Metamaterials show perfect physics characteristics for controlling elastic wave propagation. Their potential offers a lot of useful applications in low-frequency sound absorption and vibration reduction systems. However, traditional materials have inherent deficiencies in terms of functionality. There are a few designs in both acoustic and solid-mechanics domains that simultaneously exhibit sound attenuation bands and vibration bandgaps. The question poses new challenges for metamaterial development. To address this, we propose a gradient-symmetric multilayered metamaterial. The structure is capable of concurrent sound and vibration absorption. First, we established an acoustic model based on Helmholtz resonators and a vibration model by spring-mass systems. This model can predict the sound attenuation frequencies and natural frequency positions accurately. Second, through a combined simulation and experimental approach, we investigated how variations in the number of structural layers affect sound attenuation bandwidth. In addition, we analyzed the mechanisms of sound pressure distribution inside and outside the bandgaps. Finally, we elucidated the influence of lattice constants on vibration bandgap positions, demonstrating possibilities for passive control of metamaterials. This research provides robust support for the dynamic design of acoustic and mechanical metamaterials, structural modeling methodologies, bandwidth regulation strategies, and the development of sound-absorbing and vibration-damping devices.

This study systematically analyzes the dynamic behavior of bearing tilt-misalignment coupling faults in rotary joints and establishes a high-fidelity nonlinear dynamic model for a dual-support bearing–rotor system. By integrating Hertzian contact theory, the nonlinear contact forces induced by the tilt of the inner/outer rings and axial misalignment are considered, and expressions for bearing forces incorporating time-varying stiffness and radial clearance are derived. The system’s vibration response is solved using the Newmark-β numerical integration method. This study reveals the influence of tilt angle and misalignment magnitude on contact forces, vibration patterns, and fault characteristic frequencies, demonstrating that the system exhibits multi-frequency harmonic characteristics under misalignment conditions, with vibration amplitudes increasing nonlinearly with the degree of misalignment. Furthermore, dynamic models for single-point faults (inner/outer ring) and composite faults are constructed, and Gaussian filtering technology is employed to simulate defect surface roughness, analyzing the modulation effects of faults on spectral characteristics. Experimental validation confirms that the theoretical model effectively captures actual vibration features, providing a theoretical foundation for health monitoring and intelligent diagnosis of rotary joints.