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In the framework of electro-elasticity theory and the finite element method (FEM), a model is set up for the computation of quantities in surface acoustic wave (SAW) devices accounting for nonlinear effects. These include second-order and third-order intermodulations, second and third harmonic generation and the influence of electro-acoustic nonlinearity on the frequency characteristics of SAW resonators. The model is based on perturbation theory, and requires input material constants, e.g., the elastic moduli up to fourth order for all materials involved. The model is two-dimensional, corresponding to an infinite aperture, but all three Cartesian components of the displacement and electrical fields are accounted for. The first version of the model pertains to an infinite periodic arrangement of electrodes. It is subsequently generalized to systems with a finite number of electrodes. For the latter version, a recursive algorithm is presented which is related to the cascading scheme of Plessky and Koskela and strongly reduces computation time and memory requirements. The model is applied to TC-SAW systems with copper electrodes buried in an oxide film on a LiNbO3 substrate. Results of computations are presented for the electrical current due to third-order intermodulations and the displacement field associated with the second harmonic and second-order intermodulations, generated by monochromatic input tones. The scope of this review is limited to methodological aspects with the goal to enable calculations of nonlinear quantities in SAW devices on inexpensive and easily accessible computing platforms.
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.
Experimental and numerical investigations into the forming of tailored strips and tailored tubes
(2008)
Through the application of tailored strips and tailored tubes, the wall thickness of components can be manufactured in a load-optimised manner. Thus, it is also possible to optimise component weight. Prior to the application of tailored products, wall thicknesses and the respective degree of deformation as well as the welding seam position can be determined in a FEM (finite element method) simulation. These results are then verified in test series on transfer presses and tube bending machines, with the necessary tool adaptations being determined in the process. This results in weight and cost reductions for deep-drawn components and tube sections. Moreover, this means that especially with regard to tubes, multiple sections can be combined in one component. A feasibility study shows that the level of possible weight and cost savings depends on the respective component geometry and load situation. Additional costs for the production of tailored products and - if necessary - tool modifications also need to be considered. Thus, the amount of savings possible for a part can only be determined on an individual basis.
Die Wichtigkeit des Faches FEM ist sicher unumstritten. Um in der gegebenen Zeit eine ausreichende Einarbeitung in die Methode und die Uebung am Rechner durchfuehren zu koennen, ist der Einsatz eines auf PC lauffaehigen FE-Lernprogramms eine gute Hilfe. Sind die Grundlagen da, weiss der Student, welche Eingaben bei einem FE-Programm zu machen sind. Fuer manche Fachgebiete genuegt schon die Arbeit mit einem solchen Programm. Sind entsprechende Uebungen mit dem Lernprogramm erfolgt, kann auf professionellen Programmen wie z.B. CAEDS das Zusammenspiel CAD/FEM ernsthaft betrieben werden. Es sollte ein Fachsemester ausgesucht werden, in dem CAD und FE angeboten wird. Dieses Fachsemester sollte, um den Nutzen der FEM in moeglichst vielen Fachgebieten zu haben, zum Ende des Grundstudiums, spaetestens aber zu Beginn des Hauptstudiums liegen.
Um eine gleichbleibende Mahrspalthoehe und gleichmaessige Lastverteilung waehrend des Betriebes zu erreichen, werden Mahlwalzen bombiert hergestellt. Das theoretische Bombierungsprofil wird aus der elastischen Walzenverformung bei gegebener Belastung abgeleitet. Die Verformung kann mit Finiten Elementen berechnet werden. Werden zwei Walzen mit zylindrischer Oberflaeche gegeneinander gedrueckt, so ergibt sich ein nichtlinearer Kontakt. Die Druckverteilung laengs der Walze laesst sich unter Hinzunahme von Einflusszahlen mit Hilfe eines linearen Gleichungssystems ermitteln. Die Autoren untersuchen mit diesem Berechnungsverfahren die Wirkungen unterschiedlicher Bombierungen und den Einfluss von veraenderter Anpresskraft. (Rohlf)