Low frequency ship vibration isolation using the band gap concept of sandwich plate-type elastic metastructures

Sandwich structures are widely applied in modern industry such as aerospace, automobile as well as marine structures. However, the vibroacoustic properties of sandwich structures are adversely influenced by low effective mass. In this study, the flexural wave propagation characteristics and vibration mitigation performances of the periodic sandwich plate-type metastructures are investigated. The proposed sandwich plate-type metastructures are constituted of a sandwich plate with periodic thin-wall circular tube cores and periodically attached local stepped resonators. A finite element method combining Solid-Shell coupling numerical method and Bloch theory is presented to calculate the dispersion relations and the displacement fields of the eigenmodes of the infinite periodic sandwich plate-type metastructures. In addition, the acceleration frequency responses and vibration attenuation performances of finite periodic sandwich plate-type metastructures are numerically investigated and compared with the experimental measurements. Furthermore, the influences of geometric parameters on flexural wave band gaps are conducted. Results show that the sandwich plate-type metastructures can yield a low-frequency broad flexural wave band gap, in which the flexural wave propagation is conspicuously suppressed, resulting in significant flexural vibration attenuation. The flexural wave band gap and vibration attenuation performances can be effectively manipulated by designing geometric parameters of the sandwich plate-type metastructures.

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On vibration isolation of sandwich plate with periodic hollow tube core

Journal of Sandwich Structures & Materials ◽

10.1177/1099636217707933 ◽

2017 ◽

Vol 21 (3) ◽

pp. 1119-1132 ◽

Cited By ~ 6

Author(s):

Gui-Lan Yu ◽

Hong-Wei Miao

Keyword(s):

Vibration Isolation ◽

Sandwich Plate ◽

Experimental Studies ◽

Low Frequency ◽

Dispersion Relations ◽

Frequency Responses ◽

Vibration Attenuation ◽

Potential Applications ◽

Vibration Isolation Performance ◽

Isolation Performance

The vibration isolation performance of a PC sandwich plate with periodic hollow tube core is investigated experimentally and numerically. The experiment results reveal that there exist vibration attenuation zones in acceleration frequency responses which can be improved by increasing the number of periods or tuning some structure parameters. The presence of soft fillers shifts the attenuation zone to lower frequencies and enhances the capability of vibration isolation to some extent. Dispersion relations and acceleration frequency responses are calculated by finite element method using COMSOL MULTIPHYSICS. The attenuation zones obtained by experiments fit well with that by simulations, and both are consistent with the band gap in dispersion relations. The numerical and experimental studies in the present paper show that this PC sandwich plate exhibits a good performance on vibration isolation in low frequency ranges, which will provide some useful references for relevant research and potential applications in vibration propagation manipulations.

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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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Flexural wave propagation and vibration isolation characteristics of sandwich plate-type elastic metamaterials

Journal of Vibration and Control ◽

10.1177/1077546320942689 ◽

2020 ◽

pp. 107754632094268

Author(s):

Yinggang Li ◽

Huan Zi ◽

Xiong Wu ◽

Ling Zhu

Keyword(s):

Vibration Isolation ◽

Sandwich Plate ◽

Offshore Structures ◽

Geometric Parameters ◽

Band Gaps ◽

Flexural Wave ◽

Wave Band ◽

Thin Wall ◽

Elastic Metamaterials ◽

Plate Type

Sandwich structures are widely used in the fields of aerospace, automobile as well as ship and offshore structures because of their excellent mechanical performances such as lightweight, high specific strength and high specific stiffness. In this study, the flexural wave band gaps and vibration isolation characteristics of sandwich plate-type elastic metamaterials are numerically and experimentally investigated. The proposed sandwich plate-type elastic metamaterials are constituted of local resonant stubs periodically deposited on a sandwich plate with periodic thin-wall aluminium tube cores. An efficient finite element method combined with a solid-shell coupling method and Bloch periodic boundary conditions is presented and validated by experimental measurements to calculate the dispersion relations and the acceleration frequency responses of sandwich plate-type elastic metamaterials. The influences of geometric parameters on the flexural wave band gaps are performed and discussed. Results show that the proposed sandwich plate-type elastic metamaterials can yield flexural wave band gaps in the low-frequency range and show significant performance on the flexural vibration isolation. Moreover, the flexural wave band gaps can be effectively modulated by the geometric parameters.

