In the preceding paper, the authors showed the Bolt-clamped electrostrictive torsional vibrator for ultrasonic power applications (Fig. 1). The electrostrictive ceramics of the vibrator were polarized circumferentially in one body by dividing it into n portions (in Fig. 2, n=8) and by sequential polarization ; polarizing conditions of the ceramics, such as ratios of [electrodes gap]/[thickness of ceramics](which is 2a/2t in Fig. 3) or [width of electrode]/[thickness of ceramics](which is (e-a)/2t in Fig. 3), were chosen without any definite basis. In the present paper, the authors determined the electric lines of force and equipotential lines of inner portion of the ceramics by means of conformal mapping. Assuming a thin pipe within the ceramic, the authors expanded it (Fig. 3), and reduced the problem to a two-dimensional one as shown in Fig. 4, by neglecting the radial component of the electric field. Because they are symmetrical as to the GHG' line in Fig. 4, the authors considered only half of the ceramics(hatched portion in Fig. 4), and converted it into the half-infinite-plane as shown in Fig. 5 . The transformation function here used is eq. (1). This half-infinite-plane can be converted into the internal area of the rectangle shown in Fig. 6 by eq. (5), which is an elliptic-integral of the first kind, and the size of the rectangle is given by K and K' which are the complete-elliptic-integrals of the first kind. In Fig. 6, electric lines of force are horizotal, and equipotential lines are vertical, because two electrodes are in parallel. These lines are inversely transformed into the half-infinite-plane as shown in Fig. 5, by means of eq. (6) or eq. (7) which is Jacobi's elliptic function. Fig. 7 is an example of the chart showing the lines of electric force and equipotential lines. Fig. 8-11 show the group of charts showing the distribution of these lines within a ceramics. From these charts, the assumptions the authors adopted in the preceding paper are shown to be valid. The concentration of the electric field near the surface of ceramic is evaluated as shown in Fig. 12. In this figure, ratios of [maximum value of the mean potential gradient between the electrodes and the equipotential surface the potential of which is 19/20 of the voltage across the electrodes]/[mean electric field between electrodes given as (potential difference)/(electrodes gap)] are shown in the letters Z, Y, X or W which means 26 times, 25 times, 24 times or 23 times etc. For example, in the region we utilized to polarized ceramics (a/t=1. 5〜2. 0 and e/t=2. 0〜3. 0), the letters are shown in B or C, which means the ratio mentioned above is 2 or 3.
The propagation of ultrasonic waves in a liquid layer sandwiched between rigid bodies is equivalent to the propagation of SH waves in an elastic plate as pointed out by Sato. Hence the lowest branch of a dispersion equation is nondispersive and can be utilized to advantage in ultrasonic information processing devices. The distribution of energy in a cross section is uniform for low frequencies at which only the lowest branch can propagate and suitable for ultrasonic imaging. Real solid is not rigid but elastic. The present paper examines the effect of elasticity of solid bodies. Dispersion equations are derived for symmetric and antisymmetric modes. Dispersion curves(Fig. 2), phase velocity(Fig. 3) and group velocity(Fig. 4), displacement(Figs. 6〜9) and energy flow distribution (Figs. 10〜13) in a cross section are numerically calculated for the first few modes in a water layer sandwiched between two sheets of glass. An examination of these results shows that:(1) The lowest branch has now an imaginary wave number along the direction perpendicular to boundaries, but essentially retains the features in the case of rigid bodies. The velocity measured by a light diffraction method shows few dispersion as predicted. (2) Each higher branch has a cut-off frequency when its phase velocity becomes equal to the shear velocity of solid bodies. (3) The overall view of dispersion curves can be interpreted as a result of coupling between the branches in case of rigid bodies and those of the surface waves on solid boundaries.
