Viaduct-Like Phononic Crystal Beams with Point Elastic Supports for Robust Transverse Wave Transport

This paper aims to bridge the topologically protected phenomena in phononic crystals or acoustic metamaterials and a classical civil engineering structure namely viaduct. Viaducts can be designed in the form of a bridge deck supported by a periodic array of columns, piers or arches either over land or water. The previous research on topological beam-support systems focuses on continuous elastic foundations. Comparatively, inspired by the design principles of viaducts, this paper introduces a novel periodic beam-support system and investigates the topological states. The Euler–Bernoulli beam theory and transfer matrix method are employed to theoretically solve the dispersion relation, while the numerical counterpart is obtained by the commercial software COMSOL Multiphysics. Excellent agreement between theoretical and numerical band structures is obtained, where two bandgaps with different mechanisms can be observed. The topologically protected interface mode with great energy localization is obtained. The tunability of interface mode by piezoelectric parameters and the large-area waveguide is demonstrated. Topologically protected interface states with tunable path width induced by alternative point supports are realized. The highly localized wave signals can be further extended to many practical applications such as vibration energy harvesters, and the design principles can provide guidance for other kinds of periodic systems such as photonic crystals.