Active control of power flow in a three dimensional coupled Timoshenko beam

The power flow propagation and its active control in a three dimensional coupled beam structure were studied. Firstly, based on Timoshenko beam theory, the dynamic model including bending, longitudinal and torsional waves of the three dimensional coupled beam structure was established with the travelling wave method. Its accurate dynamic response was obtained. Then the active power flow transmission in the structure was determined, and the effects of longitudinal and torsional waves on the total power flow results were analyzed. The active power flow was taken as the objective function, and the optimized control force amplitude and phase were gained with an optimization algorithm. Optimal control force was applied to the structure. Ultimately, the active control of power flow in the three dimensional coupled beam structure was realized. The numerical simulation was made and the results showed that the dynamic response of the three dimensional coupled beam structure calculated with the travelling wave method is correct and reliable; the effects of longitudinal and torsional waves should be taken into account when calculating the total power flow of the three dimensional coupled beam structure; the results of Timoshenko beam model containing the effects of shear deformation and rotary inertia is more accurate than those of Euler-Bernoulli model, especially, in the medium and higher frequency ranges; active control of power flow can efficiently reduce the vibrational power flow of the three dimensional coupled beam structure in frequency domain and spatial domain, the small excursion of the optimal control force and the locations of the error sensor have slight effects on the control results.