This paper deals with the elastodynamic finite integration technique for axisymmetric wave propagation in a homogeneous and heterogeneous cylindrical medium ͑CEFIT͒. This special variant of a finite difference time domain ͑FDTD͒ scheme offers a suitable method to calculate real three-dimensional problems in a two-dimensional staggered grid. In order to test the accuracy of the numerical CEFIT code, problems for which analytical solutions are available are presented. These solutions involve wave propagation in an elastic plate, the scattering of a plane longitudinal wave by a spherical obstacle, and ultrasound generation by a thermoelastic laser source. For the latter problem experimental results are included. The CEFIT code also allows the treatment of more complicated problems. Further possible applications are the investigation of elastic waves generated in an acoustic microscope, the simulation of impact-echo measurements in multi-layer systems, axisymmetric wave propagation in arbitrary bodies of revolution, the calculation of elastic wave fields of longitudinal wave transducers with a circular aperture, and the investigation of multi-layer models for particulates.
The Elastodynamic Finite Integration Technique (EFIT), originally developed by Fellinger et al., 1-3 represents a stable and efficient numerical code to model elastic wave propagation in linearly-elastic isotropic and anisotropic, homogeneous and heterogeneous as well as dissipative and nondissipative media. In previous works, the FIT discretization of the basic equations of linear elasticity, Hooke's law and Cauchy's equation of motion, was exclusively carried out in Cartesian coordinates. For problems in cylindrical geometries it is more suitable to use cylindrical coordinates. By that, axisymmetric problems can be treated in a two-dimensional staggered grid in the r, z-plane. The paper presents an EFIT version for axisymmetric problems in cylindrical coordinates called Cylindrical EFIT (CEFIT). After demonstrating the accuracy of the numerical code by a comparison between simulation results and analytical solutions, different examples of application are given. These examples include modeling of sound fields of ultrasonic transducers, thermoelastic laser sources, geophysical borehole probes, impact-echo measurements in layered media, and load simulations of the European Spallation Source (ESS) mercury target.
Many ultrasonic nondestructive testing applications have cylindrical geometries. Examples involve the excitation of ultrasound by cylindrical piezoelectic probes or by laser, x rays, electron beams [A. C. Tam, Rev. Mod. Phys. 58, 381–431 (1986)], or ion beams [L. Sulak et al., Nucl. Instrum. Methods 161, 203–217 (1979)]. Thus, calculations of cylindrical wave propagation are important for a better understanding and interpretation of many testing situations. This paper deals with the AFIT Code or finite volume method for numerical simulation of sound propagation in fluids adapted to cylindrical geometries (CAFIT). A comparison is made with standard difference-equations techniques also utilized for cylindrical geometries. Two examples are dealt with: (1) The sound generation by a high energy beam of heavy ions stopping in water; (2) the multimode sound propagation in a medical doppler injection device excited by a disk probe.
Measurement results on the Damping Loss Factor (DLF) and Coupling Loss Factor (CLF) between two steel plates is presented for 19 different junction types. The junctions involve joining technologies, such as line welding, point welding, bolting, riveting, gluing or their combinations, and with varying spacing between the junction points and the angle between the plates. From the measurement results, the DLF and CLF values were calculated by the Power Injection Method for the purposes of being applied in Statistical Energy Analysis simulations. Four excitations were applied at each subsystem by impact hammer, while the response was recorded at sixteen response points at each subsystem. The measured CLF values were compared to each other from various aspects. Data were compared to the results obtained from SEA simulations by using the built-in analytical formulas. In general, good comparison was observed, although the results appeared to be somewhat dependent on the frequency band. Finally, it was examined whether replacing the DLF values with data obtained for an uncoupled flat plate, as well replacing the CLF values with data from analytical formulas leads to acceptable accuracy of the simulation results.
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