Band Gap Analysis and Vibration Reduction of Metamaterial Periodic Timoshenko Beam with Inertial Amplification Mechanism

By combining the inertial amplification (IA) mechanism and Bragg scattering mechanisms, a metamaterial periodic Timoshenko beam with IA is designed to enhance the capability of flexural vibration reduction in the low-frequency range. The band structures of flexural vibration band gap (BG) are calculated using the transfer matrix method (TMM). The results based on the Euler–Bernoulli and Timoshenko beam theory are compared to show the necessity of using the Timoshenko beam model for small slenderness ratio beams. The formation mechanism of the BG of the proposed periodic Timoshenko beam with the IA mechanism is revealed theoretically. The vibration experiments with different excitation approaches are carried out to validate the theoretical results. The effects of the beam and IA mechanism parameters on the BG properties are investigated and the rules of parameter influences are discovered. It can be found that increasing the Segment II length, decreasing the Segment I and Segment III length and thickness, and increasing the IA mass and angle are beneficial for reducing low-frequency vibrations. This research will contribute to the development of innovative smart materials and structures for vibration and noise reduction.