An Analytical Study of Intensity Flow for Active Structural Acoustic Control in Cylinders

The effect of different types of control force actuator models and geometries on the intensity flow between a cylindrical shell and the contained acoustic space has been analytically investigated. The primary source was an external monopole located adjacent to the exterior surface of the cylinder midpoint. Actuator models of normal point forces and in-plane piezoelectric patches were assumed attached to the wall of a simply-supported, elastic cylinder closed with rigid end caps. Control inputs to the actuators were determined such that the integrated square of the pressure over the interior of the vibrating cylinder was a minimum. Test cases involving a resonant acoustic response and a resonant structural response were investigated. Significant interior noise reductions were achieved for all actuator configurations. Intensity distributions for the test cases show the circuitous path of structural acoustic power flow. For the cases tested, regions remote from the primary source contributed more significantly to the inward intensity flux than regions adjacent to the exterior source. The effect of using discrete small scale control actuators in the minimization of the interior acoustic field was to break the shell wall into many higher order spatial sources (regions) that transferred less overall energy into the acoustic medium. The use of extended piezoelectric actuators dramatically reduced the energy exchange over the whole structure. This occurred due to the reduced excitation of higher order structural modes.