Wave attenuation in a metamaterial beam with time delay control

This paper studies the bandgap characteristics of a locally resonant metamaterial beam with time delays. The dispersion relations are addressed based on transfer matrix method. The governing equations of motion of the beam in the frequency domain are given according to spectral element method. The amplitude-frequency responses of the forced beam are determined by solving linear algebraic equations. The obtained results show that the time-delayed feedback control has great relationships with the location, width and number of the bandgaps. It is interesting that the time delay can change the direction of the movement of the bandgap and give rise to the generation of multiple bandgaps. The influences of different combinations of control parameters on the bandgap properties are shown, such as broadening effects.