In view of the influence of variability of low-frequency noise frequency on noise prevention in real life, we present a novel two-dimensional tunable phononic crystal plate which is consisted of lead columns deposited in a silicone rubber plate with periodic holes and calculate its bandgap characteristics by finite element method. The low-frequency bandgap mechanism of the designed model is discussed simultaneously. Accordingly, the influence of geometric parameters of the phononic crystal plate on the bandgap characteristics is analyzed and the bandgap adjustability under prestretch strain is further studied. Results show that the new designed phononic crystal plate has lower bandgap starting frequency and wider bandwidth than the traditional single-sided structure, which is due to the coupling between the resonance mode of the scatterer and the long traveling wave in the matrix with the introduction of periodic holes. Applying prestretch strain to the matrix can realize active realtime control of low-frequency bandgap under slight deformation and broaden the low-frequency bandgap, which can be explained as the multiple bands tend to be flattened due to the localization degree of unit cell vibration increases with the rise of prestrain. The presented structure improves the realtime adjustability of sound isolation and vibration reduction frequency for phononic crystal in complex acoustic vibration environments.

A two-dimensional phononic crystal sensor model with high-quality factor and excellent sensitivity for sensing acetone solutions and operating at 25–45 kHz is proposed. The model for filling solution cavities is based on reference designs of quasi-crystal and gradient cavity structures. The transmission spectrum of sensor is simulated by the finite element method. High-quality factor of 45,793.06 and sensitivity of 80,166.67 Hz are obtained for the acetone concentration with 1–9.1%, and quality factor of 61,438.09 and sensitivity of 24,400.00 Hz are obtained for the acetone concentration range of 10–100%, which indicated the sensor could still achieve high sensitivity and quality factor at operating frequencies from 25 to 45 kHz. To verify the application of the sensor to sensing other solutions, the sensitivity for sound velocity and density is calculated as 24.61 m^-1 and 0.7764 m³/(kg × s), respectively. It indicates the sensor is sensitive to acoustic impedance changes of the solution and equally suitable for sensing other solutions. The simulation results reveal the phononic crystal sensor possessed high-performance in composition capture in pharmaceutical production and petrochemical industry, which can provide theoretical reference for the design of new biochemical sensors for reliable detection of solution concentration.

Based on the analogy of the quantum valley Hall effect, a ligament-type phononic crystal plate with local resonators is designed in this study to facilitate the valley state transport of low-frequency elastic waves. We analyze the key factors affecting the local resonance modes and reduce the frequency of the Dirac cone by changing the connection form of the structure’s beams. The spatial inversion symmetry of the structure is broken to open a new band gap by introducing a mass difference in the resonator pair. The robustness of the designed structure’s topological valley waveguide under defects and bends is verified. Based on this characteristic, we introduce the gradient heights into the supercell structure where elastic waves at different frequencies split and stop significantly on the supercell structure to achieve sub-wavelength topological rainbow trapping. This design provides a theoretical reference for exploring the low-frequency elastic topological mode and the application of topological rainbow capture in sub-wavelength structures.

Based on the quantum valley Hall effect analogy, this work proposes a phononic crystal plate with ligament-type beams to obtain the topological valley transmission of elastic waves. A pure Bragg degenerate state appears in the high-frequency region with a resonator introduced. By rotating the central scatterer and the beams, the mirror symmetry is broken to form a topological bandgap. Subsequently, this work finds that two selective edge states also appear beside the commonly non-trivial crossing edge states in the topological bandgap by calculating the projected band and eigenvalue spectrum of the supercell with different valley Hall phases phononic crystals. Their appearance is due to band separation of the topological edge states caused by an increase in the rotation angle. Both selective edge states can transmit topologically in specific paths. They will help further to broaden the width of the frequency band of topological transmission. Besides, an elastic wave splitter is designed and demonstrated numerically, which can form two channels and three channels in different frequency bands. With the topological selective edge state disappearing, a topological corner state exists in the edge bandgap. This work provides a theoretical reference for practical applications of broadband elastic wave topological transmission and elastic energy trapping.

Phononic crystals are a kind of artificial acoustic metamaterial whose mass density and elastic modulus are periodically arranged. The precise and efficient design of phononic crystals with specific bandgap characteristics has attracted increasing attention in past decades. In this paper, an improved adaptive genetic algorithm is proposed for the reverse customization of two-dimensional phononic crystals designed to maximize the relative bandwidth at low frequencies. The energy band dispersion relation and transmission loss of the optimal structure are calculated by the finite-element method, and the effective wave-attenuation effect in the bandgap range is verified. This provides a solution for the custom-made design of acoustic metamaterials with excellent low-frequency bandgap sound insulation or other engineering applications.