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.
Highlights
Models consisting of Kirchhoff plate with attached mass-springs that can clearly explain the related physics of the vertical resonance phenomena, the physics related to the rotational resonance phenomena has not been clearly explained yet
To explain the related physics, we developed a discrete Timoshenko beam model in which an idea of ‘effective rotational inertia’ is introduced in addition to the generally known ‘effective mass’
A new model dedicated on the resonance-based flexural elastic metamaterial was developed by extending Timoshenko theory
Summary
These peculiar characteristics cannot be explained with previous theories on negative density or stiffness, and there has been a need for a new theory of resonance-based flexural metamaterial. As a possible application of the current findings, a new type of frequency filter is shown by combining both the rotational and vertical resonance phenomena
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