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introduce
Studying machine vibration behavior is critical to diagnosing faults and identifying isolation techniques.
Porous materials (PM) are considered a good choice for controlling vibration and mitigating effects.
PM consists of randomly distributed, closed-shaped cells in three-dimensional space, similar to cancellous bone, coral, and sponge in nature.
Artificial metal foam can also be used as PM. Experiments and finite element analysis tested the mechanical properties and vibration behavior of PM. The closed foam unit was found to have limited damping capacity and strength in all directions.
Due to the random distribution of cells, it is difficult to design and control the properties of powder metallurgy. As a result, researchers are developing complex designs to predict performance.
The table summarizes the important literature related to vibration isolation and control of mechanical metamaterials in recent years. These studies include investigations of PM, PCS, and LCS, as well as experimental and numerical methodological studies in a variety of applications such as passenger seats, landing gear, and vibration isolators.
Going forward, we need to explore and study further to gain a broader view of vibration isolation of mechanical metamaterials.
Researchers have developed mechanical metamaterials constructed from periodic cellular structures (PCS) or lattice cell structures (LCS) to enhance their vibrational properties.
PCS can be designed as body-centered cubic (BCC) and face-centered cubic (FCC) unit cells. When vibration waves propagate in metamaterials, they are attenuated and the amplitude decreases due to the influence of topology and geometry.
The researchers studied the performance of PCS using 3D printing technology. Studies have pointed out that compared to solid density pillars, solid density printing produces pillars with greater cross-sectional area and weight, but there are also some cavities.
The printing orientation also has an impact on the vibration characteristics. In addition, LCS can be used to attenuate vibrations. Proper design controls the stiffness and damping characteristics of metamaterials to achieve the desired vibration mitigation.
Finite element analysis can be used to study the performance of LCS and predict natural frequencies. In conclusion, these studies provide new perspectives on vibration isolation of mechanical metamaterials.
Metamaterials can be manufactured using traditional or additive manufacturing methods.
While traditional methods require highly skilled labor and more raw materials, additive manufacturing can manufacture complex structures in a short time and save material.
Different additive manufacturing technologies include FDM, SRM, SLS, and SLA. Current research covers modeling of metamaterials, mechanical properties, and vibration methods and highlights the advantages of metamaterials over porous materials.
The researchers recommend further research to fill in gaps and gaps in the literature.
First, vibration isolation and control theory
The excitation force is usually expressed as F(t) = F0*sin(ωt), where F0 is the amplitude of the excitation force and ω is the frequency of the excitation.
When the frequency is > √2 than r, the vibration isolation effect is good. Damping has an effect on the vibration isolation effect, the smaller the damping, the better the vibration isolation effect. In order to control machine vibration, two parameters need to be considered: natural frequency and damping ratio.
The natural frequency ωn represents the natural frequency of the undamped system in hertz. The damping natural frequency ωd is the natural frequency of the damping system.
The damping ratio (ζ) is a unitless measure of the buffering capacity of an oscillating system. Damping causes energy dissipation, avoiding excessive oscillation of the system and putting the system into stable mode.
A ζ of 0 indicates no damping, ζ< 1 is underdamping, ζ=1 is critical damping, and ζ> 1 is overdamped. A high damping ratio indicates rapid attenuation of oscillation. The frequency ratio can be used to check the isolator operating status (r > √2.32).
Transmittance is an important factor in evaluating the effectiveness of an isolation system, which refers to the degree of reduction in force or motion transmitted to the foundation. The minimum transmittance indicates a good isolator, where a small amount of force or motion is transferred.
Research has focused on the use of LCS, foams, and other structures to model and control vibration systems, including device-isolator systems consisting of two-stage isolation.
Second, it is used as a porous material for vibration isolation and control
Porous material
PM (metal foam) can be found in nature in a shape similar to a fork, can be manufactured by sophisticated techniques such as steel foam or 3D printing, and is commonly used in biomedical engineering. Figure 2 shows an example of aluminum foam as a porous material.
Modeling porous materials
Artintas 43 uses image processing techniques for finite element analysis to create a porous bone model that approximates the true bone shape.
Cross-sectional images of bone were collected by Micro-CT scanning, constructing accurate 3D porous bone geometric features. The entire model was created and studied in the Abaqus software for vibration analysis.
The results of the porous model are compared with the uniform model, showing numerical differences in mode values and unique patterns in the porous model.
In addition, Sahmani et al.44 found that nanoscale porous biomaterials with nanoscale pore sizes help to improve the isolation ability of materials by studying the mechanical properties and kinetic behavior of nanoporous biomaterials.
