Active tuning of elastic wave propagation in a piezoelectric metamaterial beam

In this paper, an active control strategy is employed to actively tune the vibration and wave propagation properties in a piezoelectric metamaterial beam. The piezoelectric actuator and sensor are periodically arranged along the piezoelectric metamaterial beam. By using the extended Hamilton principle, the governing equations for the fully coupled piezoelectric metamaterial beam are obtained. The negative proportional feedback control strategy is introduced to achieve the periodical active stiffness for the piezoelectric metamaterial beam. The band structures and natural frequencies of the proposed periodic structure are derived by the transfer matrix method, and the spectral element method is applied as numerical validation. The influences of the feedback control gain ratio, length ratio, and the number of the unit cells on natural frequencies and bandgaps are discussed. Results indicate that the natural frequencies of the system are reduced with the increase in the feedback control gain ratio and length ratio. In addition, multiple bandgaps can be generated by using the negative proportional feedback control strategy. It is found that bandwidths can be obviously broadened by selecting the proper feedback control gain ratio and length ratio. The theoretical and numerical results show that the vibration and wave propagation properties of the proposed piezoelectric metamaterial beam can be controlled by using the negative proportional feedback control strategy.