利用波的反射和透射系数确定波导结构不连续点的动力学参数

截面均匀的梁、管道等细长结构在工程中有着广泛应用，这类结构具有沿结构伸展方向长距离传递机械波的波导特性，称为波导结构。此类结构通常包含联结件、支撑件等不连续点，这些不连续点的动力学参数，如质量，刚度，阻尼等，是波导结构动力学建模的关键参数。由于实际不连续点结构复杂，往往需要用实验方法确定其动力学参数。基于行波分析方法，本文建立了波导结构不连续点的动力学参数与不连续点处的反射、透射系数之间的一般性解析关系式。根据此关系式，提出了通过测量有效频率范围内的不连续点处的反射、透射系数，结合最优化曲线拟合，进行不连续点动力学参数识别的方法。文中以无限长梁附加质量块不连续点为例，用该方法测量附加质量块的质量和转动惯量参数。蒙特卡罗法仿真结果表明，该方法受测量噪声的影响较小。用该方法对不同附加质量块进行参数识别的实验结果表明，质量误差在5%以内，转动惯量误差在15%以内，测量准确度与所选择的识别频率范围有关。

Dynamic parameters identification of waveguides using reflection and transmission coefficients

Thin and long structures like uniform beams and pipes are widely used in many engineering fields. These structures usually act as waveguides, conveying vibrational energy away from the source of excitation via wave propagation through the structure. Built-up beam or piping systems often comprise many joints or discontinuities in the form of flanges, hangers, supports, valves, pumps and changes in section. Dynamically, these discontinuities contribute stiffness, inertia and damping and can dramatically alter the response of the system. A robust technique for parametric joint identification would benefit many areas of dynamic modeling. Because of the complexity of discontinuities in practice, experiments are normally introduced to determine their dynamic parameters. Based on the wave propagation method, this paper presents a general analytical relationship between the dynamic parameters of a discontinuity and the reflection and transmission coefficients of the discontinuity. This relationship can be adopted to identify the dynamic parameters of the discontinuity by using the optimization curve-fit method. The case study, which involves an infinite uniform beam with a mass-like discontinuity formed by an attached steel block, is proposed to identify the dynamic parameters of the discontinuity through the wave reflection and transmission coefficients. The Monte Carlo simulation is applied to investigate the influence of the simulated measurement noise on the reflection coefficients. The experimental results show that the accuracy of the identified parameters has close relation with the identification frequency range and the errors of the identified mass and moment of inertia are within 5% and 15%, respectively.