The size-dependent effects and responses of nonlinear vibrations were predicted by applying the truncated cube cell model and the non-local strain gradient beam model. An accurate hyperbolic beam management equation is proposed.
Mechanical properties of porous materials
The effects of different material combinations on mechanical properties were studied and improved by heat treatment and polycarbonate shielding.
The results show that increasing the heating time can improve the mechanical properties, and the polycarbonate shielding layer can improve the tensile and compressive strength. This research is very useful when pursuing high mechanical properties and lightweight designs.
Shahveldi and Bharati46 developed models based on the theory of non-local strain gradients for analyzing the vibration behavior of nanoporous plates made of gradient materials on elastic substrates.
The two additional parameters of temperature and humidity are considered to simulate the actual dynamic behavior of the nanoplate as a nanosensor.
A new power function was used to represent the gradient of the material composition of nanoporous plates, and the elastic field control equation was established using Hamilton's theory. The control equation was solved by the Galerkin method, and the natural frequency equation was obtained.
Vibration analysis of porous materials
The vibration test analysis of the foam aluminum legs of the bus seat was carried out, and the vibration of the seat and the comfort of the passengers were measured.
The results show that the porous leg has better vibration damping ability and comfort than the original leg. Yin and Light 5 performed vibration excitation experiments on composite aluminum foam and polymer, applied variable pressure, and studied dynamic stiffness and loss factors.
Different vibration loading settings are shown, including vertical load, torsional, shear, traction-compression, point force, and line loading. These studies provide experimental and theoretical support for the advantages of porous materials in vibration analysis and applications.
Metamaterial modeling
The design of LCS can be implemented using CAD software such as SolidWorks and AutoCAD, as LCS often has complex shapes.
At the same time, LCS can be constructed using traditional methods or 3D printing. Al Rifaie et al.49 used SolidWorks modeling to study the mechanical properties of LCS.
Mechanical properties of metamaterials
Metamaterials can achieve vibration attenuation due to their proper stiffness and damping properties.
Sahmani et al.18 explored the behavior of nanobeams under vibration using experimental methods and evaluated the difference in frequency ratio by dimensionless maximum amplitude.
Mechanical properties, such as the stiffness of a structure, can be determined by calculative, experimental, or analytical methods.
In the analytical method, the degrees of freedom of the single-cell connecting rods are critical to construct the stiffness matrix of the entire structure. The mechanical properties of LCS were verified by experiments and finite element analysis.
In this study, the structure combining sinusoidal beam and semicircular arch combined with 3D printing was experimentally and theoretically analyzed, and its vibration isolation performance was studied.
Third, the study of metamaterials in the vibration band gap
Simulate 1D waves
In this study, Matrarch et al.69 constructed a model from unit cells arranged in directional arrays.
They used COMSOL software to conduct finite element analysis studies, and experimented and analyzed the wave propagation of 1D models.
By arranging unit cells in one dimension, the wave propagation through this structure and its bandgap frequency were studied. At the same time, a 1D periodic bar combined with a local resonator was introduced, which made it possible to create an extremely low band gap in the longitudinal wave propagating along it.
70 The rod consists of a rigid frame and rubber, in which the local resonant cavity is called a high-static low-dynamic stiffness resonator, based on a geometrically nonlinear negative stiffness mechanism.
The dispersion of longitudinal waves in 1D periodic bars was analyzed using harmonic balance method, revealing the effects of damping and nonlinearity of the resonator. The results show that the damping affects the width and depth of the bandgap, while nonlinearity only affects the center frequency and bandgap depth.
In addition, by using multiple negative stiffness resonators in one unit, multiple low-frequency bandgaps can be provided for the bending wave in the beam.
Each negative stiffness resonator consists of a vertical spring connected to the mass and two inclined springs that control the stiffness and reduce it to the desired value.
71The band gap of the bending wave in the beam was analyzed based on the plane wave unfolding method, and the calculation was carried out. The results show that the band gap in the low frequency range can be extended by using multiple negative stiffness resonators per unit unit.
Model 3D bandgaps
The vibrating band gap in three directions on a metal plate consisting of periodically repeating unit elements was studied through a three-dimensional model.
Quality-spring system shapes were manufactured using 3D printing to reduce vibration, and finite element analysis modeling was performed using COMSOL Multiphysics and experimentally verified.
They apply external vibrations at anchor points and measure the response of the center to predict vibration isolation.
Vibration attenuation in a cantilever made of ABS, made of periodically repeating single cells, but with a different pattern. The samples were coated with a PVDF film that was used to convert kinetic energy into electrical energy to study vibration isolation and energy harvesting effects.
