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  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 83 (1998), S. 1213-1223 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A system of two-dimensional (2-D) governing equations for piezoelectric plates with general crystal symmetry and with electroded faces is deduced from the three-dimensional (3-D) equations of linear piezoelectricity by expansion in series of trigonometric functions of thickness coordinate. The essential difference of the present derivation from the earlier studies by trigonometrical series expansion is that the antisymmetric in-plane displacements induced by gradients of the bending deflection (the zero-order component of transverse displacement) are expressed by the linear functions of the thickness coordinate, and the rest of displacements are expanded in cosine series of the thickness coordinate. For the electric potential, a sine-series expansion is used for it is well suited for satisfying the electrical conditions at the faces covered with conductive electrodes. A system of approximate first-order equations is extracted from the infinite system of 2-D equations. Dispersion curves for thickness shear, flexure, and face-shear modes varying along x1 and those for thickness twist and face shear varying along x3 for AT-cut quartz plates are calculated from the present 2-D equations as well as from the 3-D equations, and comparison shows that the agreement is very close without introducing any corrections. Predicted frequency spectra by the present equations are shown to agree closely with the experimental data by Koga and Fukuyo [J. Inst. Elec. Comm. Engrs. of Japan 36, 59 (1953)] and those by Nakazawa, Horiuchi, and Ito [Proceedings of 1990 IEEE Ultrasonics Symposium (IEEE, New York, 1990)]. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 83 (1998), S. 7822-7833 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A system of two-dimensional first-order equations for piezoelectric crystal plates with general symmetry and with electroded faces was recently deduced from the three-dimensional equations of linear piezoelectricity. Solutions of these equations for AT-cut plates of quartz were shown to give accurate dispersion curves without corrections, and the resonances predicted agree closely with the experimental data of Koga and Fukuyo [I. Koga and H. Fukuyo, J. Inst. Electr. Commun. Eng. Jpn. 36, 59 (1953)] and that of Nakazawa, Horiuchi, and Ito (M. Nakazawa, K. Horiuchi, and H. Ito, Proceedings of the 1990 IEEE Ultrasonics Symposium, pp. 547–555). In this article, these equations are employed to study the free as well as the forced vibrations of doubly rotated quartz plates. Solutions of straight-crested vibrational modes varying in the x1 and x3 directions of SC-cut quartz plates of infinite extent are obtained and from which dispersion curves are computed. Comparison of those dispersion curves with those from the three-dimensional equations shows that the agreement is very close without any corrections. Resonance frequencies for free vibrations and capacitance ratios for piezoelectrically forced vibrations are computed and examined for various length-to-thickness or width-to-thickness ratios of rectangular SC-cut quartz plates. The capacitance ratio as a function of forcing frequency is computed for a rectangular AT-cut quartz and compared with the experimental data of Seikimoto, Watanabe, and Nakazawa (H. Sekimoto, Y. Watanabe, and M. Nakazawa, Proceedings of the 1992 IEEE Frequency Control Symposium, pp. 532–536) and is in close agreement. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Journal of Ultrasructure Research 73 (1980), S. 310-317 
    ISSN: 0022-5320
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Biology
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    The international journal of advanced manufacturing technology 13 (1997), S. 109-115 
    ISSN: 1433-3015
    Keywords: Convex hull property ; Freeform curve ; NC machining ; Overcut ; Pocket
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The objective of this paper is to generate tool paths for pockets with freeform curves, i.e. Bezier curves or B-spline curves. Time efficiency and overcut avoidance are two of the most important factors in NC machining. A method, based on the convex hull property of Bezier curves, is thus developed so that the portion of the boundary defined by a Bezier curve is replaced by parts of its convex hull on the cavity side. Therefore, the new pocket boundary, redefined by only segments of straight lines, can be solved efficiently based on current algorithms without overcuts. Cutting tool paths can be generated for pockets with islands avoiding computation of higher degree curve/curve intersections. Furthermore, recursive subdivisions on Bezier curves are used to improve the accuracy of the cut with an allowance criterion based on sizes of convex hulls. The portion of the boundary defined by a B-Spline curve is transformed into piecewise Bezier curves. The tool-path generation for pockets with B-spline curves can thus be solved by reducing the problem to one of pockets with Bezier curves.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Microchimica acta 58 (1970), S. 207-213 
    ISSN: 1436-5073
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Zusammenfassung Unterwirft man Butyllävulinat in wäßrigem oder alkoholischem Milieu der reduktiven Aminierung, so entstehen unter anderemγ-Valerolactam undγ-Valerolacton. Diese wurden nach weitgehender Entfernung der flüchtigen Anteile (Ammoniak, Wasser oder Alkohol) durch isotherme Gaschromatographie unter Verwendung von Phenyläther oder Isoamylsalicylat als interne Standards bestimmt. Mit einem Wärmeleitfähigkeitsdetektor wurde eine 2 m lange Säule mit 6 mm i. D. aus Kupferrohr mit einer Füllung aus 25% Glykoladipat und Chromosorb W verwendet, mit Wasserstoff als Trägergas. Die Genauigkeit betrug ± 0,4% fürγ-Valerolacton und ± 0,5% fürγ-Valerolactam. Wurde hingegen ein Ionisierungsdetektor mit Wasserstoff-Flamme verwendet, so diente eine 2 m lange Säule mit 3 mm i. D. aus rostfreiem Stahl mit einer Füllung aus 10% Glykoladipat und Chromosorb W und Stickstoff als Trägergas. Die Genauigkeit betrug dann ± 0,5 bzw. ± 1,8%.
    Notes: Summary Theγ-valerolactam andγ-valerolactone in the reductive amination products of butyl levulinate in water or alcoholic medium, after removing most of the light fractions, ammonia, and water or alcohol, have been determined by isothermal gas chromatography using phenylether or isoamyl salicylate as the internal standard. With the thermal conductivity detector, a column of 6 mm I. D., 2 m long copper tubing packed with 25% glycol adipate/chromosorb-W was used, with hydrogen as the carrier gas. The accuracy was ± 0.4% forγ-valerolactone and ± 0.5% forγ-valerolactam. Using the hydrogen flame ionization detector, a column of 3 mm I. D., 2 m long stainless steel tubing packed with 10% glycol adipate/chromosorb-W was used, with nitrogen as the carrier gas; the accuracies forγ-valerolactone andγ-valerolactam were ± 0.5% and ± 0.8% respectively.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Brookfield, Conn. : Wiley-Blackwell
    Journal of Vinyl and Additive Technology 2 (1980), S. 74-76 
    ISSN: 0193-7197
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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