Mechanical stress alters the velocity of acoustic waves, a phenomenon known as AE ͑acoustoelastic͒ effect, which is of particular importance for the wave propagation in layered heterostructures. In order to calculate the AE effect of layered systems in the presence of stress we extended the transfer-matrix method for acoustic wave propagation by considering the change of the density, the influence of residual stress, and the modification of the elastic stiffness tensor by residual strain and by third-order constants. The generalized method is applied to the calculation of the angular dispersion of the AE effect for transverse bulk modes and surface acoustic waves on the Ge͑001͒ crystal cut. The AE effect is found to depend significantly on the propagation direction and can even change sign. The maximum velocity change occurs for transversally polarized waves propagating parallel to the ͓110͔ direction. For the layered Ge/Si͑001͒ system the AE effect is investigated for Love modes propagating in the ͓100͔ and ͓110͔ directions. The AE effect increases rapidly with increasing layer thickness and reaches almost its maximum value when the wave is still penetrating into the unstressed substrate. For higher-order Love modes the increase of the AE effect is even steeper and, furthermore, can reach higher values.
Theory and algorithm for the acoustic boundary element solver will be described. The solver represents the core of the package AField (acronym for acoustical field) and can be used for getting fast and stable solutions for huge as well as for small boundary elements models on PCs under Windows. The boundary element solver includes an early proposed GMRES iterative linear system solver (which can be used for big and huge models) and several traditional linear system solvers (for small and medium models). Implementation of the Burthon and Miller regularization method for constant boundary elements will be discussed. Approximations in proposed boundary element solver and their influence on solution errors are investigated. Results for several models are included. Several possibilities of Afield package are illustrated.
We investigated the influence of stress on the acoustic wave propagation in single crystalline heterostructures using a transfer matrix method. Both Rayleigh-type and Sezawa modes exhibit an acoustoelastic anomaly, where the stress-induced change of the phase velocity is maximum for finite film thicknesses, considerably smaller than the acoustic wavelength. For Ge/Si͑001͒ compressed by 1 GPa the velocity shift of Sezawa modes reaches exceptionally high values of about 2%. These results demonstrate the importance of stress effects on the determination of elastic constants of thin film heterostructures.
The sound radiation from vibrating structures is studied using an iterative boundary-element method. The starting point is a self-adjoint formulation of the Helmholtz integral equation. The generalized minimum residual method (GMRES) is used for solving the corresponding system of equations. Three aspects of the method are investigated. First, the accuracy of the iterative solver is checked by performing multipole error tests: The body is forced to vibrate with the corresponding surface normal velocity of a multipole. Hence, the radiated sound field is analytically known and can be used for determining the exact error caused by the boundary-element solver. Second, instabilities at irregular frequencies are suppressed by combining the iterative solver with a special variant of the CHIEF method, where the total boundary of the body is retracted to an auxiliary surface lying totally within the interior of the structure. CHIEF points can be placed on such an auxiliary surface. The effectiveness of this combined dual-layer GMRES–CHIEF approach and of the Burton–Miller method will be compared. Third, the radiation from a structure with mixed boundary conditions will be investigated. One part of the surface is coated with an absorbing impedance, another part is vibrating with a prescribed normal velocity.
The parameters of diffraction tomography methods for inhomogeneity reconstruction is investigated. For a two-dimensional case with linear multi-element transceiver one single frequency and two multi-frequency measurement schemes are introduced. For these schemes the data regions in the spatial frequency domain of inhomogeneities function are presented. The new two-stage approach is developed for resolution investigation and image quality estimation. In the first stage, it is proposed to find the resolution for ideal measurement conditions (infinite measurement aperture, ideal transducers). Then in the second stage for real measurement conditions, it is enough to determine only the degradation factor which is calculated for all measurement schemes dependent on measurement parameters. For examination of this approach also the images for complicated inhomogeneity model are calculated. It is shown that resolution and point spread functions cannot fully describe image quality, especially for complicated data regions in the spatial frequency domain of the inhomogeneities function. Many numerical examples are presented.
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