Abstract
The capability of periodic structures to act as filters for traveling waves is used to control the longitudinal wave propagation in rods. Shape memory inserts placed periodically along the rods act as sources of impedance mismatch with tunable characteristics. Such characteristics are attributed to the unique behavior of the shape memory alloy whereby the elastic modulus of the inserts can be varied up to three times as the alloy undergoes a phase transformation. With such a controllable capability, the inserts can introduce the proper impedance mismatch necessary to reduce the wave propagation.
An analytical model based on the transfer matrix approach is developed to predict the performance of the periodic rods with shape memory inserts. The activation temperatures of the shape memory inserts are controlled using two different strategies. The propagation constants as well as the response of the composite rod are first evaluated when the inserts are all activated at the same temperature. The obtained results show that changing the thermal activation modifies the width and location of the pass and stop bands. The rod can therefore be tuned to attenuate waves propagating at selected frequencies.
The tunable characteristics of the shape memory alloy are also used to introduce irregularities in the periodic structure. The source of disorder is the variance in the activation temperature of the inserts. Disorder in the periodicity typically extends the stop bands into adjacent propagation zones. More importantly, it produces the localization of the vibration energy near the excitation source. The obtained results demonstrate the localization phenomenon and its control through appropriate tuning of the level of disorder in the activation temperatures. The theoretical investigations presented here provide guidelines for designing tunable periodic structures with high control flexibility where propagating waves can be attenuated and localized.
Export citation and abstract BibTeX RIS