Bending–torsion coupled wave in thin-walled mono-symmetric metabeam: A non-dimensional analysis

Abstract

The influence of the periodic resonators on wave dispersion of a thin-walled mono-symmetric beam is studied in this paper. The primary focus is to develop a non-dimensional framework to investigate the coupled bending–torsion wave propagation analytically. The resonators are placed eccentrically and are capable to form a subwavelength attenuation band in the beam due to its periodicity. The governing equations corresponding to the bending and torsional motion of a metabeam are presented in a dimensionless form, including the warping effect. The transfer matrix approach is adopted to obtain the dispersive phenomena using the Bloch–Floquet principle. The modal characteristics of a mono-symmetric beam without a resonator are computed from the frequency response function and are validated with finite element results. Subsequently, the impact of various non-dimensional parameters on the attenuation band and band merging, conversion, and bifurcation phenomena are investigated through a comprehensive parametric study. It is observed that the occurrence of the band gap primarily depends on the resonator properties and its location. A substantial band gap is achieved in the low-frequency range, which will be useful for the application in the field of vibration control and acoustics.