黏弹性正交各向异性空心圆柱中纵向导波的传播

《复合材料学报》优先在线发表论文。

摘  要：基于线性三维弹性理论和Kelvin-Voigt模型，采用勒让德正交多项式展开法推导了黏弹性正交各向异性空心圆柱中纵向导波的波动方程，数值求解了波动方程并阐述了相关方程的含义。首先计算了大径厚比下黏弹性管的相速度频散曲线和衰减曲线，并与已发表文献的结果进行了对比，验证了程序的正确性，并进一步计算了低阶纵向导波的位移分布和应力分布曲线，验证了方法的可靠性。然后利用方程的解耦特性，分别求解了不同径厚比、不同黏性常数下纵向模态和扭转模态的频散和衰减曲线，研究了径厚比和黏性常数效应对两种模态的影响。最后针对扭转模态导波，研究了材料相关黏弹性常数对其频散特性和衰减特性的影响。

关键词：正交多项式；纵向导波；黏弹性；频散曲线；衰减曲线

Abstract: Based on the linear three-dimensional elastic theory and Kelvin-Voigt model, the wave equation of longitudinal guided waves in the viscoelastic anisotropic hollow cylinder was derived by using the Legendre polynomial expansion method, and the decoupled wave equation was solved numerically while the implications of the related equa-tions were fully expounded. Firstly, in order to validate our program, the dispersion curves and attenuation curves of the viscoelastic hollow cylinder with a large ratio of radius to thickness were calculated in comparison with the available date. Meanwhile, the displacement distribution and stress distribution were further calculated for the reliability of the method. Then, the influence of the ratio of radius to thickness and the effect of viscous constants were investigated respectively, which contains the dispersion curves and attenuation curves of longitudinal modes and torsional ones. Finally, the effects of viscoelastic parameters to the torsional waves were illustrated.

Keywords: orthogonal polynomials; longitudinal guided waves; viscoelastic; dispersion curve; attenuation curve

作者：李思宇等，上海理工大学 光电信息与计算机工程学院，上海

通讯作者：刘宏业，上海理工大学 光电信息与计算机工程学院，上海

全文详见中国知网学术期刊优先数字出版。