A theoretical analysis on the active structural acoustical control of a vibration isolation system with a coupled plate-shell foundation

An analytical description of active structural acoustical control of vibration isolation with a plate-shell coupled foundation is presented. The vibration isolation system is composed of a two-stage isolation and a flexible supporting plate coupled with an elastic cylindrical shell, which are connected via passive-active mounts. The model of the flexible foundation is derived based on the Spectro-Geometric Method (SGM) in which the displacements of the plate and shell are expressed as a modified Fourier series expansion. The response of the whole structure is available obtained by the Flexible Foundation Rigid Equipment (FFRE) modeling method. Different feed-forward control strategies are applied and their corresponding optimal control forces are calculated, including: (a) Minimizing the acoustic power radiated from the coupled structure, (b) Minimizing the sum of the square velocity of the isolators on the supporting plate, and (c) Minimizing the input power. Numerical results are presented and discussed. The performances of all feed-forward control strategies are evaluated and compared in terms of the acoustic radiation power, transmission power flow, control force amplitudes and sound pressure directivity. The effects of location of the actuators are also discussed.