Active control of coupled wave propagation in fluid-filled elastic cylindrical shells
A control approach to reduce the total power propagating along fluid-filled elastic cylinders is analytically investigated. The motion of the cylinder is described by the Kennard shell equations fully coupled to the interior acoustic field. The vibration disturbance source is a pre-determined free propagating wave of either n = 0 or n = 1 circumferential order and the control forces considered are appropriate harmonic line forces radially applied to the structure. The radial displacement of the shell wall at discrete locations downstream of control forces is minimized using feedforward quadratic optimal theory. The difference of total power flow through the system before and after control is then used to evaluate the impact of the fluid on the performance of the control approach. For the breathing circumferential mode (n = 0), owing to the coupling between the two media, the fluid decreases the control performance when the disturbance is a structural-type incident wave. When the disturbance is a fluid-type incident wave, with a pressure near field concentrated at the shell wall, significant reductions of the transmitted power flow can be achieved. For the beam mode (n = 1), even though the control is applied to the structure, the fluid increases the control performances below the first acoustic cut-off frequency and decreases it above this frequency.