片持梁振動子及び, 音叉振動子の固定端条件

抄録

The fixed end condition of a cantilevever vibrator or a tuning fork vibrdtor is usualy handled as a perfect fixed end condition as shown in Fig. 1. Practically even if a vibrator is fixed as perfect as possible, the vibrator should be treated to be built in a semi - infinite elastic body as shown in Fig. 2. In that case, the deflection is calculated by the finite element method. The results are as follows. (1) The inclination of a fixed end is shown in Eq. 12, where C is a constant, M is the moment at the fixed end, h is the depth of the beam, E is Young's modulus and I is the second moment of area of a cross - section of the beam. lnclination of the fixed end is equivalent to make the length of the berm longer by the amount of Δl expressed in Eq. 16. (2) The frequency deviation is shown in Eq. 21, where m is the mass of the top of the beam, ρ is the density and S is the cross - sectional area of the beam. (3) In the case of Fig. 9, the value of C is shown in Fig. 11; in the case of Fig. 13, it is shown in Fig.15: and in the case of Fig. 16, it is shown in Fig. 19.