Response Analysis and Vibration Suppression of Fractional Viscoelastic Shape Memory Alloy Spring Oscillator Under Harmonic Excitation

This study investigates the dynamic behavior and vibration mitigation of a fractional single-degree-of-freedom (SDOF) viscoelastic shape memory alloy spring oscillator system subjected to harmonic external forces. A fractional derivative approach is employed to characterize the viscoelastic properties of shape memory alloy materials, leading to the development of a novel fractional viscoelastic model. The model is then theoretically examined using the averaging method, with its effectiveness being confirmed through numerical simulations. Furthermore, the impact of various parameters on the system's low- and high-amplitude vibrations is explored through a visual response analysis. These findings offer valuable insights for applying fractional sliding mode control (SMC) theory to address the system's vibration control challenges. Despite the high-amplitude vibrations induced by the fractional order, SMC effectively suppresses these vibrations in the shape memory alloy spring system, thereby minimizing the risk of catastrophic events.