Bandgap Properties of Periodically Supported Beam with Inertial Amplification Mechanism

Periodically supported beams are widely employed in engineering structures, where effective control of low-frequency vibration and noise is often required. To achieve broadband elastic wave manipulation, an inertial amplification (IA) mechanism was introduced to generate low-frequency and ultra-wide bandgaps. Based on the Timoshenko beam theory, analytical models for flexural wave propagation in periodically supported beams with IA structures were established using the generalized state transfer matrix method and the Floquet transform method, respectively. The validity of the analytical models was verified by vibration transmission analysis using a finite element model. The results demonstrate that the Floquet transform method enables rapid and accurate solution of the wave model. The introduction of the IA mechanism can generate low-frequency bandgaps, which are most sensitive to the amplification angle and amplification mass. The bandgap formation mechanism arises from the modulation of Bragg scattering in the periodically supported beam by the IA structure. This modulation causes the standing wave mode frequencies to shift to lower frequencies, thereby widening the bandgaps. Furthermore, hybrid IA structure configuration can achieve broader bandgaps, facilitating elastic wave control in the ultra-wide low-frequency range. These findings provide valuable insights for low-frequency vibration and noise attenuation in engineering structures.