Bandgap analysis of partial-interaction composite beams periodically attached vibration absorbers

Abstract

Elastic metamaterials with local resonant components exhibit unique bandgap behavior that can be utilized to control the vibration and noise of mechanical structures. This study aims to introduce the bandgap characteristics into the vibroacoustic control of partial-interaction composite beams (PICBs) widely adopted in civil engineering, aviation, and marine fields. Vibration absorbers are arranged periodically on the beam to generate a bandgap in PICBs, thereby transforming a conventional PICB into a metamaterial beam. An analytical approach is proposed to establish the spectral element (SE) matrix of a metamaterial beam based on the Timoshenko–Ehrenfest beam theory. Specifically, the governing equations of motion for PICBs follow Hamilton's principle. This model considers the effects of shear slip between two-layer sub-beams, shear deformations, and rotary inertia. The SE matrix of PICBs is then constructed and applied to obtain the SE matrix of the metamaterial beam by assembling the SE matrix of the vibration absorbers. Subsequently, the wave finite element (WFE) method is employed to predict the dispersion curve of the infinite metamaterial beam and the dynamic response of the finite metamaterial beam. In a benchmark example, the complex band structure and transmission indicated by the proposed approach are validated compared to those calculated by evaluation formulas of the literature and the finite element method. Lastly, the bandgap behavior for the vibration absorber parameters, lattice constants, and shear connector stiffness is investigated based on the defined dimensionless parameters. These results are valuable for optimizing vibration and noise reduction in PICBs equipped with attached vibration absorbers.