Bending-bending-torsion coupled wave propagation in thin-walled asymmetric metabeam: An analytical and experimental analysis


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The primary focus of this paper is to analyze the impact of the periodic resonators on the wave dispersion phenomenon of a thin-walled asymmetric beam. An analytical framework has been developed to study the triply coupled flexural and torsional wave propagation in an asymmetric metabeam. The resonators are modeled as a beam with a lumped mass at the center and placed eccentrically from the shear center. Their periodicity allows them to generate a subwavelength attenuation band in the beam. The governing equations for the coupled bending-bending-torsion vibration of a metabeam having an asymmetric cross-section are considered for generating the dispersion phenomenon, including the warping effect. Applying the BlochFloquet principle, the dispersive characteristics of the asymmetric metabeam are obtained by using the transfer matrix method. The modal characteristics of an asymmetric beam without a resonator are computed using the spectral element method and are validated with previously published results. Subsequently, the attenuation band is investigated due to the presence of a resonator and followed by the transmittance spectrum to verify the suppression of the elastic waves in the attenuation band. The experimental analysis is carried out to validate the analytical framework by obtaining the modal frequencies from the frequency response function. The detailed parametric investigation reveals that the resonator's position and characteristics significantly impact the occurrence of the band gap. A substantially wide attenuation band gap is attained by considering a continuous beam-mass resonator instead of a discrete spring-mass type resonator. This type of novel structure has the potential for the application of vibration control and acoustics.
Thin-walled asymmetric beam,Coupled wave propagation,Attenuation band,Spectral element matrix,Transfer matrix,Frequency response function
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