中文摘要：

由振动方程的近似解得到了具有大尺寸比的圆柱变幅杆的二维等效电路，用于带外载或不带外载的圆柱轴对称振动分析。以及尺寸比变化引起的频率变化评价。与有限元及一维模型进行了对比。发现该模型计算频率比一维模型更准确。与有限元模态分析相一致。进而由此确定了这些频率所对应的振动模态。计算发现轴向和周向水负载对应的圆柱振动频率接近，可用于超声变幅杆的优化。

英文摘要：

A 2-D equivalent circuit of column horn with large aspect ratio is obtained from an approximated solution of vibration equations. It is used in axisymmetric vibration analysis with or without external load, and also Comparison is made with other used in models frequency variation evaluation due to various aspect ratios. such as the finite element and the traditional 1-D models. It has been shown that this model gives a more accurate frequency calculation than the 1-D models, and agrees with the finite element mode analysis. In turn, the frequency associated vibration mode is determined. When water-loaded, in these two cases are rather close. This model axially or circumferentially, vibration frequencies is expected to have a further use in optimizing ultrasound horn.