Mono-shell submarine's acoustical coating is supposed to possess the multifunctional characteristics of mechanical noise, hydrodynamic noise and acoustic target intensity control. Two difficulties need to be addressed for this purpose: the first one is to improve the mechanical noise low-frequency control effect; the other one is to achieve multifunctional compatibility of acoustical coating. In this paper, from the perspective of reducing the sound radiation of mechanically excited shells, modal superposition method was adopted to establish the vibro-acoustic coupling and sound radiation model of multilayer graded acoustical coating and finite length ribbed cylindrical shell in ideal aqueous medium of infinite size. Based on the acoustic coating modal transfer function characteristics, the acoustic coating gradient distribution characteristics, thickness, the number of layers and other parameters were analyzed to reduce sound radiation of the ribbed cylindrical shell. The characteristic acoustic impedance asymptotic parameter distribution of the layered gradient acoustic cover was given and compared with the sound reduction characteristics of laying a uniform acoustic cover. The results indicate that the acoustic coating with increased acoustic impedance and slow wave velocity from the inner to the outer layer of the ribbed cylindrical shell has the property of reducing the vibration displacement of the outer surface more effectively than the uniform coating, which can significantly increase the sound reduction effect and extend the low frequency range of noise reduction. Optimisation of the acoustic coating should increase the acoustic impedance mismatch of the inner layer and the outer layer adaption effect, in order to help reduce the low frequency acoustic radiation of the ribbed cylindrical shell and to take the reduction of the acoustic target intensity into account.