微扰法研究薄膜负载对Lamb波传播的影响

Study to influence of thin layer loading on propagation of Lamb waves using perturbation method

摘要: 许多Lamb波传感应用中,板周围环境的微小变化即待检测的外部微小变化,可看作是对于薄板中Lamb波的自由边界条件的微扰。本文选择合适的微扰边界条件,推导了适用于多种薄膜负载的各向同性板中弹性波传播的一般特征方程,应用此一般特征方程讨论了传感应用中常见的液体薄膜负载、各向同性固体薄膜负载对薄板Lamb波传播的影响,并与精确理论进行了比较,同时本文还用此方法分析了传感中常见而且精确理论计算较为复杂的粘滞液层负载和固体复合层负载的情况。最后我们对负载液层薄膜时的情况进行了初步实验研究,验证了我们的微扰近似理论。

Abstract: In many Lamb wave sensing applications,the changes of the environment of the plate to be detected are considered as small perturbations to the free boundary conditions of free Lamb waves ina thin plate.General dispersion equations for Lamb waves in a plate with proper perturbed boundary conditions are derived.The equations are then applied to various sensing applications including viscous liquid layer loading and thin solid layer loading.Numerical solutions of the equations show that the phase velocity of Lamb waves changes linearly with the boundary impedance defined in this paper.