶数对色散曲线的影响，为实验提供理论指导。通过对实验结果和理论结果的比较和修正，可以确定使实验衰减系数等于理论衰减系数的分数阶数，从而在理论上更准确地描述粘弹性材料的导波衰减特性。