Locally resonant phononic crystals are a kind of artificial periodic composite material/structure with an elastic wave band gap that show attractive application potential in low-frequency vibration control. For low-frequency vibration control problems of ship power systems, this paper proposes a phononic crystal board structure, and based on the Bloch theorem of periodic structure, it uses a finite element method to calculate the band structure and the displacement fields corresponding to the characteristic mode and vibration transmission curve of the corresponding finite periodic sandwich plate structure, and the band gap characteristics are studied. The mechanism of band gap formation is mainly attributed to the mode coupling of the phononic crystal plate structure. Numerical results show that the sandwich plate structure has a double periodicity, so it has a multi-stage elastic wave band gap, which can fully inhibit the transmission of flexural waves and isolate the low-frequency flexural vibration. The experimental measurements of flexural vibration transmission spectra were conducted to validate the accuracy and reliability of the numerical calculation method. On this basis, the potential application of the proposed vibration isolation method in a marine power system is discussed. A vibration isolation platform mounted on a steel plate is studied by numerical simulation, which can isolate low-frequency vibration to protect electronic equipment and precision instruments.

Intended for the vibration and noise control problems faced by many engineering fields, a fresh variety of phononic crystal beam structure was constructed by attaching a one-dimensional periodic multilayer cylinder to a double-layer beam structure. Utilizing the finite element method and the Bloch theorem, the vibration modes of the band structure, the critical point of the band gap and the associated finite structure’s vibration transmission is estimated, and then the band gap characteristics of the structure are comprehensively studied. The results show that reasonable parameter design can achieve vibration and noise control in a certain frequency range. Based on the modal analysis, the mechanism of band gap opening is revealed. By comparing the single-layer beam and double-layer beam with the same parameters, the advantages of the double-layer beam in vibration reduction and noise reduction are shown. The study’s findings offer a fresh concept for ship engineering disciplines including vibration and noise reduction technology.

By introducing nonlocal elastic theory and Kirchhoff plate theory to plane wave expansion (PWE) method, the band structure of a nonlocal piezoelectric phononic crystal (PC) nanoplate is calculated. A complete band gap with magnitude order gigahertz (GHz) is opened. In order to investigate the characteristics of such a band gap in detail, the corresponding influence rules of thermo-electro-mechanical coupling fields, nonlocal effects and geometric parameters on band gaps are studied. During the researches, temperature variation, electrical voltage and external axial force are picked as the influencing parameters corresponding to thermo-electro-mechanical coupling fields. Nonlocal coefficient is chosen as the influencing parameter related to surface effects. Lattice constant, PZT-4 hole radius and nanoplate thickness are picked as the influencing parameters of geometric parameters. All the results are expected to be of help for nano electro mechanical system (NEMS) based on piezoelectric periodic nanoplates.

This paper proposes a local resonance-type pentagonal phononic crystal beam structure for practical engineering applications to achieve better vibration and noise reduction. The energy band, transmission curve, and displacement field corresponding to the vibration modes of the structure are calculated based on the finite element method and Bloch-Floquet theorem. Furthermore, an analysis is conducted to understand the mechanism behind the generation of bandgaps. The numerical analysis indicates that the pentagonal unit oscillator creates a low-frequency bandgap between 60–70 Hz and 107–130 Hz. Additionally, the pentagonal phononic crystal double-layer beam structure exhibits excellent vibration damping, whereas the single-layer beam has poor vibration damping. The article comparatively analyzes the effects of different parameters on the bandgap range and transmission loss of a pentagonal phononic crystal beam. For instance, increasing the thickness of the lead layer leads to an increase in the width of the bandgap. Similarly, increasing the thickness of the rubber layer, intermediate plate, and total thickness of the phononic crystals results in a bandgap at lower frequencies. By adjusting the parameters, the beam can be optimized for practical engineering purposes.