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Vibration Propagation Characteristics of Binary Periodic Sandwich Panels

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.226-228.172 ◽

2012 ◽

Vol 226-228 ◽

pp. 172-175 ◽

Cited By ~ 2

Author(s):

Pei Pei Ge ◽

Gui Lan Yu

Keyword(s):

Band Gap ◽

Young’S Modulus ◽

Frequency Band ◽

Vibration Isolation ◽

Young's Modulus ◽

Low Frequency ◽

Sandwich Panels ◽

Geometrical Parameters ◽

The Finite Element Method ◽

Steel Cylinder

By using the finite element method, the band structures of the periodic hollow cylinder sandwich panels are investigated, and the influences of the material and geometrical parameters on the band gap are discussed in detail. The results show that The Young's modulus of panel and the coated layer have the greatest influences on the band gap of binary periodic hollow steel cylinder sandwich panels. The smaller the Young's modulus, the lower the frequency band gap. The material and geometrical parameters of the core have important influences on the lower edges of the band gap. Thicker and higher hollow steel cylinder with large density is favorable to gain a wide low-frequency band gap. The work presented will provide a theoretical guidance in the vibration isolation research.

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Vibration isolation characteristics of finite periodic tetra-chiral lattice coating filled with internal resonators

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406215602913 ◽

2016 ◽

Vol 230 (16) ◽

pp. 2840-2850 ◽

Cited By ~ 6

Author(s):

Dawei Zhu ◽

Xiuchang Huang ◽

Hongxing Hua ◽

Hui Zheng

Keyword(s):

Band Gap ◽

Vibration Isolation ◽

Periodic Structures ◽

Low Frequency ◽

Band Gaps ◽

Stiffened Plate ◽

Frequency Range ◽

Vibration Attenuation ◽

Unit Cells ◽

Internal Resonators

Owing to their locally resonant mechanism, internal resonators are usually used to provide band gaps in low-frequency region for many types of periodic structures. In this study, internal resonators are used to improve the vibration attenuation ability of finite periodic tetra-chiral coating, enabling high reduction of the radiated sound power by a vibrating stiffened plate. Based on the Bloch theorem and finite element method, the band gap characteristics of tetra-chiral unit cells filled with and without internal resonators are analysed and compared to reveal the relationship between band gaps and vibration modes of such tetra-chiral unit cells. The rotational vibration of internal resonators can effectively strengthen the vibration attenuation ability of tetra-chiral lattice and extend the effective frequency range of vibration attenuation. Two tetra-chiral lattices with and without internal resonators are respectively designed and their vibration transmissibilities are measured using the hammering method. The experimental results confirm the vibration isolation effect of the internal resonators on the finite periodic tetra-chiral lattice. The tetra-chiral lattice as an acoustic coating is applied to a stiffened plate, and analysis results indicate that the internal resonators can obviously enhance the vibration attenuation ability of tetra-chiral lattice coating in the frequency range of the band gap corresponding to the rotating vibration mode of internal resonators. When the soft rubber with the internal resonators in tetra-chiral layers has gradient elastic modulus, the vibration attenuation ability and noise reduction of the tetra-chiral lattice coating are basically enhanced in the frequency range of the corresponding band gaps of tetra-chiral unit cells.

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Study on Tunable Band Gap of Flexural Vibration in a Phononic Crystals Beam with PBT

Crystals ◽

10.3390/cryst11111346 ◽

2021 ◽

Vol 11 (11) ◽

pp. 1346

Author(s):

Peng Zhao ◽

Lili Yuan ◽

Tingfeng Ma ◽

Hanxing Wei

Keyword(s):

