矩形断面を有する棒の捩り振動

概要

論文の詳細を見る
Usually, a vibration system with a circular crosssection has been used for transmission of ultrasonic torsional vibration energy, but that with a rectangular crosssection is also of use, as the case may be. A static solution concerning the torsion of a prismatic bar was completely given by Saint-Venant. In this paper, the authors derived an equation of motion(Eq. (4))and K_x in Eq. (4)is given from the Saint-Venat's solution on the assumption that the torsional wave is propagated only to the direction of x-axis and the crosssection is twisted uniformly with a definite angle θ_x(Fig. 1). From this equation of motion, in the case that the cross section is uniform in dimensions(2b×2a)along x-axis, the following expressions were obtained:(1)Velocity of torsional wave in Eq. (12)and Fig. 3. (2)Frequency equation and distribution functions of rotary displacement and twisting moment in Eq. (14). (3)Maximum shearing stress in Eq. (16)and Figs. 7 and 8. And the values of these expressions are determined not only by the material constant but also by the value of 'b/a', which is given by the dimensions of crosssection. Further, we have actually measured the torsional resonant frequencies about some test specimens shown in Table 1, using the non-contact electromagnetic type torsional vibration exciter/detector which was already reported by the authors(Reference(4)). From the experiments mentioned above, the following results were obtained. The deviation of the measured velocity of torsional wave from the calculated value is(1)less than 1. 0 percent when the ratio b/a is up to 6 for 2b/λ=0. 27(at half wave resonance)as seen in Fig. 4 and Table2, (2)less than 2. 0 percent when 2b/λ is up to 0. 5 for b/a≦3 as seen in Fig. 5, and(3)less than 1. 0 percent when 2b/λ is up to 0. 8 for b/a=1, namely the cross section is of square form. Therefore, considering the accuracy of machining and the deviation of acoustical characteristics of the materials and so on, the method of analysis mentioned in this paper was confirmed to be available for designing a torsional vibration system for ultrasonic power applications, because in such cases the dimensions of the crosssection(2b×2a)are usually smaller than the wave length(λ)and a rigorous design is not always required.
社団法人日本音響学会の論文
1973-03-01

矩形断面を有する棒の捩り振動

スポンサーリンク

概要

著者

関連論文

スポンサーリンク