In the field of vibration and noise reduction, phononic crystals and their ability to regulate elastic wave propagation have attracted significant attention. Leveraging the bandgap characteristics of phononic crystals, researchers can precisely control elastic wave transmission within specific frequency ranges. To this end, numerous scholars have dedicated efforts to designing and optimizing novel phononic crystals while investigating their bandgap formation mechanisms. Biomimetic design, which innovates engineering solutions by emulating forms, structures, and functions from nature or existing systems, has emerged as a vital source of inspiration for developing advanced phononic crystals in recent years. Furthermore, the acoustic black hole (ABH) structure, an engineered design that leverages wave manipulation characteristics to achieve energy focusing and absorption of acoustic waves, has been demonstrated to effectively optimize phononic crystal configurations, thereby significantly enhancing their bandgap properties. Aiming to achieve broad bandgap implementation in phononic crystal design, this study integrates biomimetic concepts with the ABH structures and proposes a flying saucer shaped phononic crystal configuration based on local resonance theory.

Currently, the bandgaps of phononic crystals are primarily determined through plane wave expansion (PWE), finite-difference time-domain (FDTD), lumped mass methods, and finite element method (FEM). The FEM demonstrates distinct advantages in calculating unit cell bandgaps and has been widely adopted. The fundamental principle of bandgap computation using FEM involves three key stages: First, the unit cell analytical model is discretized into finite elements, where the continuous field within each element is characterized by nodal forces and displacements. Subsequently, finite element equations are established based on equilibrium conditions, incorporating Bloch-Floquet periodic boundary conditions to derive an eigenvalue equation containing wavevector-frequency relationships. Ultimately, solving this eigenvalue equation yields the dispersion relations of the equivalent model. This study employs the COMSOL Multiphysics finite element analysis platform to solve the eigenvalue problem, thereby obtaining the band structure of the phononic crystal while simultaneously acquiring its vibration modes.

The flying saucer shaped phononic crystal proposed in this study exhibits pronounced bandgap characteristics, generating a local resonance bandgap within the 0-1000 Hz frequency range. Specifically, the bandgap spans from 294 Hz to 944 Hz with a width of 650 Hz, exhibiting a relative coverage ratio of 65% over the target frequency spectrum.

The parametric analysis reveals significant geometric sensitivity of bandgap characteristics: 1) With the rectangular width h₁ increasing from 2 mm to 4 mm, the bandgap starting frequency decreases from 352 Hz to 280 Hz while the cut-off frequency elevates from 845 Hz to 961 Hz, resulting in a 38.1% bandwidth enhancement from 493 Hz to 681 Hz; 2) As the large trapezoidal height a₂ grows from 0.6 mm to 1.4 mm, the bandgap shifts downward from 402-1312 Hz to 248-734 Hz, accompanied by a 46.6% bandwidth reduction from 910 Hz to 486 Hz. 3) When the small trapezoidal height a₃ escalates from 0.3 mm to 1.2 mm, the initial frequency increases by 13.2% (288 Hz to 326 Hz) whereas the cut-off frequency drops by 33.3% (1170 Hz to 780 Hz), collectively causing a 48.5% bandwidth decrease from 882 Hz to 454 Hz.

The bandgap characteristics of the flying saucer shaped phononic crystal are determined by the vibration modes of its constituent structures. Specifically, the bandgap starting frequency is primarily governed by the translational vibration of the resonator, while the cut-off frequency results from the reverse-phase vibrations on both sides of the edge structure.

When the excitation frequency falls within the bandgap range, the flying saucer shaped phononic crystal effectively localizes vibrational energy. Most energy is confined within the internal structure, particularly at the resonator and edge regions, with minimal energy transmitted to the output terminal. This process achieves strong vibration suppression, thereby fulfilling the objectives of vibration reduction and noise control.

The bandgap characteristics of the flying saucer shaped phononic crystal, especially the bandgap position and width, are predominantly influenced by the equivalent mass of the resonator, the equivalent mass of the edge structure, and the equivalent stiffness of the soft coating. Geometric parameter optimization enables precise bandgap tuning: increasing the small trapezoidal height elevates the bandgap starting frequency; enlarging the rectangular width adjusts the cutoff frequency; and modifying the height of the large trapezoid alters the bandgap width.

The flying saucer shaped phononic crystal proposed in this study exhibits bandgap characteristics. By configuring the flying saucer shaped phononic crystal into composite acoustic absorption panels through periodic array arrangements, this design fully exploits its low-frequency local resonance bandgap characteristics spanning 650 Hz, providing innovative solutions for multi-domain vibration and noise control. In automotive engineering, the panels can be embedded within door cavities, roof structures, or chassis interlayers to suppress road-induced tire noise (200-500 Hz) and engine resonance harmonics. For rail transit applications, integrating the panels into carriage wallboards, bogie systems, or track underlayments enables simultaneous attenuation of wheel-rail friction noise (500-800 Hz) and carbody structural vibrations (300-600 Hz). This innovative approach offers a mechanism-driven yet engineering-feasible solution for industrial noise and vibration mitigation, demonstrating significant practical potential.