Objective  Due to the difficulty of accurately converting the experimental results of acoustic radiation and vibration from scale models of complex stiffened combined shells into prototypes, the acoustic vibration similarity laws of this type of combined shell are studied in order to provide a basis for scale model experimental research on the acoustic vibration of such underwater structures.

  Method  First, a complex stiffened cone-cylinder combined shell model and its scale model are constructed by shell element reinforcement simulation. Next, based on the hybrid finite element method-boundary element method (FEM-BEM) method, the acoustic vibration response of the combined shell is calculated. Combined with the model experiment, the accuracy of the calculated response of the complex shell structure using the hybrid FEM-BEM method is then verified. Finally, the acoustic vibration similarity laws of the complex stiffened cone-cylinder combined shell are studied systematically.

  Results  The vibration modal frequency of the complex combined shell is in inverse proportion to the geometric scale ratio with the model under the same material parameter boundary conditions and excitation force, while the vibration modal in the corresponding frequency is the same. Under conditions of the same excitation force, the vibration response of the combined shell is also in inverse proportion to the geometric scale ratio, whereas the acoustic pressure is in inverse proportion to the product of the geometric scale ratio and measurement distance of the shell. The radiation efficiency and acoustic directivity of the scale model and prototype are the same.

  Conclusion  The stiffened cone-cylinder combined shell shows good acoustic and vibration similarity under similar conditions to those of the model, and the model constructed using shell element reinforcement simulation is more consistent with the experimental results.