The vibration characteristics of granular carbon aggregates of a telephone transmitter are closely connected with the telephone transmission performance. In this paper, for the purpose of establishing a reasonable design method for telephone transmitter's vibrating system, study of the electro-acoustic characteristics of granular carbon aggregates in a cylindrical carbon chamber is described. The granular carbon aggregates have hysteresis and non-linear characteristics with regard to the driving displacement amplitude(See Fig. 1 and reference 7, 4), due to sliding friction in the granular contacts. For small driving displacement in which the slidings are negligible, the electro-acoustic transformation of granular carbon aggregates is supposed to work in the same way as in a piezo-resistive material (See reference 5). However, when granules are filled in a vessel, at the boundary wall of the vessel, material constants and the arrangement of contact between granules are different from those in the interior of the granular aggregates. Moreover the surrounding wall restricts the vibrating mode of the granular aggregates. In consideration of these facts, the author analyzed the relation between the electro-acoustic characteristics of granular carbon aggregates and the chamber size by using an elastic model which consists an elastic rod buried in some elastic medium in a way to receive a restoring force (Fig. 3), and having concentrated mechanical elements at both ends corresponding to the boundary irregularities. By comparison with experimental data obtained for compressive and shearing vibration (See Fig. 4, Fig. 6, Fig. 8 and Table 1. ), the model was confirmed to represent the effects of chamber dimensions・・・・・・namely, chamber diameter, chamber length (gap length between electrodes), driving area (electrode area), etc. , ・・・・・・on the mechanical vibrating characteristics. The model is also applicable to represent the effect of chamber size on the inter-eletrode electric resistance and electro-acoustic transducing efficiency, by separating the effect of electric current passage in the neighborhood of the electrodes. At the boundary of the electrodes specific resistance and strain-resistance transducing factor as well as the mechanical vibration constants are different from those in the interior of the granular aggregate (See Fig. 10 and Fig. 13). Moreover, because of the circumferential effect of the electrode, the specific resistance (normalized by the electrode area) and the electro-acoustic transducing efficiency of the granular carbon aggregates are related to the electrode area and chamber diameter(Fig. 9, Fig. 11, Fig. 14, Fig. 15, ). By the above mentioned studies, the three dimensional effect of carbon chamber on the electro-acoustic characteristics of granular carbon aggregates has become considerably clearer than before. Theoretical analysis of the form effect on the electro-acoustic characteristics of granular carbon aggregates in a semi-spherical carbon chamber, is left for future investigation. Finally, in appendix, theoretical analysis of the variation in resistance of piezo-resistive material of arbitrary form subject to electric field and elastic deformation is described.

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An electroacoustical calculation was made of bending distrotion of an asymmetric piezoelectric bimorph, considering the space charge effect(piezoelectric interaction) proposed by Marutake. In determining the neural plane, such an extensional strain as to permit a lengthwise displacement of each cross section but make no contribution to bending moment must be taken into account. This additional strain is proportional to applied voltage, and vanishes in the case of symmetric bimorph or of ignoring the space charge effect. The position of neutral plane was thus determined, and the neutral plane retains the position where V=0. Displacement and charge of a statically bent bimorph with one end clamped were calculated against applied voltage and force. The "bending-clamped" capacitance C^&ltBC&gt is equal to the sum of C^&ltLC&gt for lengthwise-clamping and C^&ltLF&gt due to to the above additional extensional strain. The electromechanical coupling coefficient of bending mode can be befined as k_B^2=(C^&ltBF&gt-C&ltBC&gt)/(C^&ltBF&gt), C^&ltBF&gt being a "bending-free" capacitance. It may be fairly concluded from the comparison of the electroacoustic constant thus calculated with that calculated by ignoring the space charge effect that taking this effect into account only brings a modification of the compliance to bending. Calculations of bending vibrations piezoelctrically driven were carried out under various boundary conditions. Piezoelectric admittances were examined, and their relations to equivalent circuit for resonance were considered. Free admittances of clamped-pinned and pinned-pinned beams were the same as damped admittances of clamped-free and free-free ones respectively. In the low frequency limit, static piezoelectric charges and accordingly coupling coefficient were in agreement with those determined by static calculation. Values for clamped-free, free-free and pinned-pinned beams were a fourth of these. In the case of clamped-free beam, the result applied to symmetric bimorph was the same as that reported by Marutake.

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