## 1 Introduction  
Underwater noise is an important factor restricting the performance of submarines and ships [1]. Since the power cabin is located at the stern of a submarine, the vibroacoustic characteristics of the submarine stern directly determine the vibroacoustic level of the whole hull [2, 3]. Therefore, research on the vibroacoustic characteristics of the submarine stern structure has great significance for the performance of submarine. For the vibroacoustic simulation of a submarine, the middle part of the submarine can be simulated as a multi-cabin cylindrical shell, and the stern structure can be simulated as a ring-stiffened conical shell. The vibroacoustic problem of the regularly shaped structures has been thoroughly studied [4, 5], while there are few studies on the effect of viscoelastic damping on underwater acoustic radiation in the open literature [6]. Thus, the suppression of the vibration and radiation from underwater structures using viscoelastic damping layers is urgent and necessary. Numerous studies on vibration characteristics of shells in the air have been carried out in the past two decades [7, 8, 9, 10]. However, the structural vibration in the fluid medium is quite different from that of air or vacuum. In addition to the vibration of structure, there is an interaction between the structure and fluid medium. When the structure is excited to produce vibrations, the vibration boundary may compress the surrounding fluid to make the vibration propagate outwards in the form of a wave, i.e., acoustic radiation. Meanwhile, the vibration of the surrounding fluid will occur and act on the structure as a radiation force, which is called the acoustic-structure coupling problem [11, 12]. The underwater acoustic radiation of the submarine occurs in a complex environment with an interaction of the structural vibration and water medium. As for the submersed equipment, applying damping on the structure is an effective approach to reduce vibration and noise. Since the viscoelastic materials have high damping characteristics, researchers have carried out numerous studies in this field, including on the free damping beam, plates, shells and influence of external conditions [13, 14, 15, 16, 17, 18, 19]. However, the effect of self-factors of damping, such as the damping thickness and damping location, on the acoustic radiation field has not been thoroughly studied. Therefore, it is essential to study the effect of viscoelastic damping on underwater vibration and acoustic radiation. Generally speaking, for the underwater acoustic radiation of elastic structures, the FEM and BEM are two basic numerical methods. The FEM is a traditional but effective way that requires the discretization of both structure and fluid [20, 21]. Furthermore, for large-scale complex structures or far-field radiation problems, the calculation cost will be extremely large. Therefore, the FEM is applied to obtain the vibration responses of the fluid-structure interface [22], and it is used for the low-frequency acoustic and near-field problems [23, 24]. Differing from FEM, BEM is governed by the Helmholtz equation, and can satisfy the boundary condition at infinity and simplify the calculation. Researchers have analyzed the vibroacoustic responses based on the BEM method [25, 26, 27]. However, BEM requires a large number of computing resources to store a large amount of data. Hence, the combination method of FEM and BEM is usually applied for fluid-structure coupled vibration problems employing the BEM modeling the fluid and the FEM modeling the structure. Since only the structural surface needs to be discretized in the BEM method, the calculation cost would be greatly reduced. Researchers have confirmed that the combination method is a direct and feasible way [28, 29, 30, 31, 32]. It is worth mentioning that underwater sensor networks (UWSNs) are considered powerful technology to observe and explore underwater environments. The Medium Access Control (MAC) layer protocol is the most important part.