Band Gaps In Low-frequency Range Research Articles

Lateral flexural vibration reduction in a periodic piping system enhanced with two-degrees-of-freedom resonators

Pipe systems are commonly used in the process and power industries to transport fluid from one terminal to others. Propagation behaviour of lateral flexural waves in a pipe coupled with periodic rack structure is investigated. The pipe-rack system considered in this study is a practical case and is realized as a pipe on periodic elastic supports, while a pipe on simple and without supports represents special cases when the rack stiffness leads to extreme values. The propagation constant relations in terms of frequency are derived using Bloch–Floquet theorem which are successively verified with finite element models. The results show that a pipe with rack creates a narrow locally resonant band gap in low-frequency range which is caused by the first natural mode of the rack. Conversely, a pipe on simple supports entails only Bragg-type band gaps, while a pipe without supports carries no band gap. For tuning the band gap properties, a two-degrees-of-freedom lateral localized resonator is attached to the centre of each unit cell of the pipe. It is found that certain frequency ranges in the targeted pass bands are effectively controlled by the resonator. Furthermore, the effect of various resonator parameters, i.e. mass ratio, stiffness and damping, on band gaps is examined. It is observed that the band gaps are vanished when damping is introduced in the system. The results show a promising way to flexural vibration control of a periodic piping system with various boundary conditions.

Inertial amplification induced band gaps in corrugated-core sandwich panels

Corrugated-core sandwich panels (CSPs) have numerous applications but suffer from poor vibration performance in low-frequency range. To address this issue, a type of four-bar inertial amplification (IA) mechanism, whose inertia is increased by amplifying the movement of small masses, is proposed here to enhance the low-frequency vibration reduction capability of CSPs. The proposed structure is modelled by using finite element method (FEM) with considering the in-plane and out-of-plane degrees of freedom of IA mechanisms simultaneously. After validating the proposed model by the commercial software from the perspective of the band-structure, the vibration characteristics of the IA-CSP are investigated numerically. The results show that the attachment of the IA mechanisms can obtain wide bandgaps in low-frequency range, which hence greatly enhancing the vibration suppression performance of typical CSPs. Compared with the local resonators attached CSP, the proposed IA-CSP achieves broader band attenuation in low-frequency range with the same additional mass. Considering spatial constraints, the parametric studies are performed, which reveals that the spans and local stiffness of the IA attached locations determine the degree of nonlocality and hence influence the edge frequencies of bandgaps. The concept of tunable bandgap knob is finally presented to realize the dynamic manipulation of bandgaps under the spatial constraints.

Topological design of square lattice structure for broad and multiple band gaps in low-frequency range

Several studies have demonstrated that the design of square lattice is an efficient approach to obtain band gap characteristics. However, there are still some challenges in the design of phononic crystals capable to prohibit the propagation of low-frequency waves. In the present paper, aiming to broaden and manipulate the low frequency band gaps, an innovative structure with filling materials in a square lattice is proposed, where the spatial distribution of the materials has been optimized using an improved genetic algorithm. By analyzing the band structure and vibration modes of the designed structure, it becomes evident that the low-frequency band gaps are obtained due to the local resonance of the constituent materials. The transmission spectrum of the finite designed structure confirms an efficient wave attenuation performance in the low-frequency range. Furthermore, the effect of ligament thickness on band gaps was also investigated. The designed phononic porous plate, featuring prominent band gap properties, can be used as an example to guide the topological design of phononic crystal structures for a wide range of engineering implementations.

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.

Lamb waves propagation in a novel metal-matrix phononic crystals plate

In this paper, the propagation properties of Lamb waves in a novel phononic crystals (PCs) plate composed of a square array of double-sided composite taper stubs, which are deposited on a 2D locally resonant PC plate that composes of an array of rubber fillers embedded in the steel plate is studied. It is shown that the spring–mass system of the resonator will be decoupled by introducing the rubber filler, and then the out-of-plane band gap (BG) and the in-plane BG can be adjusted into the same lowest frequency range, respectively (the out-of-plane BG is adjusted by the rubber filler and the in-plane BG is adjusted by the taper stub). As a result, the frequency range of the generated complete BG is between 59–93 Hz due to the overlap between the in-plane and out-of-plane BG. Compared with the classic double-sided stubbed PC plate, the relative bandwidth of the BG is enlargement by a factor of 5.5 and the location of the BG is reduced by a factor of 5.5 in the proposed structure. It provides an effective way for metal-matrix PCs to obtain complete BGs in low-frequency range (below 100 Hz), which has potential for the reduction of the vibration at low frequency in practical case.

Research on the Band Gap Characteristics of Two-Dimensional Phononic Crystals Microcavity with Local Resonant Structure

A new two-dimensional locally resonant phononic crystal with microcavity structure is proposed. The acoustic wave band gap characteristics of this new structure are studied using finite element method. At the same time, the corresponding displacement eigenmodes of the band edges of the lowest band gap and the transmission spectrum are calculated. The results proved that phononic crystals with microcavity structure exhibited complete band gaps in low-frequency range. The eigenfrequency of the lower edge of the first gap is lower than no microcavity structure. However, for no microcavity structure type of quadrilateral phononic crystal plate, the second band gap disappeared and the frequency range of the first band gap is relatively narrow. The main reason for appearing low-frequency band gaps is that the proposed phononic crystal introduced the local resonant microcavity structure. This study provides a good support for engineering application such as low-frequency vibration attenuation and noise control.

Low-frequency locally resonant band-gaps in phononic crystal plates with periodic spiral resonators

In this paper, low-frequency band-gaps (BGs) in a phononic crystal (PC) thin plate with periodic spiral resonators are investigated numerically and experimentally. The formation mechanisms of the BGs in the proposed structure are explained based on the modal analysis. We find that the interaction between the local resonances and the traveling wave modes in the plate is responsible for the formation of the BG in low-frequency range. This interaction strength greatly affects the bandwidth of the BG, of which the lower edge depends on the corresponding local resonance frequency. It is shown that the out-of-plane BG can be modulated by changing the geometrical parameters. The proposed PC plate is demonstrated to possess a broad out-of-plane BG in low-frequency range from 42 Hz to 150 Hz, by combining the numerical calculations with experimental measurements. The structure design and its results provide an effective way for phononic crystals to obtain broad BGs in low-frequency range, which has potential applications in the low-frequency vibration and noise reduction.

Low-frequency band gaps in phononic crystals with composite locally resonant structures

In this paper, a novel locally resonant structure with composite units is proposed. Formation mechanisms and low-frequency characteristics of the band gaps in the proposed structure are investigated using finite element methods. Frequency positions of band gaps depend on natural frequencies of the corresponding locally resonant modes. And the gap width is related to both the Q factor of the locally resonant modes and the interaction strength in-between the locally resonant structural units. Phononic crystal structures with composite units exhibit multiple resonances and band gaps in low-frequency range, depending on the arrangement of locally resonant units. Due to the mode degeneracy of the vertical and horizontal local resonances, the composite structures possess band gaps below 200Hz with the total gap width more than 60% and the lowest frequency down to 18Hz. The structures and results provide a new effective method for phononic crystal structures to obtain broadband gaps in low-frequency range.