The Low-Frequency Vibration Control Mechanism of a Finite Locally Resonant Beam with Elastic Supports

PurposeThis paper studies the low-frequency vibration control mechanism of a finite locally resonant beam with elastic supports.MethodsA theoretical model of the finite locally resonant beam consisting of periodic resonators attached to a beam with elastic support boundaries is established, and the power flow of the elastic supported beam is calculated by the modal superposition and harmonic-balance methods. In addition, the study investigates the influence of the periodic number of resonators on the isolation performance of the elastic supported beam, and the difference between local resonance and anti-resonance is determined. Finally, the equivalent Young's modulus of the locally resonant beam is obtained using the parameter inversion method.ResultsThe periodic number of resonators can affect the bandgap characteristics, and the anti-resonance of the resonators dominates the attenuation performance when the number of resonators is not sufficient to form a locally resonant bandgap. The bandgap created by the local resonance has a wider frequency range than the anti-resonance, and the periodic resonators will change the equivalent Young's modulus of the beam in a pattern consistent with the bandgap.ConclusionIt is shown that the periodicity of the resonators has a significant effect on the low-frequency bandgap characteristics and equivalent parameters of the elastic supported beam.