Research on the control method of Bragg bandgap characteristics of phononic crystal beams based on Cantor fractals

Abstract Phononic crystals possess unique advantages in the control of elastic wave vibrations. Among them, locally resonant phononic crystals have been proven to exhibit bandgaps even under aperiodic conditions, whereas the performance of Bragg scattering phononic crystals still relies on their specific periodic structures. As a result, the application of Bragg phononic crystals is limited in many scenarios. Quasi-periodicity lies between periodicity and aperiodicity, offering greater flexibility in practical applications and demonstrating the potential to expand the versatile use of metamaterials. Fractals are geometric forms characterized by self-similarity and non-integer dimensions, existing between order and disorder, and inherently exhibit quasi-periodic properties. This paper introduces a Bragg scattering-type phononic crystal beam structure with Cantor fractal characteristics. The transfer matrix method is employed to establish a bandgap calculation model for this type of quasi-periodic phononic crystal, revealing the correlation between fractal parameters (such as fractal dimension and fractal order) and the bandgaps of phononic crystals. This enriches the methods for controlling flexural elastic waves and enables the regulation of phononic crystal bandgaps without altering the mass density of the unit cell structure. Finally, through a combination of theoretical analysis and experimental testing, the proposed phononic crystal beam’s ability to regulate low-frequency elastic waves is jointly verified. The proposed Cantor fractal phononic crystal beam structure provides a technical foundation for the quasi-periodic application of phononic crystals.