Low-Frequency Bandgap Characterization of a Locally Resonant Pentagonal Phononic Crystal Beam Structure

Abstract

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.

Keywords

• phononic crystal double-layer beam
• local resonance
• energy band structure
• transmission attenuation
• vibration modes
• displacement field