Active vibration control of space truss structures: power analysis and energy distribution

This work concerns the analysis of power flow in truss structures, such as those used in space, when active control is used to attenuate vibration levels at some point in the structure. A truss structure consisting of 93 aluminum beams connected by 33 joints is studied. A model of the structure is obtained by the dynamic stiffness method using the exact solution for wave propagation in the beams; the model is also compared to a finite element model of pin-jointed bars to illustrate the localized dynamic behaviour of the structural members of the truss. Joint masses are used in the model, however dissipation is considered to occur only in the beams. Reaction forces for individual beam ends can be calculated after solving the equation of motion for the overall system. Knowing the forces and velocities on a beam end makes it possible to calculate the power flow at that end. The sum of the coupling power at both beam ends gives the power dissipated by that beam. It is found that around 80% of power dissipated is by bending motion of the beams and only 20% of power is transmitted by bending. The principal mechanism of power flow is by longitudinal motion of the beams. Overall power flow and dissipated power is analyzed before and after multichannel feedforward control is implemented in order to help understand the physical mechanisms of this form of active vibration control. Results show that on average, the controller reduces the primary source input power and supplies energy to the system. The amount of energy dissipated by the controller can be neglected, which leads to conclusion that the controller is not dissipative