Displacement Fields Of Eigenmodes Research Articles

Wave Propagation in a LRPC Composite Double Panel Structure with Periodically Attached Pillars and Etched Holes

The locally resonant phononic crystal (LRPC) composite double panel structure (DPS) made of a two-dimensional periodic array of a two-component cylindrical LR pillar connected between the upper and lower composite plates is proposed. The plates are composed of two kinds of materials and periodically etched holes. In order to reveal the bandgap properties of structure theoretically, the band structures, displacement fields of eigenmodes and transmission power spectrums of corresponding 8 × 8 finite structure are calculated and displayed by using finite element method (FEM). Numerical results and further analysis demonstrate that if the excitation and response points are picked on different sides of the structure, a wide band gap with low starting frequency is opened, which can be treated as the coupling between dominant vibrations of pillars and plate modes. In addition, the influences of filled-in rubber, etched hole and viscidity of soft material on band gap are studied and understood with the help of “base-spring-mass” simplified model.

Attenuation Characteristics of Vibrationin a Locally Resonant Phononic Crystal Frame Structure

In this paper, a frame structure based on the locally resonant (LR) mechanism of phononic crystals (PCs) is designed on account of the wide application of frame structures in high-rise buildings, and the band structures, displacement fields of eigenmodes, and transmission power spectrums of corresponding finite structure are calculated by finite element (FE) method. Numerical results and further analysis demonstrate that a full band gap with low starting frequency can be opened by the frame structure formed by periodically combining soft and hard materials, and the starting frequency can be further lowered with the adjustment of corresponding geometric parameters, which provides a theoretical basis for the studies on vibration insulation and noise reduction of high-rise buildings.

Band gap and experimental study in phononic crystals with super-cell structure

Abstract The phononic crystals (PCs) have the wide application prospects in the field of regulating sound waves and vibration reduction due to their unique band gaps (BGs) characteristics. In this paper, a new phononic crystal of which the super-cell is composed of a simple combination of traditional PCs is proposed to open BGs in low frequency range. The dispersion relations, displacement fields of eigenmodes and transmission spectra are obtained by the finite element method. Both theoretical and experimental results verify that the improved PCs obtained low-frequency BGs range from 153 Hz to 196 Hz, which is generated by the rigid body resonance. The effect of the geometrical parameters and shapes on the dispersion relations are further analysed and discussed. Finally, the experimental transmission spectrum of the improved PCs is presented by a hammer test. This study might provide theoretical and practical support to the design of PCs components in the field of low-frequency vibration reduction.

Bandgap properties in locally resonant phononic crystal double panel structures with periodically attached pillars

The locally resonant (LR) phononic crystal double panel structure made of a two-dimensional periodic array of a two-component cylindrical LR pillar connected between the upper and lower plates is proposed, and the bandgap properties of the structure are investigated theore- tically in this paper. The band structures, displacement fields of eigenmodes and transmis- sion power spectrums of the corresponding 8×8 finite structure are calculated by the finite element method. Numerical results and further analysis demonstrate that a band gap with a low starting frequency and a wide band width is opened by the coupling between dominant vibrations of the pillars and plate modes of the upper and lower plates when the vibration source and the receiver are considered on different sides of the structure. By comparing the band structures and displacement fields of the double panel and those of the single plate with the same parameters, many common characteristics are displayed. Then, the influence of geometrical parameters on the band gap are studied and understood with the help of a simple ‘spring-mass’ model.