Research on the tunability of longitudinal wave resonance rainbow trapping in the periodic non-uniform magnetostrictive rods

The rainbow trapping effect, characterized by the presence of multiple band gaps (BGs) and wave energy accumulation, holds great promise in applications such as wave filters and vibration energy harvesters. To achieve the tunability of longitudinal wave propagation and further enhanced energy localization, a thickness-induced periodic array of magnetostrictive rods with the rainbow trapping effect is designed in this paper. Firstly, the analysis of longitudinal wave propagation in a periodic non-uniform magnetostrictive rod is conducted using the differential quadrature method, and the correctness is validated by comparing theoretical results with finite element simulations performed for various thickness profiles. Subsequently, according to the combined BGs caused by the proposed metamaterial rods, the formation mechanism of longitudinal wave rainbow trapping is analyzed by time and frequency domain analysis, respectively. Furthermore, the variations in resonance rainbow trapping frequencies are investigated considering the magneto-mechanics coupling in the periodic non-uniform magnetostrictive rods. Numerical simulations demonstrate that resonance rainbow trapping frequencies lead to the most pronounced vibration localization compared to initial and cut-off rainbow trapping frequencies. Notably, the resonance rainbow trapping frequency can be significantly manipulated through applied magnetic field and compressive pre-stress. Those conspicuous phenomena from proposed magnetostrictive metamaterial rods are expected to provide engineers with a new avenue to construct tunable wave filters and vibration signal amplifiers.