Low-frequency Vibration Reduction Research Articles

Novel Phononic-Like Crystal Wave Barrier Structure for Vibration Isolation

As an efficient, environmentally friendly, and economical urban public transportation tool, the subway has significant advantages compared to other urban public transportation tools and plays an irreplaceable role in the urban rail transit system. While the subway brings many conveniences to people, its operation has also brought a series of problems to urban development and residents’ lives, especially the vibration and noise problems generated by the subway have become unavoidable and urgent problems to be solved. The traditional wave barriers have a certain effect on attenuating and suppressing the vibration generated by the subway, but it has shortcomings in terms of the width and quantity of elastic wave bandgap (BG), so its application in low-frequency vibration reduction and isolation of subway systems is greatly limited. In order to broaden the elastic BG width and quantity of the wave barrier, this paper designs a novel phononic-like crystal subway wave barrier (PLCSWB) for subway vibration isolation based on locally resonant theory. Firstly, the dispersion curves of the novel PLCSWB are calculated using the improved plane wave expansion method and finite element method (FEM), and compared with the dispersion curves of traditional phononic crystal (PC) wave barriers. Secondly, the frequency response function of the novel PLCSWB is calculated using FEM to evaluate its attenuation effect on vibration, and the energy distribution characteristics at its BG boundary are analyzed. Then, the main factors affecting the BG of the novel PLCSWB are analyzed, and a spring–mass system equivalent model of the novel PLCSWB is established to theoretically estimate its BG range. Finally, the vibration data of the tunnel wall monitored on site are used to analyze and verify the vibration isolation effect of the novel PLCSWB. The results show that the novel PLCSWB opens five low-frequency BGs in the 200[Formula: see text]Hz frequency band, which increased the total width of the opened BGs by 49% compared to traditional PC wave barriers. In the frequency range of the BG, the attenuation value of the novel PLCSWB to vibration is mostly above 30[Formula: see text]dB, and the energy distribution inside the structure is mainly concentrated in the primitive cell that controls the BG, indicating good attenuation and control effects on vibration. The main factors affecting the BG of the novel PLCSWB are the density of the scatterer material, the elastic modulus, and the thickness of the wrapping layer material. Moreover, during subway operation, the novel PLCSWB has a good attenuation effect on the vibration transmitted from the tunnel wall to the soil. Among them, the maximum vibration acceleration amplitude of the novel PLCSWB with nine rows is reduced by 47%, and the vibration isolation performance is remarkable. The relevant research results of this paper provide a novel approach and method for the study of subway vibration reduction and isolation, and can also provide specific references for the design and development of wave barriers.

Low-frequency vibration reduction of an underwater metamaterial plate excited by a turbulent boundary layer

Flow-induced structural noise is an important component of hydrodynamic noise of underwater structures. Local resonance metamaterials are considered to have excellent performance and enormous potential in the field of low-frequency vibration and noise control. To verify its potential, the paper derived the underwater band gap of a lateral local resonance (LLR) plate through the plane wave expansion (PWE). Then, utilizing the modal superposition approach and Rayleigh integral technique, the vibro-acoustic response of a LLR plate under a turbulent boundary layer (TBL) excitation is obtained. Finite element certification is also conducted through an uncorrelated wall plane wave technique. Parametric study is conducted to analyse the factors which influence the control effects. The result shows that the plate exhibits excellent suppression performance for flow-induced vibration at band gap frequencies. The band gaps and suppression ranges generated by the underwater metamaterial plate, are dramatically narrowed due to the thick fluid load. The paper provides theoretical guidance for the control of flow-induced structural vibration and the application of acoustic metamaterials.

Low-frequency broadband vibration reduction based on a square spiral beam local resonance phononic crystal

Low-frequency vibration poses a great danger to both industrial production and human health. Therefore, the development of efficient low-frequency vibration reduction structures remains a focus of academic and engineering research. In this paper, a novel low-frequency vibration reduction local resonance phononic crystal (LRPnC) plate with a square spiral beam LRPnC design is proposed. Through finite element simulation, the band structure and vibration characteristics of the LRPnC are first analyzed. On this basis, a gradient LRPnC plate with rainbow trapping effect is constructed by gradient arranging unit cells with different structural parameters to achieve broadband vibration reduction. Finally, the vibration reduction performance of the designed structure is experimentally verified. The finite element analysis results show that the designed gradient LRPnC plate can provide more than 20 dB of transmission attenuation over the full frequency range of 20–200 Hz. And the experimental results are consistent with the simulation results.

