Multiple resonances, fragmented propagation and homogenized attenuation of the beam model coupled with bi-periodic resonators

Abstract

Wave propagation and attenuation behaviours of beam-resonators coupling model are dominated by the local resonators and the periodicity. Inspired by bi-periodic structures in engineering practice and based on a previous study, beam models coupled with bi-periodic resonators are proposed by introducing a parametric variant resonator into the periodic model. Wavenumber spectrum relation of the bi-periodic coupling system with a parametric variant resonator and several regular resonators is obtained by means of the method of reverberation-ray matrix and solved by numerical techniques. Effects of various parameters of the parametric variant resonator on the wavenumber spectrum characteristics of the bi-periodic models are investigated in numerical examples, which show that the parametric variant resonator results in an additional resonant peak and extra non-local resonant attenuation bands. Bandwidth of the local resonant attenuation band can be broadened by either increasing the translational stiffness or decreasing the mass of the parametric variant resonator. Compared to wavenumber spectrum curves of the beam model coupled with periodic resonators, the introduction of the parametric variant resonator makes the wavenumber spectrum curves of the real part divided into more curved and straight segments in an alternating presentation. The appearance of extra non-local resonant attenuation bands and the decrease of attenuation performance of the original non-local resonant attenuation bands indicates that the attenuation capability of the non-local resonant attenuation bands is homogenized in the frequency domain for the bi-periodic coupling system. The innovative findings and practical suggestions in the whole frequency range could provide potential references for the researchers and engineers in vibration reduction design of bi-periodic structures in engineering practice.