An electromagnetic induction type sound source is a useful sound source for detection of the bodies buried at depth of less than 2 or 3 meters under the ground surface by the pulse-echo method due to radiating an intense impulsive wave of good reproducibility. In this study, theoretical and experimental analyses about the radiation characteristics of this sound source placed on the ground surface were performed. This sound source is composed of a flat spiral coil cemented on a bakelite plate, an aluminum diaphragm contacting with the coil and a weight set on the bakelite plate as shown in Fig. 1. Equation (8) expresses sound pressure of an impulsive sound wave radiated from the sound source and transmitting towards the direction just below the sound source. Fig. 2 shows a waveform of radiated sound pressure calculated by Eq. (8). Eq. (8) indicates that the peak pressure of the impulsive sound is proportional to the frequency of driving current fe and the input energy N, but independent of the radius of diaphragm a. Power-spectrum and directional characteristics of the radiated sound are expressed by Eq. (11) and Eq. (12) and shown in Fig. 3 and Fig. 4 respectively. Experiments in the laboratory and in the field were carried out in order to justify the theoretical expression. In the laboratory semi-cylindrical acrylite sand bath shown in Fig. 5 and a small sound source were used. The directional characteristics and the peak pressure as functions of the input energy were measured. The results are shown in Fig. 4 and Fig. 6 respectively. In the field test, a sound source shown in Fig. 7 was used. As shown in Fig. 8, the radiated sound pressure was measured with a piezoelectric microphone (sensitivity in water:-101. 3 dB at 8 kHz) buried at depth of 1 m in sand just below the sound source, and the distance from the sound source to the microphone was varied from 1 m to 20 cm by digging a hole. In this experiment, the frequency of driving current was increased from 200Hz to 1200Hz by decreasing condenser capacitance from 180μF to 5μF, and the input energy was kept at 250 joule by increasing the charging voltage as the capacitance is decreased. The power-spectrum and the peak pressure as functions of the driving current frequency were measured. The results are shown in Fig. 9 and Fig. 3 respectively. In Table 1, the measured values of the peak pressure are compared with the theoretical values obtained by Eq. (8) or Eq. (9) using n=350, L=3mH. Cp=340m/s, d=0. 2m and N=250 Joule. In Fig. 10, a waveform of microphone output in case of 20 cm in distance and 200Hz in driving current frequency is shown. From the fact that the measured values agree with the theoretical ones with reasonable accuracy, the equation (8) was proved to be appropriate as a theoretical expression of the sound pressure radiated from the electromagnetic induction type sound source.
According to the result of our previous report, the partial autocorrelation coefficients (PAC) seem to be the best parameter for Japanese spoken digit (limited vocabulary) recognition. In this paper, further improvement of the recognition score and several methods to prevent the recognition score from deterioration, when the simplified method of PAC extraction is used, are described. We adopted the nonuniform time pattern matching algorithm. and speaker's own utterances were used as the standards. The extraction error of PAC increased when the speech wave amplitude is small (Fig. 1). So the contribution of the matching of PAC to the recognition decision is weighted by the form of w(t)=(1+a(t))/2, where a(t) represents the normalized relative amplitude (a(t)≦1). Relatively good result was obtained (Fig. 2). We checked some techniques for the prevention of score from deteriorating when fixed point arithmetics with a short accumulator length are used in the PAC extraction. The use of only reliable PAC in the recognition improve the recognition score remarkably, for example, 88% to 99% using 18 bits fixed point accumulator. Smoothing of parameters along the time axis is also effective (Fig. 3). A few other method are tried but the results are rather negative. After all, the two methods proved to be useful . . . 1) weighted matching of PAC by signal amplitude of standard utterance when computation accuracy of PAC extraction is adequately high, 2) A combination of the use of only reliable PAC and smoothing of each parameters in the time axis when the accuracy is relatively low. We verified the validity of these two methods through recognition experiments with various standard utterances of the same speaker (Fig. 7, 8, 9), different speakers (Fig. 8), and another extraction calculation method (Fig. 9).