紙の弾性常数に関する模型的考察

抄録

In our researches on the cone type dynamic loud-speaker, we studied the dynamic properties of the paper used as material for the conical radiator, and methods of producing better paper for this purpose were explored. To attain this end, we have devised a schematic paper model based on the following assumptions founded on experiment: i) The fibres are assumed to be straight between two adjoining junctions with other fibres. ii) When the paper is deformed, no slip occurs between two fibres, while at the junctions of the fibres the angles between two connected fibres remain constant. iii) Each fibre is rigidly fixed at the junctions, and the direction of the fibre remains stationary as referred to coordinates fixed in space, when a uniform stress is imposed on the paper. Calculations on the above schematic model resulted in the following conclusious: 1. The young's modulus changes proportionally to the square of the volume density when the paper (pulp) is pressed while wet and then dried. 2. The Young's modulus, the propagation velocity of longitudinal waves through the paper and the density of the paper are each proportional to the respective constants of the fibres. 3. The effect of the structure of the paper on the Young's modulus, the density, the porpagation velocity and the Poisson's ratio of the paper were made clear. 4. When the directions of the fibres are not evenly distributed, the Young's modulus is maximum in the direction of the maximum concentration of the fibres. 5. The Poisson's ratio depends upon the structure of the paper, and may exceed 0. 5 in cases where the directional distribution of the fibres is sharply biased.