Three-Dimensional Analysis of Spurious Vibrations of Rectangular AT-cut Quartz Plates.

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  • Ishizaki Akio
    Department of Electronics and Information Engineering, Faculty of Engineering, Tokyo Metropolitan University, 1–1 Minami–Ohsawa, Hachioji, Tokyo 192–03, Japan
  • Sekimoto Hitoshi
    Department of Electronics and Information Engineering, Faculty of Engineering, Tokyo Metropolitan University, 1–1 Minami–Ohsawa, Hachioji, Tokyo 192–03, Japan
  • Watanabe Yasuaki
    Department of Electronics and Information Engineering, Faculty of Engineering, Tokyo Metropolitan University, 1–1 Minami–Ohsawa, Hachioji, Tokyo 192–03, Japan

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  • Three-Dimensional Analysis of Spurious

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We have developed a technique for the three-dimensional (3-D) analysis of all the spurious vibrations of rectangular AT-cut quartz plates. The 3-D displacements are described with a linear combination of modes guided along the X crystal axis of an AT-cut quartz strip. We accurately calculate each guided mode by applying the one-dimensional finite element method to the two-dimensional strip waveguide problem. To uniquely determine the amplitudes of guided modes in the 3-D solutions we employ the variational expression for the stress-free conditions on the X-length edges. The present technique makes it possible to perform 3-D analysis of spurious vibrations within a reasonable computational time. Frequency spectra for rectangular AT-cut quartz plates are computed as a numerical example and are compared with the numerical results obtained using an extended version of the previous method and with Koga's experimental data. Vibrational patterns of spurious modes are shown, and a convergence study is carried out.

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