Determination of fractional order for layered viscoelastic materials in cement grouted resin anchor bolt by using guided wave technology

作者：Zhi Li, Jiangong Yu, Yanwei Liu, Xiaoming Zhang, Bo Zhang, L. Elmaimouni · 发表于：Mechanical Systems and Signal Processing · 年份：2024 · DOI：10.1016/j.ymssp.2024.112101 · 被引用次数：5 · 研究领域：Ultrasonics and Acoustic Wave Propagation、Acoustic Wave Resonator Technologies、Numerical methods in engineering

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.