The bandgap characteristics of periodically arranged functionally graded stepped beams are studied based on the energy variational principle in this study. The displacement field of the beam is uniformly described using an improved Fourier series. The coupling between beam segments is achieved through artificial spring technology, which simultaneously decouples the periodic boundary conditions and the shape functions. An energy method with good convergence and accuracy has been established to solve the bandgap characteristics of the beam. Through parameter research, the influence of geometric dimensions and material properties on bandgap was analyzed. The key innovation lies in introducing the simplex method to improve the beetle optimizer, optimizing the structural parameters for the first bandgap bandwidth, effectively enhancing the local search capability of the optimizer. The first bandgap bandwidth of the optimized structure has significantly increased, which has been verified through forced vibration analysis of a 10-period beam. The bandgap characteristic exhibits good stability under different boundary conditions.
Tang et al. (Thu,) studied this question.