A locally resonant metamaterial beam with tunable electromagnetic stiffness based on the electromechanical analogy network

Locally resonant acoustic metamaterials offer distinctive advantages in controlling low-frequency elastic waves. However, passive structures often face limitations due to narrow bandgaps and fixed working band once they are fabricated. This paper introduces a novel metamaterial beam with tunable bandgaps. This achievement is made possible by employing one electromagnet and three permanent magnets to create an electromagnetic spring. The initial stiffness, provided by the spiral beam, collaborates with the electromagnetic components to establish a local resonant unite cell featuring tunable composite stiffness. Subsequently, an analogy network is formulated for the metamaterial beam based on electromechanical analogy theory. This network not only elucidates the generation mechanism and regulatory principles of bandgaps but also serves as a paradigm for the proactive design of the metamaterial beam with external control sources, particularly under finite period conditions. Finally, theoretical analysis and experimental results collectively demonstrate the flexibility of the proposed metamaterial beam in effectively suppressing low-frequency elastic waves across a wide frequency range.