Actively controllable flexural wave propagation in phononic crystal beam

Abstract

This research presents the active control of band structures and topological properties of a phononic crystal beam resting on elastic foundations and dampers. The beam is a piezoelectric beam attached with periodical alternative negative capacitance, which makes the beam an A-B-A type beam. This kind of system has great application potential like vibration control in railway and other geotechnical work. One of the important properties of metamaterial is bandgap. The flexural wave propagation could be stopped within the bandgap region. With negative capacitance, the proposed beam system could easily tune the bandgap in a wide frequency range. Elastic foundation and damping are found with the ability to lift up and dropping down band structures respectively. Based on the phase transition observed in unitcell analysis, we further design a supercell to investigate the topological properties. A TPIM point, which is a peak value of transmission line in the bandgap region can always be observed. At the TPIM frequency, beam deflection concentrates on the interface while the deflection only exists near the excitation point for the other frequencies in bandgap region. Although active control of TPIM frequency could be achieved by tuning capacitance parameter, the tuning range is very limited because of the restriction of electrical boundary conditions and mechanical instability. Then, elastic foundation is found to tune TPIM frequency and maintain high quality factor meanwhile. Finally, transmission line with the presence of dampers is plotted and the phenomenon of TPIM disappearance or vibration absorbing is observed.