The active vibration control of a cylindrical shell coupled with complex inner foundations is theoretically investigated using a hybrid analytical-numerical approach. The motion and solution of the shell are described by Flugge theory and wave based method, respectively. Inner foundations are analyzed by using finite element method due to their irregular shapes. These two substructures are connected through virtual springs with six degrees of freedom (DOFs), which is convenient for simulating the rigid and elastic coupling between the shell and interior structures. By employing the continuity conditions at the junction nodes, the final governing equation of the whole structure is assembled. Two types of frequency response functions are chosen as the cost functions and the optimal control force corresponding to every control strategy is derived. Numerical analysis is conducted to evaluate the performance of these control strategies in terms of mean quadratic velocity and amplitude of control forces.
Vibration characteristics of cylindrical shells and associated coupled structures have received extensive attention. At present, the research papers involving vibration responses of cylindrical shells directly excited by point forces are really sufficient. In fact, a considerable part of the noise radiated by the shells is caused by the vibration of the equipment inside the hull transmitted to the shell via the bases. Therefore, it is very critical to study the active control characteristics of the vibration transmitted from the internal equipment. Pan et al. (2008) and Caresta (2011) studied the active control of the submarine hull-shafting coupled system subjected to a harmonic force on the propeller. By placing an inertial vibration isolator on the shell, the vibration caused by the wake-excited blades decreased. Jin et al. (2011) presented some active control strategies to reduce the vibration of a cylindrical shell and then carried out an experiment to verify the effectiveness of the methods. Ma and Liu (2014) presented a two-stage vibration isolation system, which consisted of the rigid machine and a rigid vibration isolation stage connected with each other by some isolators. The vibration from the devices is significantly counteracted by applying a control force on the intermediate body. Further, Xu et al. (2019) introduced a flexible deck acting as a base under this mass-equipment system, and considered the role of the elastic partition during the vibration control research. Using the energy method, the theoretical model of shell-plate-mass sound vibration is established. This model is closer to the real hull structure. However, the internal structure considered is only a rectangular plate, which can be analytically modeled. In the real submarine, many equipment is installed on bases irregular shapes. It is difficult establish the dynamic model of the shell-base coupled system by above unified analytical methods.