A study on low-frequency vibration mitigation by using the metamaterial-tailored composite concrete-filled steel tube column

The bandgap properties exhibited by local resonant metamaterials provide a potential approach for structural vibration reduction. In this work, we introduce the local resonance mechanism into the composite structure for the first time and propose a novel metamaterial column with 33.8–47.2 Hz low-frequency vibration mitigation based on practical engineering materials and utilizing material shear deformation. By vertically arranging metamaterials, the metamaterial concrete-filled steel tube column with low-frequency vibration reduction bandgap is designed. Its equivalent bandgap model is proposed by combining the Timoshenko beam and Bloch theorem. The bandgap formation mechanism and vibration mitigation effect of the metamaterial are clarified by finite element analysis. It is revealed that the bandgap generation depends on the contrary motion between the resonator and the substrate, thus the reaction force from the relative motion can cancel the external excitation. Then, the bandgap vibration mitigation effect of the metamaterial column is proved by shaking table tests at different amplitudes. This also supplies a feasible solution for vibration mitigation control and even earthquake protection for buildings, bridges, and major infrastructures. Finally, the theoretical, numerical, and experimental results are discussed to verify the validity of the theoretical approach and numerical model, and the rubber damping is found to widen the bandgap but weaken the vibration reduction capacity.

Low frequency vibration isolation characteristics and intelligent design method of hull grillage metastructures

In this paper, the wave propagation mechanics theoretical model of hull grillage metastructures with local resonators is established, and the intelligent design method of hull grillage metastructures is proposed based on deep learning. The flexural vibration isolation characteristics of periodic hull grillage structures and the proposed hull grillage metastructures are theoretically studied using the spectral element method. Numerical calculation and experimental tests of the flexural wave vibration transmission of hull grillage metastructures are conducted to validate the proposed theoretical model. In addition, the data set is constructed by using the wave mechanics theoretical model of hull grillage metastructures, and the forward prediction neural network model of vibration transmission characteristics as well as the inverse design neural network model of hull grillage metastructures are established. Results show that compared with periodic hull grillage structures, the proposed hull grillage metastructures possess significant low-frequency flexural wave vibration isolation characteristics which almost completely covers the low-frequency range from 27 Hz to 169 Hz. Both forward prediction and inverse design network models have good performance, which verifies the correctness of the intelligent design method based on deep learning, and provides a new direction for the structural design on demand of low-frequency vibration reduction of ship and offshore structures.

Lever-type inertial amplification plates for low-frequency vibration reduction

In this work, a lever-type inertial amplification (LIA) metastructure is proposed to enhance the vibration reduction capability of thin plates in the low-frequency range. The mechanism consists of a rigid lever hinged on the host plate at two separate locations and a small mass mounted at the end of the lever. Band-structures of the unit cell and vibration transmissibility of the finite LIA plate are computed by using the combination of analytical method and finite element method. Numerical results show that compared with the local resonant (LR) plates with the same added mass, the proposed LIA plates generate wider and deeper complete bandgaps at the same target frequency. The Bragg bandgaps occurring at higher frequencies are also broader compared with those of the LR plates due to a stronger impedance mismatch between the host plate and the attachments. Moreover, the vibration reduction performance of the LIA plate presents unique direction-dependent characteristics: maximum vibration attenuation is achieved when the LIA mechanisms are installed parallel to the wave propagation direction. To address the issue that single-level LIA takes up too much space to install, a multi-level LIA design is proposed. On one hand, the multi-level design makes the LIA mechanisms much more compact without hampering their vibration reduction performance; on the other hand, the combination of sub-levels greatly enhances the design flexibility of LIA mechanisms. Finally, experiments are performed to further confirm the vibration reduction performance of the proposed LIA plates.

Enhanced energy transfer and multimodal vibration mitigation in an electromechanical acoustic black hole beam

Owing to their unique energy focusing capability and high-frequency damping effects, Acoustic Black Hole (ABH) structures show promise for numerous engineering applications. However, conventional ABH structures are mostly effective only above the so-called cut-on frequency, a bottlenecking deficiency that needs to be addressed if low-frequency problems are of concern. Meanwhile, achieving simultaneous high frequency ABH effects and low-frequency vibration reduction is also a challenge. In this paper, electrical linear and nonlinear shunts are intentionally added to an ABH beam via PZT patches to tactically influence its dynamics through electromechanical coupling. Both numerical and experimental results confirm that the effective frequency range of the ABH can be broadened as a result of the electrical nonlinearity induced energy transfer (ET) from low to high frequencies inside the beam. However, increased nonlinearity strength, albeit beneficial to energy transfer, jeopardizes the linear dynamic absorber (DA) effects acting on the lower-order resonances. Solutions are exploited to tackle this problem, exemplified by the use of negative capacitance in the nonlinear shunts with the embodiment of parallel linear electrical branches. On top of the nonlinear ET effects, simultaneous DA effect is also achieved for the low-frequency resonant vibration mitigation. Studies finally end up with a design methodology which embraces the principle of ET and DA to tactically cope with different frequency bands. The final outcome is the broadband multi-modal vibration reduction and the breaking down of the frequency barrier existing in conventional linear ABH structures.

