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内容記述 |
In the measurement of damping capacities or Young's moduli of materials the method of lateral vibration of thin beams is often used. With respect to the damping capacities, the influence of external air resistance upon the logarithmic decrement seems to be not negligible, but comparable with that of internal friction. Therefore, this neglect of air resistance which was indistinct or untouched so far, would lead to an inaccurate measurement of internal friction. In the present work, this vibrational damping of thin cantilever beams due to the air resistance was first treated phenomenologically from the standpoint of mechanical vibration, not of aerodynamics. The following nonlinear partial diffierential, equation was formulated, introducing two kinds of air resistance, that is, "viscous" and "hydrodynamic" air resistances. [numerical formula] where p is the densityof meterial, p_a the pressure of air, E Young's modulus, ξ the coefficient of solid viscosity, η_1, η_2 the coefficients of air resistances, b the breadth. I, A the moment of inertia, the area of a cross section of the beam restectively. Our approximate analysis using Galerkin's method and the perturbation method gave a satisfactory agreement with our experimental results on lograrithmic decrements which were obtained from a series of specimens under various air pressures. That is to say, apart from the constancy of logarithmic decrement due to old theories, its dependencies on almost all factors such as t (time), y (amplitude), h (thickness), p_a and p ets. where individually verified, Such a phenomenological procedure would be expected to be also effective in making clear the nature of internal friction. In Appendix, details of the measuring apparatus using wire resistance strain gages are described. The apparatus was specially made for the above experiment, the specimen being placed in a vacuum chamber. |
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