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基于Flgge壳体理论,利用严格解法得出了自由边界条件下超声管形振子纵径耦合振动的频率方程,研究了长径比、径厚比及泊松比等参数对振子振动频率的影响,并和薄膜简支边界条件下的振动情况进行了对比;通过与表观弹性法进行比较研究,探讨了表观弹性法的精度;最后用严格解法计算了管形振子的振型曲线,对其纵径转换效率进行了分析。研究表明:在自由和薄膜简支两种边界条件下,随着长径比的增大,两种边界条件对管形振子纵径耦合振动无量纲频率影响的差异性减弱,且径厚比越大其差异性越小;在自由边界条件下,对于径厚比a/h>10的薄壳振子,径厚比的变化对无量纲频率的影响很小;在长径比一定时无量纲频率随泊松比的增大而减小,且泊松比对其的影响程度随长径比的变化而不同,当长径比l/a=π时影响最大;通过比较研究,证明三维表观弹性法具有很高的计算精度。
Based on Flögge shell theory, the frequency equation of longitudinal coupling coupling vibration of ultrasonic tube-shaped vibrator under free boundary conditions was obtained by using rigorous solution. The effects of the parameters of aspect ratio, radius-thickness ratio and Poisson’s ratio on vibration frequency of vibrator And compared with the vibration condition under the simple supported boundary conditions. By comparing with the apparent elastic method, the precision of the apparent elastic method was discussed. Finally, the mode shapes of the tube-shaped vibrators were calculated by the strict solution method. The efficiency of its longitudinal conversion is analyzed. The results show that with the increase of the aspect ratio, the difference between the two boundary conditions on the dimensionless frequency of the longitudinal coupling vibration of the tube-shaped vibrator is weakened under the two boundary conditions of free and thin-film simply supported, In the free boundary condition, for the thin-walled vibrator with radius-thickness ratio a / h> 10, the variation of radius-thickness ratio has little influence on the dimensionless frequency. When the aspect ratio is constant, dimensionless frequency The Poisson’s ratio decreases with the increase of Poisson’s ratio, and the influence of Poisson’s ratio is different with the ratio of aspect ratio. When the aspect ratio l / a = π, the influence is the greatest. By comparison, the three-dimensional appearance Elastic method has a high calculation accuracy.