Analytical modeling and numerical analysis for tunable topological phase transition of flexural waves in active sandwiched phononic beam systems

Topological phononic crystals (PnCs) have attracted tremendous research attention in recent years. A significant hallmark of these structures is that these crystals can support interface modes that are robust to structural disturbance and protected by topology. In this study, we propose a new type of active sandwiched PnC beam for inducing topological geometric phase transition and topologically protected interface modes (TPIMs) for one-dimensional (1D) systems. The layered system comprises two commonly used active materials, i.e., barium titanate (BaTiO₃) and cobalt ferric oxide (CoFe₂O₄). Analytical modeling for this layered system is derived in the framework of linearly constitutive relations of a magneto-electro-elastic (MEE) material with temperature effects. Two analytical approaches, i.e., the spectral element method (SEM) and the plane wave expansion (PWE) method, are applied to derive the theoretical band structure of the system and excellent agreement is reported. A numerical analysis based on the finite element method (FEM) is adopted for further validation. The influence of outer fields in the bandgap frequency is examined and the size-dependent properties are also analyzed. Moreover, the transmission response is determined via analytical modeling and numerical analysis. It is found that the robust TPIMs are immune to defects and disorders. Conclusively, this study puts forward a new type of beam system for inducing topological phase transition. It can be readily extended to more complex systems and higher-order models.