Touré Ibrahima, Bilodeau Maxime, Quaegebeur Nicolas
Dept of Mechanical Engineering, CRASH-UdeS, Université de Sherbrooke, 2500 Boul de l'Université, Sherbrooke, J1K2R1, Québec, Canada.
Dept of Mechanical Engineering, CRASH-UdeS, Université de Sherbrooke, 2500 Boul de l'Université, Sherbrooke, J1K2R1, Québec, Canada.
Ultrasonics. 2025 Oct;154:107670. doi: 10.1016/j.ultras.2025.107670. Epub 2025 May 21.
This study investigates the transmission and reflection of axisymmetric longitudinal L(0,n) modes in miniaturized cylindrical waveguides. The theoretical framework developed herein focuses on the analysis of the propagation of longitudinal modes within a homogeneous, elastic, and isotropic cylindrical waveguide with a varying cross-section. The novelty of this paper is found in the energy calculations and the consideration of higher-order modes for accurately describing the transmission and reflection coefficients at waveguide transitions. A 2D axisymmetric Finite Element Method (FEM) is used to calculate these coefficients based on the modal energy of propagating modes across different frequencies. The influence of geometrical and material properties, along with modal density, is examined numerically. Results demonstrate that optimal transmission occurs when the wavenumber ratio of propagating modes in connected waveguides is an integer, leading to effective coupling. Experimental validation on steel rods with diameters from 4 mm to 0.8 mm shows strong agreement with numerical results. It is observed that the L(0,1) mode around 1 MHz is the most suitable mode for efficient transmission between the waveguides. In contrast, the higher-order modes (L(0,2) around 1.25 MHz, L(0,3) between 1.3 and 1.5 MHz, and L(0,4) from 2.25 MHz) exhibit weak or irregular transmission, with more pronounced reflection behaviors, indicating that they are not optimal for efficient transmission in this configuration. These findings underline the importance of an optimized geometric transition in enhancing the transmission efficiency in such miniaturized waveguides.
本研究探讨了轴对称纵向L(0,n)模式在小型圆柱形波导中的传输与反射。本文所建立的理论框架着重分析纵向模式在具有变化横截面的均匀、弹性且各向同性圆柱形波导内的传播。本文的新颖之处在于能量计算以及对高阶模式的考虑，以准确描述波导过渡处的传输和反射系数。基于不同频率下传播模式的模态能量，采用二维轴对称有限元方法（FEM）来计算这些系数。通过数值方法研究了几何和材料特性以及模态密度的影响。结果表明，当相连波导中传播模式的波数比为整数时，会出现最佳传输，从而实现有效耦合。对直径从4毫米到0.8毫米的钢棒进行的实验验证与数值结果高度吻合。据观察，1兆赫兹左右的L(0,1)模式是波导间高效传输最适合的模式。相比之下，高阶模式（1.25兆赫兹左右的L(0,2)、1.3至1.5兆赫兹之间的L(0,3)以及2.25兆赫兹以上的L(0,4)）表现出较弱或不规则的传输，反射行为更为明显，这表明它们在此配置下并非高效传输的最佳选择。这些发现强调了优化几何过渡对于提高此类小型波导传输效率的重要性。
