A practical approach to evaluate periodic rods composed of cells with geometric and material periodicity

Abstract

The use of a periodic structure is an useful alternative for suppressing vibrations without requiring strategies of active control. The main characteristic of this type of strategy is to conveniently define the geometry and material of the structure. Although there are different techniques for designing periodic structures, these methods typically require a candidate structure for computing the desired band gap. Thus, if a specific target frequency (or frequency range or band gap) is required, these methods need to be solved repetitively for different candidate structures, until the desired result is achieved. In this context, the present article introduces an approach for designing periodic rods considering both geometric and material periodicity. A new equation is derived from the state vector notation and the longitudinal transmitted wave is examined in computing the vibration transmissibility. The proposed equation allows one to define a target frequency, for which the band gap is specified, and its solution provides two parameters which are used to design the periodic rod. Alternatively, the proposed approach allows verification of the frequency of minimum transmissibility for a pre-defined candidate structure. Numerical simulations and experimental tests are presented to demonstrate the approach. The results show that the proposed approach is a useful strategy for designing periodic structures.