中文摘要：

基于Flgge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。

英文摘要：

The frequency equation of the axisymmetric coupled vibration of a ultrasonic tubular resonator with both ends free is derived by an exact solution method,based on Fliigge classical thin shell theory.The dependence of the dimensionless frequency Ω on the ratio of length to radius l/a,the ratio of radius to thickness a/h and Poisson＇s ratio v is investigated,and the axisymmetric coupled vibration of a ultrasonic tubular resonator with both ends shear diaphragm is compared with that with both ends free.The accuracy of two-dimensional and three-dimensional apparent elasticity method is also assessed by the comparison with the exact solution method.Finally,the mode shape of the ultrasonic tubular resonator is calculated by the exact solution method,and its transform efficient is analyzed.The results show that as for two boundary conditions of both ends free and shear diaphragm,the difference of the effect of the boundary condition on the dimensionless frequency of the axisymmetric coupled vibration of a ultrasonic tubular resonator becomes smaller as l/a increases,and the larger a/h,the smaller the difference.Moreover,for free-free boundary conditions,the change of a/h has nearly no effect on the dimensionless frequency of the thin tubular resonator usually considered to mean a/h10.Furthermore,the dimensionless frequencyΩdecreases as v increases for a given l/a,and the impact of v onΩis different for different l/a,and the maximum impact will appear when l/a=π.Finally,the study also shows the three-dimensional apparent elasticity method has very high calculation accuracy.