Influence of boundary conditions on the stop band effect in finite locally resonant metamaterial beams

This paper investigates the influence of the boundary conditions on the stop band effect in finite locally resonant metamaterial beams. In a first step, a Timoshenko beam with tuned vibration absorbers is used to describe a metamaterial beam. The influence of different boundary conditions for beams with different lengths as well as of tuned vibration absorbers with different amounts of added mass or different tuned frequencies is assessed numerically. It is found that edge modes are present inside the stop band frequency region predicted by the unit cell analysis and these edge modes reduce the level of vibration attenuation achieved. Three solutions are analysed to reduce the effect of the edge modes: (i) varying the tuned frequency, (ii) the number or (iii) the positions of the individual tuned vibration absorbers added to the host structure. In a second step, the results of the numerical investigation are experimentally validated: the experimental results are in good agreement with the numerical results.