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This work is concerned with the influence of corrugated surfaces on waves diffracted from an object in an elastic layer. A boundary value problem is formulated to simulate an anti-plane problem for a harmonic load acting on the upper surface of the layer. By using the boundary integral equation method and the perturbation technique, the considered problem is reduced to a pair of integral equations. By constructing the Green’s function, the scattering problem in a one-mode frequency range is solved. To check the validity of the proposed technique, several numerical examples for different geometrical shapes of the corrugated bottom are presented.

In this work, we have investigated the scattered elastic waves from an object in a system consisting of an elastic layer above a fluid half-space. A time-harmonic load is applied upon the upper boundary surface, while the object is free of stresses. By constructing the corresponding Green's functions, a coupled system of boundary integral equations (BIE) over the contour of the object is formulated. The scattered waves are obtained by using the collocation technique which reduced the BIE to a system of linear algebraic equations. The results are compared with the case without the fluid to show the influence of the fluid pressure on the scattered waves. Numerical examples are carried to demonstrate the scattered waves from an object in different geometrical shapes. K E Y W O R D S boundary integral equations, elastic-fluid layered medium, elastic waves, Green's functions, scattering theory Z Angew Math Mech. 2019;99:e201800054.

This study investigates the effect of mechanical load and electric voltage on the scattering waves of a buried object in a piezoelectric layer, added to that, the study examines the detection of the buried object through its scattering surface waves. The procedure of the study includes two cases which include two steps each. During step 1 of case 1, the researchers applied a periodic mechanical load upon layer containing an elliptic void, where the size and location are predetermined. A system of coupled boundary integral equations utilizing the generalized Green’s identity and the reciprocal work theorem is formulated. The boundary element method supported by Green’s functions was employed to solve the formulated integral equations. Hence, the deformation and electric potential over the object’s contour are identified. Step 2 examined optimization problem to identify the object’s parameters, i.e., its size and location, by minimizing a structure of discrepancy functional. The quasi-Newton iterative method and the Genetic Algorithm (GA) are used for solving the inverse problem. Case 2 of the study examined the effect of electric voltage on the scattering waves of a buried object in the piezoelectric layer. The procedures of case 1 are administered to case 2 to compare the accuracy of detection results in both cases of the study. A series of practical examples are presented with random noisy data to compare the effect of such loads on the process of detection. The results indicate that using the mechanical load in detecting buried object is clearly accurate compared to voltage load detection.