Active control of wave propagation in multi-span beams using distributed piezoelectric actuators and sensors

This paper presents an integrated model of a one dimensional periodic structure with distributed piezoelectric actuators and sensors for complete active or passive wave propagation control. The periodic structures exhibit unique dynamic characteristics that make them act as mechanical filters for wave propagation. As a result, waves can propagate along the periodic structures only within specific frequency bands called 'pass bands' and wave propagation is completely blocked within other frequency bands called 'stop bands'. This basic property of periodic structures is enhanced by the application of distributed piezoelectric actuators and sensors, to actively control the wave propagation over the frequency range of interest. The finite element model, based on the transfer matrix approach, is developed to study the flexural wave propagation of the uniform beams resting on periodically spaced, rigid simple supports with distributed piezoelectric actuators and sensors. The model is used to predict pass and stop frequency bands for different proportional and derivative control gains. The results indicate that the location and width of the stop bands as well as the attenuation characteristics in the beam can be modified by proper choice of the control gains. The numerical predictions demonstrate that the attenuation characteristics can be maximized within different frequency bands by proper tuning of the control gains. Also, the finite element method is used to find the response of the active periodic beams to a convected harmonic pressure field. Computed results show that the response amplitudes at coincidence frequency can be actively controlled by proper selection of control gains. The tunable characteristics of the piezoelectric inserts are also used to introduce irregularities in the periodic structure. The source of disorder is the variance in the control gains of the inserts. Disorder in the periodicity typically extends the stop bands into adjacent propagation zones. More importantly, it produces localization of the vibration energy near the excitation source. The results obtained demonstrate the localization phenomenon and its control through appropriate tuning of the level of disorder in the control gains.