The most commonly used technique for the analysis and design of electromechanical vibrators and filters is that employing the equivalent electrical circuit analogy. The equivalent circuit for vibrators and filters making use of extensional or torsional vibrations is four terminal network, so that the well established electrical network theory can by used for analysis and design. Konno et al investigated the equivalent electrical circuits for bars in transverse vibration with electrostrictive transducers but did not include any electromechanical coupling. Transverse vibrations involve not only forces and displacements but also moments and slopes, so that equivalent electrical circuits are eight terminal networks. These circuits are so complicated that the advantages which circuits usually offer for electrical engineers are lost. Moreover, when the system has a complicated shape and higher modes have to be taken into account, the circuits become even more involved. With recent developments in digital computers, various means for the numerical analysis of mechanical structures have been developed. In this paper, a composite vibrator of flexure-type with electrical and mechanical effects coupled, is analysed by means of the finite element method. The finite element method is a variant of the Rayleigh-Ritz method in which the assumed modes are built up from simple modes relating to each of a number of elements into which the system is divided. When a mechanical system is coupled with an electrical system, the electrical terminals appear as boundary conditions. The example analysed is similar to the transversely vibrating bar with electrostrictive transducers considered by Konno et al (See Fig. 1 and Fig. 3(a)). The natural frequencies of the system are calculated for two extreme electrical boundary terminations, namely, short-circuited and open, and the results are compared with those of Konno et al. The vibrators is divided into 10 elements, so that the length of the transducer can easily be changed in the numerical calculation. The dimensional values of the vibrator are drawn from Konno's example; r_b=(b_t)/(b_m)=1. 0, r_h=(h_t)/(h_m)=1. 5, r_&lthL&gt=(h_m)/L=0. 00527, r_p=(ρ_t)/(ρ_m)=0. 962, r_y=(Y_l)/(Y_m)=0. 381 where b, h, ρ and Y are width, thickness, density and Young's modulus. The suffices t and m indicate those of the transducers and the vibrator. h_m and L are the half-thickness and the total length of the vibrator. The effect of the electrical terminals on the natural frequencies is not great, at most 10% in the example. However, if the transducer has a larger electrical mechanical coupling coefficient, the effect cannot always be neglected. It is seen that Konno's results are quite close to the results for the terminals open, whereas in fact they should be compared with those for the terminals short-circuited. These last named results are a few percent lower than Konno's, because of the negative stiffness effect (See Table 1). The reason why his results are rather close to those for the terminals open is that the two additional terms introduced by the coupling, namely the negative stiffness and the term due to the electrical charges on the electrodes, partially cancel each other in our present example. Since, the vibrator is symmetrical, the same results can be obtained for the half length under the "free-sliding" boundary conditions. The computed results for the two element case are shown in the same table whose percent errors are less than 0. 9% for the first modes. The calculation of input admittance at the electrical terminals, which is an important measure of an electrical device, is also developed. The motional admittances are shown in Fig. 4-6 in the normalized form. The suppression of the third mode for the particular dimension is clearly demonstrated in Fig. 6.

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It is well-known that directive array sources are useful for indoor and outdoor sound reinforcement systems, and such the arrays are used in many cases. But the characteristics of the directive array has not yet been fully known. In this paper, the near field sound pressure characteristics of the linear array source are made clear to give instructions for designing a sound reinforcement system. The curved array is superior to the linear array not to cause large change with frequencies in the directive pattern. But the effectiveness of the directive array is easily observed in many cases even though the liner array is used. Moreover, the fundamental properties of the directive array can be found in the linear array. For this reason the near field sound pressure characteristics of the linear array are investigated. The curved array which is superior to the linear array will be taken up in the next chance. In order to synthesize a good directive pattern, the length of the array must be much longer than the wavelength of the lowest frequency. Therefore, a very long array having the length of several meters is sometimes used. In such a case, the objective region of the sound reinforcement must be considered to be the region of near field. The sound pressure distribution and the frequency characteristic of the linear array within the objective region are remarkably different from those of single loudspeaker. In order to generally indicate the sound field characteristic of the linear array, the continuous line source of length l shown in Fig. 1 is taken up as a model of the sound source. The results of the numerical computation of the near field sound pressure distribution and the frequency characteristic of the line source are shown Fig. 2 to 7. Some important properties are found in the figures. That is, the smoothed sound pressure distribution in the near field is nearly inversely proportional to the square roots of the distance in the range kl&gt50, x/l&lt10(Fig. 2). The attenuation of the sound pressure by the distance from the source can be reduced within a limited range by use of a slightly slant line source (Figs. 4 and 5). The longer the length of line source is, the flatter the near field sound pressure distribution becomes. But the sound pressure frequency characteristics must be compensated by an electric network, because the efficiency is fairly increased at low frequencies. Next, the near field transient phenomena of the line source are investigated. The results of numerical computation of the transient phenomena of the line source are shown in Fig. 20 to 23 and the experimental waveforms are shown in Figs. 24 and 25. It is found that the transient phenomenon of the line source is out of question from the practical point of view, if the length of the line source is shorter than about 10m, though the transient characteristics of the linear array are much different from those of single loudspeaker. Some interesting results are observed in the transient phenomena which are explanated physically with a vector diagram (Fig. 19).

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It is necessary for the study of vocal quality to know characteristics of a glottal source. Many methods for the direct or indirect observation of the glottal waveform or vibration of the vocal cords have been proposed. Most of them, however, are not suitable for the study of vocal quality. An indirect method, proposed by R. M. Miller, is considered to be applicable for this purpose, because it does not restrict phonation. His theory is based on inverse filtering of the transfer character of the vocal tract by means of simple analogue equipment. This paper proposes a more sophisticated method using digital techniques. Speech waves are transformed into a frequency domain in the first place and subsequent calculation is carried out in this domain. To estimate the transfer function of the vocal tract, "Analysis by Synthesis"technique is adopted. The source spectrum is calculated of digital filtering and converted into a time function or glottal waveform by inverse Fourier transform. This paper begins with the description of the theoretical background of the proposed method. Next, the effects of mismatching in the inverse filtering are examined with synthesized speech waves. An example of calculated glottal waves is shown in Fig. 1. Systematic evaluation of mismatching on every formant frequency and bandwidth is made with the results shown in Fig. 2 to 5. η in these figures is defined by Equation (10) and used for evaluation to denote waveform distortion caused by mismatching. Fig. 6 shows data handling procedure. In this experiment data must be treated carefully because of importance of waveform information. An experiment with natural speech is carried out according to the flow chart shown in Fig. 7. The most essential part of this experiment is the determination of the transfer function of the vocal tract. Modified "Analysis by Synthesis"technique is used for this purpose and the details are illustlated in Fig. 8. The glottal wave forms extracted from vowels uttered by several male speakers are drawn in Fig. 9 and 10. It is difficult to prove that these wave forms are true ones but they are considered to be acceptable as compared with the results of the preceding experiments. To get more precise results, the transfer function of the vocal tract must be determined more correctly. Further studies are required for solving this problem with due regard paid to the zero of a glottal source in the process of analysis by synthesis procedure. This method will be useful for the studies of naturalness and the individuality of speech sounds and of the mechanism of vocal cords vibration, and will contribute to the design of the excitation source of a synthesizer.

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