Manipulation of wave motion in smart nonlinear phononic crystals made of shape memory alloys

Abstract

Abstract Thanks to the functional role of shape memory alloys (SMAs) in controlling the mechanical behavior of structures, researchers have started investigating the possibility of manipulating wave motion in phononic crystals using SMAs. While SMAs were used before to tune the wave propagation in linear phononic crystals, in this work, we aim to extend their utilization to nonlinear lattices. For this purpose, SMA helical springs are used to manipulate the dispersion curves and the location of stop-bands in weakly nonlinear monoatomic and diatomic lattice chains. Using Brinson’s formulation to describe the thermo-mechanical behavior of SMA wires and Lindstedt-Poincaré method to solve the derived governing equations, closed-form nonlinear dispersion relations in monoatomic and diatomic lattice chains are obtained and the effects of temperature-induced phase transformation and stiffness nonlinearity on the wave propagation are investigated. The results reveal that the dispersion curves of a weakly nonlinear monoatomic chain are formed at lower frequencies through the austenite-to-martensite phase transformation. Similarly, both the acoustic and optical branches of a diatomic lattice are moved to lower frequencies during the phase transformation in the cooling process. Therefore, the generated stop-bands in nonlinear diatomic lattices are also moved to lower frequencies. In addition, using auxiliary SMA ground springs, new classes of nonlinear monoatomic and diatomic chains exhibiting additional low-frequency attenuation zones are introduced. These low-frequency stop-bands are tunable and their frequency range can be modulated by exploiting the temperature-induced phase transformation in the SMA springs. The results obtained from analytic formulations are verified by numerical calculations and an excellent agreement is observed. Such tunability and the potential for adding stop-bands in low frequencies reveal that SMAs can be very helpful in designing nonlinear phononic and acoustic devices, such as vibration mitigators and wave filters with pre-defined attenuation zones.