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Existing ultrasonic stress evaluation methods utilize the acoustoelastic effect for bulk waves propagating in volume, which is unsuitable for a surface treated material, possessing a significant variation in material properties with depth. With knowledge of nonlinear elastic parameters – third-order elastic constants (TOEC) close to the surface of the sample, the acoustoelastic effect might be used with surface acoustic waves. This work is focused on the development of an independent method of TOEC measurement using the effect of nonlinear surface acoustic waves scattering – i.e. the effect of elastic waves interaction in a nonlinear medium.
In this paper, the possible three wave interactions of surface guided waves and bulk waves are described and formulae for the efficiency of harmonic generation and mode mixing are derived. A comparison of the efficiency of surface waves scattering in an isotropic medium for different interaction types is carried out with the help of nonlinear perturbation theory. First results for surface and bulk wave mixing with known second- and third-order elastic constants are shown.
The growing complexity in RF front-ends, which support carrier aggregation and a growing number of frequency bands, leads to tightened nonlinearity requirements in all sub-components. The generation of third order intermodulation products (IMD3) are typical problems caused by the non-linearity of SAW devices. In the present work, we investigate temperature compensating (TC) SAW devices on Lithium Niobate-rot128YX. An accurate FEM simulation model [1] is employed, which allows to better understand the origin of nonlinearities in such acoustic devices.
Elastic constants of components are usually determined by tensile tests in combination with ultrasonic experiments. However, these properties may change due to e.g. mechanical treatments or service conditions during their lifetime. Knowledge of the actual material parameters is key to the determination of quantities like residual stresses present in the medium. In this work the acoustic nonlinearity parameter (ANP) for surface acoustic waves is examined through the derivation of an evolution equation for the amplitude of the second harmonic. Given a certain depth profile of the third-order elastic constants, the dependence of the ANP with respect to the input frequency is determined and on the basis of these results, an appropriate inversion method is developed. This method is intended for the extraction of the depth dependence of the third-order elastic constants of the material from second-harmonic generation and guided wave mixing experiments, assuming that the change in the linear Rayleigh wave velocity is small. The latter assumption is supported by a 3D-FEM model study of a medium with randomly distributed microcracks as well as theoretical works on this topic in the literature.
Zerstörungsfreie Verfahren zur Messung von Eigenspannungen erfordern, abhängig vom gewählten Verfahren, die Kenntnis gewisser Kopplungskonstanten. Im Falle von Ultraschallmessverfahren sind das neben den elastischen Konstanten zweiter Ordnung (SOEC) vor allem die Konstanten dritter Ordnung (TOEC). Elastische Konstanten fester, metallischer Bauteile werden in der Regel in Zugversuchen bestimmt. Zur Ermittlung der TOEC werden diese mit Ultraschallmessmethoden kombiniert. Durch äußere Einflüsse, wie etwa mechanische Nachbehandlungen der zu untersuchenden Bauteile können sich diese Konstanten jedoch ändern und müssen folglich direkt am veränderten Material bestimmt werden. Mithilfe von Simulationen wird die Ausbreitung der zweiten Harmonischen und der nichtlinear erzeugten Oberflächenwellen in Wellenmischexperimenten analysiert und der akustische Nichtlinearitätsparameter (ANP) bzw. der Kopplungsparameter aus der Amplitudenentwicklung berechnet. Insbesondere wird untersucht, welchen Einfluss ein gegebenes Tiefenprofil der TOEC auf den ANP hat (Vorwärtsproblem) und inwiefern sich aus den Messungen des ANP auf ein vorliegendes Tiefenprofil der TOEC schließen lässt (inverses Problem). Außerdem wird diskutiert, welchen Einfluss lokale Änderungen der SOEC auf den ANP haben können und wie groß diese Änderungen sein dürfen, um die TOEC dennoch bestimmen zu können. Die Untersuchungen hierzu wurden auf der Basis eines 3D-FEM Modells mit zufällig orientierten Mikrorissen durchgeführt. Die numerischen Rechnungen zeigen dabei auch eine gute Übereinstimmung mit einem aus der Literatur bekannten und für dieses Problem erweiterten, analytischen Modell. Neben der rissinduzierten Nichtlinearität kann bei diesem auch die Gitternichtlinearität berücksichtigt werden.
In the present work, nonlinearities in temperature compensating (TC) SAW devices are investigated. The materials used are LiNbO₃-rot128YX as the substrate and Copper electrodes covered with a SiO₂-layer as the compensating layer. In order to understand the role of these materials for the nonlinearities in such acoustic devices, a FEM simulation model in combination with a perturbation approach is applied. The nonlinear tensor data of the different materials involved in TC-SAW devices have been taken from literature, but were partially modified to fit experimental data by introducing scaling factors. An effective nonlinearity constant is determined by comparison of nonlinear P-matrix simulations to IMD3 measurements of test filters. By employing these constants in nonlinear periodic P-matrix simulations a direct comparison to nonlinear periodic FEM-simulations yields the scaling factors for the material used. Thus, the contribution of different materials to the nonlinear behavior of TC-SAW devices is obtained and the role of metal electrodes is discussed in detail.
The existence of acoustic waves with displacements localized at the tip of an isotropic elastic wedge was rigorously proven by Kamotskii, Zavorokhin and Nazarov. This proof, which is based on a variational approach, is extended to rectangular anisotropic wedges. For two high-symmetry configurations of rectangular edges in elastic media with tetragonal symmetry, a criterion is derived that allows identifying the boundary between the regions of existence for wedge modes of even and odd symmetry in regions of parameter space, where even- and odd-symmetry modes do not exist simultaneously. Furthermore, rectangular edges with non-equivalent surfaces are analyzed, and it is shown that at rectangular edges of cubic elastic media with one (110) surface and one (001) surface, a tip-localized guided wave always exists, apart from special cases that are characterized.
Laser pulses focused near the tip of an elastic wedge generate acoustic waves guided at its apex. The shapes of the acoustic wedge wave pulses depend on the energy and the profile of the exciting laser pulse and on the anisotropy of the elastic medium the wedge is made of. Expressions for the acoustic pulse shapes have been derived in terms of the modal displacement fields of wedge waves for laser excitation in the thermo-elastic regime and for excitation via a pressure pulse exerted on the surface. The physical quantity considered is the local inclination of a surface of the wedge, which is measured optically by laser-probe-beam deflection. Experimental results on pulse shapes in the thermo-elastic regime are presented and confirmed by numerical calculations. They pertain to an isotropic sharp-angle wedge with two wedge-wave branches and to a non-reciprocity phenomenon at rectangular silicon edges.
In a recent paper it has been shown that the effective nonlinear constant which is used in a P-Matrix approach to describe third-order intermodulation (IMD3) in surface acoustic wave (SAW) devices can be obtained from finite element (FEM) calculations of a periodic cell using nonlinear tensor data [1]. In this paper we extend this FEM calculation and show that the IMD3 of an infinite periodic array of electrodes on a piezoelectric substrate can be directly simulated in the sagittal plane. This direct approach opens the way for a FEM based simulation of nonlinearities for finite and generalized structures avoiding the simplifications of phenomenological approaches.