Band gap characteristics of metamaterials
Yao et al. used the spectral elemental method (SEM) to study the bandgap characteristics of 3D printed metal template samples, and the results show that this method can be successfully used to study the vibration band gap attenuation of LCS and composite structures.
The study also examined the effect of adding defects and other factors to the 2D lattice on wave propagation and vibration isolation performance. Balaveri and Rustene studied the bandgap characteristics of chiral unit cells, and used experimental and finite element methods to predict the properties of the vibrating bandgap.
Zouari et al. used the finite element method to study the ability of metal plates to absorb and isolate elastically bending vibration waves. Hayhusseini proposed an analytical method to study periodic LCS vibration bandgaps, in which differential product (DQM) was applied.
Liang et al. developed a differential product method to solve the elastic band gap of periodic structures. Compared with the finite element and plane wave expansion methods, this method obtains accurate results in a short time.
Fourth, the advantages of metamaterials over porous materials
Application of metamaterials
The 3D printed Kagome lattice is made of nylon PA6 and is combined with polyurethane viscoelastic materials to form a metamaterial with high stiffness and competitive vibration properties.
This composite material is suitable for aerospace applications, especially in the manufacture of aircraft wings. Compared to the Kagome lattice, which has no viscoelastic material and a structure made only of nylon, it can significantly reduce the amplitude of vibration.
The study introduces a two-phase composite metamaterial made of aluminum and epoxy resin, in which star-shaped fibers are inserted to build turbine blades.
Tests were carried out using a shear dynamic test bench and a dynamic mechanics analyzer in the experiment, and the vibration parameters were calculated using the finite element method.
In seismic applications, large-scale metamaterials are recommended to mitigate the effects of seismic waves remotely.
Periodic square arrays are established to prevent earthquakes by creating a metamaterial barrier around the area that needs to be protected, employing different types of elements, such as cross-cavity elements, hollow cylindrical elements, and cylindrical elements.
The properties of these metamaterials work effectively in the frequency range of seismic waves.
The future of metamaterials as vibration isolators
With the development of additive manufacturing technology, more and more metamaterials are used in the development of vibration isolator systems, especially in the field of vibration isolation and control.
Many studies have explored the application of metamaterials in these fields, including shape memory polymers, sensors, actuators, and more.
In addition, metamaterials are used to predict and measure seismic waves. Research in this area has potential implications for vibration attenuation of seismic waves in the future.
Other aspects of metamaterials
Chen et al. proposed a three-dimensional double-arrow (DAH) stretching metamaterial based on the thermoforming method, using carbon fiber reinforced polymer (CFRP) material.
Six DAH metamaterials with different angles were designed, and damping properties were obtained through static and dynamic experimental tests.
The tangential loss factor and energy dissipation were calculated by function fitting and half-band method, and it was found that the 3D DAH metamaterial had the characteristics of high damping ability, high compressive strength and light weight.
Among them, the (15,30) and (45,60) configurations exhibit the best damping performance.
Sun et al. proposed a thin-film acoustic metamaterial as a damping mechanism for vibration structures to reduce the vibration amplitude of structures such as steel plates.
The metamaterial consists of two layers of plastic frame, a rubber film and a set of metal sheets, which are fixed by pins and hole connections. The plastic frame consists of 70 grilles, distributed over a width of 80 mm, distributed over a length of 192 mm and a thickness of 7 mm.
In addition, there are 24 semicircular iron plates, distributed in the center of the polymer frame. Four metamaterial samples were fabricated and placed in the upper, lower, right and left positions of the main structure.
An experimental work compares the vibration behavior of steel plates with no material added, steel plates with membrane-acoustic metamaterials added, and commercial rubber sheets.
The results show that the membrane acoustic metamaterial significantly reduces the amplitude of the free plate in the frequency range of 100 to 1200 Hz, reducing the overall reduction by 24.7 dB.
Compared to commercial rubber sheets, metamaterials have better damping performance in the low frequency (100-500 Hz) and high frequency (500-1200 Hz) ranges. In addition, the relatively low weight of metamaterials makes them the first choice for aerospace applications.
In another study, He proposed a new laminated acoustic metamaterial design consisting of two parallel laminates made of carbon fiber-reinforced polymers and a set of periodically distributed mass spring elements.
This new metamaterial outperforms conventional materials in vibration suppression and has a wider band gap. Experimental results show that it has been successfully applied to door manufacturing, significantly reducing door vibration.
This article reviews metamaterials and porous structures, focusing on the applications of metamaterials in vibration isolation and control.
Metamaterials are widely used in a variety of mechanical vibration systems and structures to provide unique vibration damping capabilities.
Studies have shown that metamaterials have strong vibration damping properties, so they have important application prospects in the field of vibration control.
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