## 5 Conclusions  
In this paper, the derivation of the derivative function of a thin submerged cylindrical shell is carried out by combining the plate and shell vibration equation with the Helmholtz equation, and the dynamics model of a thin submerged cylindrical shell containing a complex internal elastic coupling system is established by using the integrated derivative method. On the basis of the above work, the global sensitivity analysis of the dynamic parameters in the frequency domain is carried out using the Sobol's exponent method with the transfer power flow, vibration level dropout and acoustic radiation power of the coupled system as the objective functions, and the optimization strategy of the dynamic structure parameters based on the transfer power flow, vibration level dropout and transfer power flow + vibration level dropout as the objective functions is discussed accordingly. The main findings of the study are as follows.  
1. The radiation sound field distribution of the coupled system, including sound pressure directivity and main flap amplitude, shows a more complex variation pattern with frequency, which is related to the vibration mode of the coupled system, among which in the low frequency band where the sound pressure amplitude is large, the main flap of sound pressure mainly appears in the direction of excitation force action as well as the direction perpendicular to the excitation force.
2. On the whole, the ratio curve between the transmitted power flow and the vibration level dropout (difference in decibels) has a relatively regular linear or nearly linear nature, and the ratio between the acoustic radiated power and the transmitted power flow (ratio of decibels) grows approximately linearly in the lower frequency band and tends to 1 in the higher frequency band. However, it must be noted that in the resonance region of the coupled system, the above ratio will show large fluctuations.
3. The sensitivity analysis of the parameters with greater and lesser influence on the vibroacoustic transmission shows that the parameters of the vibration isolator and the impedance characteristics of the receptor have a significant influence in the low frequency range, while in the higher frequency range, the impedance characteristics of the receptor become the main influencing factor; the variation of the impedance characteristics of the receptor may also make the installation layout of certain vibration isolators on the receptor structure have an important influence on the vibroacoustic transmission characteristics. In addition, this paper also shows that the sensitivity calculation results of the vibration level dropout and the acoustic radiated power seem to have a high similarity.
4. Use the transferred power flow and the vibration level dropout as objective functions can effectively optimise the acoustic radiation index of the coupled system. At the same time, the ranking of the acoustic radiation optimisation effect is greater when the transferred power flow and the level drop are used as the same objective function than when the transferred power flow is used as the objective function than when the level drop is used as the objective function.  
Conceptualization, S.L., R.H. and L.W.; methodology, S.L., R.H. and L.W.; software, S.L. and L.W.; validation, S.L. and L.W.; investigation, S.L. and R.H.; data curation, S.L., R.H. and L.W.; writing--original draft preparation, S.L. and L.W.; writing--review and editing, S.L., R.H. and L.W.; visualization, S.L.; supervision, R.H.; project administration, R.H.; funding acquisition, R.H. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data used to support the findings of this study are available from the corresponding authors upon request.  
**Conflicts of Interest:** The authors declare no conflict of interest.