Abe, Kiyoshi

Inoguchi, Toshio

Murata, Akira

Tanaka, Tetsuro

Kyoto University Research Information Repository

TitleStudy on High Dielectric Constant Ceramices. (XXIII) TheModes of Vibration about Langevin Type BaTiO₃ CeramicVibrator. (3)Author(s)Abe, Kiyoshi; Tanaka, Tetsuro; Inoguchi, Toshio; Murata,AkiraCitationBulletin of the Institute for Chemical Research, KyotoUniversity (1954), 32(2): 78-80Issue Date1954-03-31URL http://hdl.handle.net/2433/75430RightType Departmental Bulletin PaperTextversionpublisherKyoto UniversityEqs. (3) and (4) give the curves very approximate to that  of Fig. 1. Eqs. (5) (6) are inferior to eqs. (3) and (4) in the approximation to the measured curve. Eqs. (5) and (6) were used in calculation, though the degree of approximation are inferior to eqs. (3) and (4), because their integration can not be solved when the eq. (3) or (4) is inserted in eq. (1). When eq. (5) was used, we have with 0= —1.5, je=6.5 and           R = 4.6Sin                      8.05cosu+5.80 sin u                                       + 41.5  cos U43.3  sin u                                    (7)          U2U3u4/15 When the values of R are calculated for every values of 8, the directional characteris-tic curve is obtained as shown in Fig. 2. When eq. (6) was used, we have with 13=5 and r= —1, R_ 6  sin u  +15 cos u 15  sin u                                            (8) U2213 This result is shown in Fig. 3.                                                              o• to. ft • N        Now 60'           A6 4eI I Ifeir I 16•,,       1111.011,ra"7-o•.InthAro"    tV4410                                                                                                                      7o'     pTA 70.                t ovto     Fp, tiro_ , *4-1111 '°                                           ehairim.... 0 02 o4 o6a to /2 /40 0204 06 68 /0 /2 /4       Fig. 2.Fig. 3.    It may be said that they coincide qualitatively with the directional characteristics measured realy in water.       5. Study on High Dielectric Constant Ceramices. (XXIII)  The Modes of Vibration about Langevin Type BaTiO, Ceramic Vibrator. (3)       Kiyoshi ABE, Tetsuro TANAKA, Toshio INOGUCHI and Akira MURATA                               (Abe Laboratory)    As a cylindrical Langevin type vibrator has simple construction and is manufac-tured easily, it has already been practically used as an underwater supersonic trans-ducer. Recently, the rectangular Langevin type vibrator is also required from a view point of the directionel characteristics, and so, such vibrator was made and the modes of vibration were inspected.                             ( 78 )          Rectangular Langevin Type Vibrator           The size of the vibrator is 100 mm. in length and 30 mm. in width and total       thickness including piezoelectric material (2 mm. in  thickness) is 44 mm. Consequent-      ly the thickness of two iron pieces are 21 mm. This vibrator was rnadefor the purpose       to utilize the thickness vibration, however, it is presumed that it hasat least two        resonant frequencies besides the thickness vibration. The measured resonant fre-       quencies were 25.31 kc, 52.78 kc and 97.40 kc and they were called the first, the second        and the third resonance respectively. The vibration in the second resonance is strong-       est among them, and assuming that the vibration has simple longitudinal mode the        calculated force foctor becomes 16.3 x107 dynes/e. s. u. volt. In the third resonance,        force factor is 9.24 x107. The first resonance is very weak.           Generally speaking, the first, the second and the third resonances correspond to       the longitudinal vibration of length, thickness and width direction respectively. It is        presumed that in the second and the third resonance the modes of vibration are com-      plicated on account of coupled vibration due to the similarity of both size.           Method and Result of Measurement           The amplitude distribution and the phase relation on the vibrator surface are meas-       ured by using a pick-up, which consist of a small Langevin type vibrator, as is       detailed in the Part 1. (This Bulletin, 31, 295 (1953)). The results of measurement       are shown in Fig. 1 and Fig. 2, which show the modes of vibration in the first and the        second resonance respectively. In these figures, the sign of + or - represents the phase        relation, that is, all the amplitude distributions are shown by the convex surfaces for        the sake of convenience. In the third resonance, the motion has not the same phase        on the surface and the figure is omitted because it is too complicated to draw.                                                                        021^^                               44:4444          OS.411                            A,01*,                                   mow                       i.71-1111!11111111-111611^! -4411h-    - • ,                                                                                                                                     '            Fig. 1.Fig. 2.            Consideration           The vibration in the first resonance is undoubtedly the longitudinal vibration of        length direction, as the results of measurement on the amplitude distribution prove it.        In the seconctresonance, it is concluded that this vibration is nearly equal to longitudinal                                      ( 79 )        thickness mode. In the third resonance, although comparatively strong vibration is         excited as is presumed from the measurement of motional admittance, it is not desira-        ble to use this resonance for the acoustic purpose, because the amplitude  distribution         is complicated and the directional characteristics of vibrator suffer harmful influences         by the existense of the part of inverse phase on a radiating surface. It is concluded          that the second resonance is the most effective among them.                     6. Study on Surface Electricity. (XIX)                     Capacity Measurement of Dropping Mercury Electrodes                                by Resonance Method. (1)                      Akira WATANABE, Fukuju TSUJI and Shizuo UEDA                                       (Tachi Laboratory)            As the interfacial phase between mercury and electrolytic solution is considered to          be equivalent to an A. C. element containing a capacitance, a resonant circuit is con-        structed by connecting it with an inductance. This circuit satisfies the resonance con-        dition when the following equatiqn exists, f=1/(27tVLC         where f is the frequency, and L and C are the inductance and capacitance, respect-         ively.            The interfacial area of a dropping mercury electrode increases continuously with         time, which can be represented by                    A3mt                   A=Lt7Z X47Z-i         where A is the interfacial area, m the rate of flow of mercury (g /sec) and t is thne.         As the (differential) capacity per unit interfacial area takes its unique value (at a         given polarization), the total capacitance of the interface increases with time i. e. C=CoA = Cokrn         where C is the total capacitance, C, the specific capacity per unit area and k is constant          for a given value of m.            Combining this equation and the above condition for resonance, we can conclude          that, by choosing proper A. C. frequency and inductance, the circuit resonates at some         instance during the growth of the mercury drop. The resonance curve can be repro-        duced on the screen of a cathode ray oscilloscope by applying the A.C. voltage occur-        ring at the two terminals of the dropping electrode cell as the vertical axis and a                                        ( 80 )

Study on High Dielectric Constant Ceramices. (XXIII) The Modes of Vibration about Langevin Type BaTiO₃ Ceramic Vibrator. (3)

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Study on High Dielectric Constant Ceramices. (XXIII) The Modes of Vibration about Langevin Type BaTiO₃ Ceramic Vibrator. (3)

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