Active control of coupled wave propagation in fluid-filled elastic cylindrical shells

The vibrational energy propagating in straight fluid-filled elastic pipes is carried by the structure as well as by the internal fluid. Part of the energy in the system may also transfer from one medium to the other as propagation occurs. For various types of harmonic disturbance, this study demonstrates that, whether the propagating energy is predominantly conveyed in the shell or in the fluid, large attenuations of the total power flow may be achieved by using an active control approach. As the shell and fluid motions are fully coupled, the implementation of intrusive sources/sensors in the acoustic field can be also avoided. The approach is based on using radial control forces applied to the outer shell wall and error sensors observing the structural motion.

A broad analytical study gives insight into the control mechanisms. The cylindrical shell is assumed to be infinite, in vacuo or filled with water. The first disturbance source investigated is a propagating free wave of circumferential order n=0 or n= 1. The control forces are appropriate harmonic line forces radially applied to the structure. The radial displacement of the shell wall at discrete locations downstream of the control forces is minimized using linear quadratic optimal control theory. The attenuation of the total power flow in the system after control is used to study the impact of the fluid on the performance of the control approach. Results for the shell in vacuo are presented for comparison. Considering the breathing mode (n=O), the fluid decreases the control performance when the disturbance is a structural-type incident wave. Significant reductions of the transmitted power flow can be achieved when the disturbance is a fluid-type of wave. Regarding the beam mode (n=1), the fluid increases the control performance below the first acoustic cut-off frequency and decreases it above this frequency.