对等截面细杆的超声弯曲振动有初等弯曲理论进行设计,可以近似满足超声工程实践的需要。对粗的等截面超声弯曲振动杆,用提摩盛科理论来设计也能满足超声工程的需要。但是对粗大的变截面超声弯曲振动杆,目前还没有精确较方便的理论设计,也就是说没有频率方程的表示式。可是随着强功率超声弯曲振动在各个技术部门的应用,要求解决这个问题的呼声越来越大。例如超声振动切削和超声焊接等部门都存在这个问题。我们通过理论和实验的证明,将提摩盛科理论扩展到变截面杆中,对等厚度的指数变化的变截面杆给出了微分方程、微分方程的解、频率方程等关系式。同时用实验验证了上述关系式,理论和实验符合的很好。 The ultrasonic bending vibration of the thin section rod with equal section has the theory of elementary bending and can meet the needs of ultrasonic engineering practice. Ultrasonic Bending Vibrating Rods with Coarse Equal Cross-Section Ultrasonic Beams, designed with Timothy Section theory, also meet the needs of ultrasonic engineering. However, there is no precise and convenient theoretical design for the coarse vibrating rod with variable cross-section ultrasonic bending, that is to say, there is no expression of frequency equation. However, with the application of high power ultrasonic bending vibration in various technical departments, calls for solving this problem are getting louder and louder. For example, ultrasonic vibration cutting and ultrasonic welding and other departments have this problem. Through theoretical and experimental proofs, we extend the Timothy theory into the variable-section rod, and give the equation of differential equation, differential equation, and frequency equation for a variable-section rod with exponential change in thickness. At the same time, the above formulas are validated experimentally, and the theory and experiment are in good agreement.