Band Gap ◽

Elastic Foundation ◽

Vibration Isolation ◽

Axial Stress ◽

Low Frequency ◽

Flexural Vibration ◽

Phononic Crystals ◽

Band Gaps ◽

Response Curves ◽

Element Method

Low-frequency flexural vibration plays a significant role in beam vibration control. To efficiently attenuate the propagation of flexural vibration at a low-frequency range, this paper proposes a new type of a phononic crystals beam with an adjustable band gap. The governing equations of flexural vibration in a periodic beam are established based on the Euler theory and Timoshenko theory. The band structures are calculated by the plane wave expansion method, the attenuation properties and transmission response curves with a finite periodic beam are calculated by the spectral element method and finite element method. The effects of the elastic foundation and axial stress on band gaps are discussed in detail, and the regulation of the temperature field on the band gap is emphatically studied. The theoretical and numerical results show that the elastic foundation and axial stress have significant influence on the band gap, and the location and width of the band gaps can be adjusted effectively when the Young’s modulus of PBT is changed by a varying temperature. The results are very useful for understanding and optimizing the design for composite vibration isolation beams.

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Band Gaps and Vibration Isolation of a Three-dimensional Metamaterial with a Star Structure

Materials ◽

10.3390/ma13173812 ◽

2020 ◽

Vol 13 (17) ◽

pp. 3812 ◽

Cited By ~ 1

Author(s):

Heng Jiang ◽

Mangong Zhang ◽

Yu Liu ◽

Dongliang Pei ◽

Meng Chen ◽

...

Keyword(s):

Band Gap ◽

Vibration Isolation ◽

Dynamic Properties ◽

Structural Parameters ◽

Mass Density ◽

Three Dimensional ◽

Low Frequency ◽

Band Gaps ◽

Acoustic Metamaterials ◽

Star Structure

Elastic metamaterials have promising applications in wave control and vibration isolation, due to their extraordinary characteristics, e.g., negative Poisson ratio, band gaps, effective negative mass density and effective negative modulus. How to develop new functional metamaterials using a special structure has always been a hot topic in this field. In this study, a three-dimensional (3D) star structure is designed to construct metamaterials with both negative static and dynamic properties. The results show that the 3D star structure formed a wide band gap at lower frequency and had a negative Poisson’s ratio. Different from conventional acoustic metamaterials, the main physical mechanism behind the low-frequency band gap of the 3D star structure is the resonance mode formed by the bending deformation of each rib plate, which made it easier to achieve effective isolation of low-frequency elastic waves with a low mass density. In addition, many structural parameters of the 3D star structure can be modulated to effectively adjust the band gap frequency by changing the angle between the concave nodes and aspect ratio. This study provides a new way to design the 3D acoustic metamaterials and develop the lightweight vibration isolation devices.

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Tunable Low Frequency Band Gap and Waveguide of Phononic Crystal Plates with Different Filling Ratio

Crystals ◽

10.3390/cryst11070828 ◽

2021 ◽

Vol 11 (7) ◽

pp. 828

Author(s):

Shaobo Zhang ◽

Jiang Liu ◽

Hongbo Zhang ◽

Shuliang Wang

Keyword(s):

Band Gap ◽

Composite Structure ◽

Structural Parameters ◽

Phononic Crystal ◽

Low Frequency ◽

Filling Ratio ◽

Height Ratio ◽

Road Vehicles ◽

Aluminum Base ◽

Gap Width

Aiming at solving the NVH problem in vehicles, a novel composite structure is proposed. The new structure uses a hollow-stub phononic-crystal with filled cylinders (HPFC) plate. Any unit in the plate consists of a lead head, a silicon rubber body, an aluminum base as outer column and an opposite arranged inner pole. The dispersion curves are investigated by numerical simulations and the influences of structural parameters are discussed, including traditional hollow radius, thickness, height ratio, and the new proposed filling ratio. Three new arrays are created and their spectrum maps are calculated. In the dispersion simulation results, new branches are observed. The new branches would move towards lower frequency zone and the band gap width enlarges as the filling ratio decreases. The transmission spectrum results show that the new design can realize three different multiplexing arrays for waveguides and also extend the locally resonant sonic band gap. In summary, the proposed HPFC structure could meet the requirement for noise guiding and filtering. Compared to a traditional phononic crystal plate, this new composite structure may be more suitable for noise reduction in rail or road vehicles.

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