Analytical approximations for low frequency band gaps in periodic arrays of elastic shells

Environmental noise problems become an standard topic across the years. Acoustic barriers have been purposed as a possible solution because they can act creating an acoustic attenuation zone which depends on the sound frequency, reducing the sound transmission through it. It was demonstrated that at high sound frequencies the effect of the barriers is more pronounced than at low frequencies, due to the diffraction in their edges. Sonic Crystals (SCs) are periodic arrays of scatterers embedded in a host material with strong modulation of its physical properties, that produces band gaps attenuation in frequencies related with their geometry. These frequencies are explained by the well known Bragg’s diffraction inside the crystal. SCs present different high symmetry directions, where the Bragg’s peaks appears in different frequencies ranges due to the variation of the geometry in each direction. Recently, some authors have studied the possibility to use SCs to reduce noise in free-field condition. Also, it was showed that SCs built by trees are acoustic systems that present acoustic band gaps in low frequency range due to the geometric distribution of the trees. These results led us think that these structures are a suitable device to reduce noise, this means SCs could be use as acoustic barriers. Nevertheless the technological application of these devices for controlling the noise present some problems. First, the angular dependence of the frequencies attenuated when the sound impinges over the SC. Second, the fact that the necessary space to put the SC is bigger than in the case of the traditional acoustic barriers. Finally, the necessity of some robust and long-lasting materials to use them outdoors. In this paper we show the possibility to use different materials (rigid, mixed or soft) to make scatterers, explaining their advantages or disadvantages. These materials in conjunction with some optimization methods will allow us find some solutions to the problems mentioned above. We will relate both acoustic systems, acoustic barriers and SCs, making a comparison of the main properties of each one and then, we will present the technological possibilities to design acoustic barriers based on SCs.

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Local resonances-induced low-frequency band gaps in two-dimensional phononic crystal slabs with periodic stepped resonators

Journal of Physics D Applied Physics ◽

10.1088/0022-3727/44/5/055401 ◽

2011 ◽

Vol 44 (5) ◽

pp. 055401 ◽

Cited By ~ 89

Author(s):

Jin-Chen Hsu

Keyword(s):

Frequency Band ◽

Phononic Crystal ◽

Low Frequency ◽

Band Gaps ◽

Two Dimensional

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Vibration Attenuation Investigations on a Distributed Phononic Crystals Beam for Rubber Concrete Structures

Mathematical Problems in Engineering ◽

10.1155/2021/9982376 ◽

2021 ◽

Vol 2021 ◽

pp. 1-14

Author(s):

Chao Li ◽

Sifeng Zhang ◽

Liyong Gao ◽

Wei Huang ◽

Zhaoxin Liu

Keyword(s):

Band Gap ◽

Frequency Band ◽

High Frequency ◽

Concrete Beam ◽

Vibration Isolation ◽

Civil Engineering ◽

Low Frequency ◽

Band Gaps ◽

Spring Force ◽

Rubber Concrete

Locally resonant phononic crystals (LRPCs) beam is characterized by the band gaps; some frequency ranges within which flexural waves cannot propagate freely. So, the LRPCs beam can be used for noise or vibration isolation. In this paper, a LRPCs beam with distributed oscillators is proposed, and the general formula of band gaps and transmission spectrum are derived by the transfer matrix method (TMM) and spectrum element method (SEM). Subsequently, the parameter effects on band gaps are investigated in detail. Finally, a rubber concrete beam is designed to demonstrate the application of distributed LRPCs beam in civil engineering. Results reveal that the distributed LRPCs beam has multifrequency band gaps and the number of the band gaps is equal to that of the oscillators. Compared with others, the distributed LRPCs beam can reduce the stress concentration when subjected to vibration. The oscillator interval has no effect on the band gaps, which makes it more convenient to design structures. Individual changes of oscillator mass or stiffness affect the band gap location and width. When the resonance frequency of oscillator is fixed, the starting frequency of the band gap remains constant, and increasing oscillator mass of high-frequency band gap widens the high-frequency band gap, while increasing oscillator mass of low-frequency gap widens both high-frequency and low-frequency band gaps. External loads, such as the common uniform spring force provided by foundation in civil engineering, are conducive to the band gap, and when the spring force increases, all the band gaps are widened. Taken together, a configuration of LRPCs rubber concrete beam is designed, and it shows good isolation on the vibration induced by the railway. By the presented design flow chart, the research can serve as a reference for vibration isolation of LRPCs beams in civil engineering.

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Low-Frequency Vibration and Radiation Performance of a Locally Resonant Plate Attached with Periodic Multiple Resonators

Applied Sciences ◽

10.3390/app10082843 ◽

2020 ◽

Vol 10 (8) ◽

pp. 2843

Author(s):

Qi Qin ◽

Meiping Sheng ◽

Zhiwei Guo

Keyword(s):

Boundary Conditions ◽

Band Gap ◽

Low Frequency ◽

Expansion Method ◽

Acoustic Power ◽

Radiation Efficiency ◽

Band Gaps ◽

Periodic Arrays ◽

Low Frequency Vibration ◽

The One

The low-frequency vibration and radiation performance of a locally resonant (LR) plate with periodic multiple resonators is studied in this paper, with both infinite and finite structure properties examined. For the finite cases, taking the LR plate attached with two periodic arrays of resonators as an example, the forced vibration response and the radiation efficiency are theoretically derived by adopting a general model with elastic boundary conditions. Through a comparison with the band structures calculated by the plane-wave-expansion method, it shows that the band gaps in the infinite LR plate are in good agreement with the vibration-attenuation bands in the finite LR plate, no matter what boundary conditions are applied to the latter. In contrast to the vibration reduction in the band gaps, the radiation efficiency of the finite LR plate is sharply increased in the band-gap frequency ranges. Furthermore, the acoustic power radiated from the finite LR plate can be seriously affected by its boundary conditions. For the LR plate with greater constraints, the acoustic power is reduced in the band-gap frequency ranges, while that from the one with fully free boundary conditions is increased. When further considering the damping loss factors of the resonators, the attenuation performance can be improved for both the vibration and radiation of the LR plate.

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