Keywords: Ultrasonic, Greens Function, Finite Element Method, Transducer, Steel

ABSTRACT

A separation approach in connection with integral transform and point source synthesis is a powerful tool to simulate the transducer generated sound field in layered media with curved interfaces. In a homogeneous isotropic medium the Green's functions for harmonic and transient excitations are given.

The description of the propagation of elastic waves emitted by a transducer into a solid is of fundamental importance in many applications of ultrasonics. Simulation calculation minimize the expense for the development of transducers. Because the sound field in the specimen depends on the parameters of the probe and the parameters of all layers passed by the sound field the wave propagation has to be modeled in the different layers. In all cases with curved interfaces between the different layers (focused probes, test of shafts) sophisticated three-dimensional geometric problems arise.

Because the full numerical appraoches such as Finite Difference and Finite Element methods are very expensive in computation time, integral transform methods have been proposed to calculate the transducer radiated field . The integral transform methods are very efficient because there is an analytical solution of the differential equation in the transformed domain. This is especially true if one of the inverse transformations can be treated analytical. In the transient field of a circular or rectangular transducer in a solid half-space and in the transient field radiated by a linear array into an immersed solid is calculated. These approaches, however, are restricted to plane interfaces. Here a separation approach is proposed for a full three-dimensional problem.

The separation method was applied successfully to obtain a calculation program for design of ultrasonic transducers with harmonic excitation. It will be extended to calculate the transient signal in layered media. This is possible by a direct calculation of the transient Green's function or by a superposition of harmonic waves in connection with a Fraunhofer approximation, which may be very effcient for exciting signals with a small bandwidth.