On the attenuation of vibration using a finite periodic array of rods comprised of either symmetric or asymmetric cells

Abstract

Periodic structures have an important role to play in the reduction of vibration within a targeted frequency range. Much of the literature concerning vibrations in periodic structures involves the description of wave behaviour in infinite structures. This paper concerns the dynamic behaviour of a finite mono-coupled periodic structure, concentrating on the prediction of the vibration transmission through the complete structure in terms of the displacement transmissibility of a single cell. An investigation is conducted into the effects of either using an array of symmetric or asymmetric cells comprised of rods, on the lowest frequency range targeted for vibration attenuation. The importance of the orientation of asymmetric cells with respect to the source is also discussed. Analysis of the systems shows that correctly orientated asymmetric cells offer better performance than an array of symmetric cells for a finite mono-coupled periodic structure. Provided that the periodic structure is not connected to a structure that significantly affects its dynamics, there is improved performance both in terms of a wider frequency range in which there is vibration attenuation, and the maximum vibration attenuation within this frequency range. Analytical expressions are derived that allow the prediction of the maximum attenuation within the attenuation band based on the number of symmetric or asymmetric cells. Some experimental work is also presented to support the theoretical predictions.