Wave manipulation of a coupling pendulum metamaterial by parametric excitation

Abstract The use of mechanical metamaterials for the purpose of controlling wave propagation is made possible by their flexibility and adjustability. In this paper, a one-dimensional metamaterial composed of compound pendulums and inverted pendulums with high-frequency parametric excitation is proposed. The pendulum system can be equivalent to a nonlocal metamaterial and effective mass and effective stiffness can be obtained. The high-frequency parametric excitation provides an equivalent additional stiffness. This additional stiffness can provide an antigravity effect to the inverted pendulum. It makes the inverted pendulum into a stable system. The stability, bandgap structure and wave velocity can be manipulated by adjusting the frequency of the parametric excitation. And a zero-frequency bandgap can be obtained. Moreover, the pendulum system is capable of splitting a wavepacket into two distinct wavepackets within the dual wavevector region. The theoretical results are corroborated by the finite element numerical method. Due to the presence of parametric excitation, the proposed model is more tuneable than conventional metamaterials. This study has the potential to establish a novel approach for the control of ultra-low frequency vibration. The wave splitting phenomenon has the capacity to provide a theoretical foundation for the design of wave separator. It is anticipated that the findings will also furnish novel insights for the design of other devices that control wave propagation.