The study demonstrates that nontrivial topological flexural edge states can be achieved without breaking the time-reversal symmetry, mirror symmetry, or inversion symmetry of the system. Such states are obtained through dimensional reduction on a gapless two-dimensional elastic metamaterial thin plate. Numerical calculations and experimental investigations confirm that flexural waves can achieve robust transmission along the boundaries of the designed structure. All states within this frequency band enable the propagation of flexural waves along the edge of the thin plate. Furthermore, this paper introduces the concept of elastic wave Shannon entropy and applies it to evaluate the frequency range of edge states in gapless metamaterials.

Huang Zhen received his Ph.D. degree from Xi’an Jiaotong University, during which he was a joint Ph.D. candidate at the Polytechnic University of Valencia, Spain. He is currently with the Rocket Force University of Engineering. His research mainly focuses on vibration and noise control of specialized equipment and acoustic metamaterials. He is committed to integrating acoustic metamaterial theory with engineering applications, aiming to provide innovative technical solutions for vibration and noise reduction in specialized equipment.