Active structural acoustic control of an elastic cylindrical shell coupled to a two-stage vibration isolation system

An analytical study of active structural acoustic control of an elastic cylindrical shell coupled to a two-stage vibration isolation system is presented. An analytical active–passive model is developed in order to attenuate sound radiating from the base shell structure, which consists of a rigid-body machine, an intermediate rigid mass, and a supporting cylindrical shell, all connected by a combination of passive and active isolators. Various active control strategies are considered and the corresponding optimal control forces are formulated, including (a) minimizing the vibratory power transmitted to the foundation, (b) minimizing the structural kinetic energy of the supporting shell, (c) minimizing the sum of the square accelerations at the isolator locations on the supporting shell, and (d) minimizing the acoustic power radiated from the supporting shell. Numerical results are presented and discussed in detail. The control performance of all control strategies and system configurations are evaluated and compared in terms of acoustic power radiating from the supporting shell. The effects of key system parameters, i.e., the number and location of the actuators, and the fact that the output forces from the actuators are limited in engineering applications, are also considered and discussed. Finally, some concluding remarks and general design principles for the active control system are also discussed.