Abnormal Stop Band Behavior Induced by Rotational Resonance in Flexural Metamaterial

Abstract

This paper investigates abnormal stop band behavior of resonance-based flexural elastic metamaterials under the rotational resonance motion. Due to the unique physics of flexural waves, we found that the stop band generated by the rotational resonance motion exhibits peculiar behavior which are quite different from general belief - it is shown that the negativity due to the rotational resonance does not provide any stop bands and the stop band generation due to the rotational resonance is governed by totally different band gap condition. To explain the peculiar behavior, a discrete Timoshenko beam model with both effective mass and rotational inertia as independent variables is introduced, and the wave behaviors of resonance-based flexural elastic metamaterial are precisely and fully described. The unique band gap condition, including the peculiar behavior, is derived with numerical validations. We expect our new model can provide a strong background for various flexural elastic metamaterials which can be effectively applied in various vibration devices.