Evaluation of Precise Measurements of Young's Modulus and Shear Modulus by the Electro-static Driving Method

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The relationship between the flexural and torsional resonance frequencies and Young's modulus, E, and shear modulus, G, is derived semiempirically for rectangular and cylindrical bars of mild steel. The measured resonance frequency, f_i, of flexural vibration is given by f_i=M_i^2k/2π^2l^2・√<E/T_i・ρ>, where T_i is the geometrical factor, M_i a constant obtained under the boundary condition of the vibration, k, the radius of gyration of the cross section of a bar with its length, l, ρ is the density and E Young's modulus which is the physical quantity of main interest here. The subscript, i, assigned for the respective quantities in the i-th mode of vibration. The geometrical factor is determined experimentally from the measurement on samples of similar shape but different in k/l. The resonance frequency, f_i' for the torsional vibration is given by f_i'=i/2l・√<G/T_i'ρ(K/I_p)> where I_p is the polar itnerita of the cross section and K is the constant as defined by T/G×l/θ for the torsional angle, θ, induced by the moment, T, which is applied at the end of the bar. The geometrical factor, T_i', depends upon the ratio S/l, where S is the cross sectional area, and it is determined experimentally by the method similar to that for determining T_i. Corrected values of E and G of mild steel are 2.110 and 0.816 T dyne/cm^2, respectively, and the compressibility, κ and Possion's ratio, μ, calculated from the corrected values of E and G are 0.59 pcm^2/dyne and 0.29, respectively.
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Evaluation of Precise Measurements of Young's Modulus and Shear Modulus by the Electro-static Driving Method

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