The flexural vibration of a circular ring that is of axis symmetry is analyzed and calculated, the solid frequency expression of the flexural vibration is obtained.

对一类轴对称圆环的面内弯曲振动进行了分析计算，给出了圆环面内弯曲振动固有频率表达式。

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Based on theoretical analysis of stepped bending vibration boring bars, the frequency equation of a stepped bending vibration boring bar with circular and square sections is established.

通过对阶梯式弯曲振动镗刀杆的理论分析，推导出了圆形截面和矩形截面组合的阶梯弯曲振动镗刀杆的频率方程，并对阶梯弯曲振动镗刀杆进行了试验研究。

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