阶梯型辐射体具有辐射面积大、辐射效率高等优点,在大功率超声领域被广泛应用.在高频大功率声辐射条件下,薄盘的机械强度明显不足;因此应考虑用厚板.从声学工程力学应用角度研究,基于Mindlin理论推导了新型阶梯环形变幅器自由边界条件下的弯曲振动频率方程;并对频率方程进行数值求解和有限元模拟及实验测试;同时还研究了各结构参数及材料对变幅器频率的影响.结果表明,自由边界条件下,有限元模拟结果与厚板理论计算结果都比较接近实验测试结果,误差较小.当其他参数一定时,在厚板范围内,前三阶频率随圆盘基底厚度、圆盘厚度的增加而增加;随内半径和外径的增加减小;随阶梯半径的增大而增大.所取材料的前三阶有限元模拟频率与厚板理论计算结果误差较小,其中45号钢频率最大,而铜频率最小,铝频率居中,研究结论对大功率阶梯型辐射体及辐射器的设计和应用提供理论参考和频率调试依据.%The ladder type radiator because of its large radiation area,higher radiation efficiency advantages have been widely used in high power ultrasonic field.In high power and high frequency sound radiation conditions,the mechanical strength of thin disk is obviously insufficient,therefore should consider the plate.The flexural vibration frequency equation of thick step ring bending vibration amplitude transformer under free boundary condition is derived based on Mindlin theory and the numerical solution of the frequency equation and the experimental test are carried out.The results show that the free boundary condition,finite element simulation results and theoretical results are quite close to the plate test results,the error is smaller.When the other parameters are constant,the first three order frequency increases with the thickness of the disk base and the thickness of the disk,decreases with the increase of the inner radius and the outer diameter,and increases with the increase of the radius of the step in the range of plate;calculation error smaller materials taken from the first three order finite element simulation and frequency plate theory.The No.45 steel and copper,the maximum frequency,the minimum frequency,the frequency of aluminum radiator design center,the bending vibration of the conclusion of the study on the high power ladder type radiator and provide the theoretical reference on the basis of debugging and frequency.
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