A frequency-domain vibro-acoustic coupling analysis method for active-passive integrated control of underwater structures with floating raft isolation system

This paper addresses the low-frequency vibration and radiated noise control of underwater structures with floating raft isolation systems by developing an active-passive integrated vibro-acoustic coupling frequency-domain analysis method. The underwater structure is divided into the main structure, isolators, and floating raft isolation system. The vibro-acoustic response of the main structure is solved using modal superposition and the simple-source boundary integral method, while the raft dynamics are formulated in modal space and the isolators are represented by dynamic stiffness matrices or measured impedance data. By introducing virtual modes and enforcing displacement compatibility and force equilibrium at the interfaces, a unified frequency-domain coupling equation is established. Multi-channel active control forces are then incorporated into the coupled system, with control-force saturation and time-delay-induced phase deviation considered. Numerical and experimental validations are conducted, and different actuator and error sensor layouts are compared. Numerical results show that path-oriented error sensing provides stable broadband control. A 1 N actuator-force limit has little influence on the path-control sound source level, whereas increasing the equivalent delay from 10 −4 s to 10 −3 s degrades control performance. The proposed method provides an effective tool for low-frequency noise prediction, active-passive control layout design evaluation, and engineering noise reduction design.