Scattering of Surface Acoustic Waves from an Elastic Plate Attached to a Half-Space with a Viscous Couplant

The results presented here are part of a study of the interaction between an electro-mechanical transducer plate element and wavelengths in the test structure that are comparable to the plate dimensions. The steady time-harmonic problem is reduced to a system of singular integral equations for determining the tractions generated at the interface between the plate and half-space where a thin viscous couplant is applied. This system is solved numerically for various values of couplant viscosity and incident wavelength. Graphical results for interface tractions and reflected power are presented. INTRODUCTION We are interested in the interaction between electro-mechanical transducers and the elastic waves in a test medium in cases when the wavelengths are comparable to the dimensions of the transducer and the propagation vector is not normal to the interface. The ultimate goal of this NSF funded project at Berkeley is to predict what mechanical disturbance is input to the transducer from the electrical output signal. As a first step we will try to predict the electrical output given the mechanical input. Under the conditions of interest the mechanical loading is not spatially uniform over the contact face of the transducer. We will therefore need a plate theory for the piezoelectric element with electroded surfaces which can accommodate the kinds of mechanical and electrical boundary conditions that are appropriate to the transducer design and mounting and the electrical circuitry to which it is connected. Such a plate theory has been derived in Bugdayci and Bogy [l]. The work presented here is also only a preliminary part of this project, but here we focus on the purely mechanical problem of determining the interaction of an elastic plate with a half-space. Specifically, we seek to understand the stresses generated between the half-space and plate when a surface wave impinges on the plate that is attached through a viscous couplant. The dependence of these interface stresses on couplant viscosity and the incident wavelength are the primary concern. We also calculate the power of the reflected and transmitted surface waves as a function of these parameters since these quantities can be compared with experiments. The results summarized here are derived in complete detail in Angel [2] and Angel and Bogy [3]. PROBLEM FORMULATION AND REDUCTION TO INTEGRAL EQUATIONS Figure l depicts the plane strain problem of a surface wave impinging on an elastic plate that is in contact through a viscous couplant with the half-space. All the physical parameters of the problem are shown. 248 Surface Wove AR,w, u0 X!~ ~~.a,' p' f[I =:::!~:::31-· x' _,-I I I r--2 b ____, 1 ~ Viscous Couplanl K ~~~~------.-~~--------~-----x~