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

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.