An analytical and experimental study on adaptive active vibration control of sandwich beam

A novel composite sandwich beam with adaptive active control system is proposed for low-frequency vibration reduction, and the experimental investigation on adaptive closed-loop vibration control is carried out. The macro fiber composite (MFC) piezoelectric patches and filtered-x least mean square (Fx-LMS) algorithm are employed to construct the adaptive closed-loop control system. An improved analytical model considering the effects of MFC piezoelectric patches is proposed to calculate the vibration characteristics of the composite sandwich beam. It provides a theoretical basis for the design of adaptive control scheme. The accuracy of present analytical model is verified by the results of experiment and numerical simulation. The adaptive vibration control is implemented analytically and experimentally, and the results demonstrate that the low-frequency vibration of the composite sandwich beam can be greatly and quickly suppressed by the proposed adaptive closed-loop control system. Moreover, vibrations induced by complex multi-frequency excitation with different amplitudes can be effectively reduced by using the proposed adaptive control system. The novelty of this work lies in the proposed adaptive closed-loop vibration control system and improved analytical method for piezoelectric composite sandwich beam. The study provides a novel design of real-time control system for the low-frequency vibration of composite sandwich structures.

Acoustic three-terminal controller with amplitude control for nonlinear seismic metamaterials

To design and optimize seismic metamaterials, the impacts of nonlinearity in different locations of locally resonant acoustic metamaterials on the dispersions and the variation of amplitude-dependent bandgaps are investigated in this paper. The research used theoretical calculations, namely, Lindstedt–Poincaré perturbation method and prediction method, and combined finite-element simulation. Summarizing from our research, the lower bandgap is sensitive when exposed to amplitude stimulation, when there arise nonlinear characteristics between matrices; while nonlinearity appears within the interior oscillator, amplitudes obtain a more intense influence on the bandgap, introducing an enormous magnitude of deviation between the upper bandgap and the lower bandgap. Based on the peculiar frequency-shift characteristics, an acoustic three-terminal controller is proposed as a conventional subsize acoustical device and nonlinear seismic metamaterials component. This controller enables the realization of modulating the value of output signals by adjusting the quantitative loading on the control port, without changing the input signals and the parameters of the apparatus validated with the finite-element simulation. The work may offer potential applications in low-frequency vibration reduction and external-controllable multi-functional acoustical devices.

New floating slab track isolator for vibration reduction using particle damping vibration absorption and bandgap vibration resistance

• A new floating slab track vibration isolator is developed using particle damping vibration absorption and bandgap vibration resistance. • Using the low-frequency vibration reduction effect of non-obstructive particle damping (NOPD), the attenuation of resonance peaks in the begin of bandgap frequency range is realized. • A coupled train-floating slab track-bridge dynamic model is established to investigate the vibration isolation capability. The environmental vibrations caused by rail transit continue to increase in importance. Even though there are a variety of efficient vibration reduction measures, there is still room for further improvement by trying new, effective vibration control mechanisms. In this paper, a new floating slab track vibration isolator is developed using particle damping vibration absorption and bandgap vibration resistance. Using the low-frequency vibration reduction effect of non-obstructive particle damping (NOPD), the particulate material is added to the outer ring vibrator to participate in vibrations, and the attenuation of resonance peaks in the begin of bandgap frequency range is realized. The energy loss factor and damping ratio of particle damping for different particle sizes are analyzed using a discrete element model. A finite element model with integrated particle damping effect is also formulated and the bandgap behavior of phononic crystal vibration isolator (PCVI) with additional particle damping is analyzed. The effect of particle damping is assessed by calculating the force transmission spectrum. In order to the investigate vibration isolation performance of the combined NOPD-PCVI when subjected to excitation from trains running at different speeds, a coupled train-floating slab track-bridge dynamic model is established. The results show that the NOPD-PCVI offers better vibration isolation than a steel-spring vibration isolator and the traditional PCVI (T-PCVI) in the frequency band of 50–150 Hz. The energy dissipation provided by particle damping and the bandgap damping of phononic crystals reduce the vertical accelerations of the bridge deck in the bandgap frequency band. Specifically, the total vertical accelerations of the bridge deck equipped with NOPD-PCVIs is reduced by 15.3 dB compared to steel springs, and 5.6 dB compared to T-PCVIs, respectively.

Radial Seismic Metamaterials Based on Layering Theory: Broadband Shielding of Ultra-Low Frequency Seismic Surface Waves

In this paper, a novel radial seismic metamaterial (LRSM) based on layering theory is proposed. Compared with traditional seismic metamaterials, the structure of LRSM is a periodic array of multi-layer rings distributed along the radial direction. By using the finite element method, the dispersion relationship and displacement vector field of LRSM with different layers are studied, and the influence of structural geometric parameters and circumferential continuity on the band gap characteristics of LRSM is discussed. The frequency domain analysis of finite periodic structure and the three-dimensional transient wave propagation analysis are carried out. The results show that the LRSM has ultra-low frequency broadband characteristics, which is produced by the coupling between the local resonance of the LRSM and the surface wave mode. Comparing three LRSMs with different layers, the initial frequency and bandwidth do not change monotonically with the increase of the number of layers. There is an optimal bandgap characteristic in two layers, and the relative bandwidth can reach 83.9%. The increase of the number causes the change of the structural stiffness, which is caused by the change of the local resonance strength. The position and width of the band gap in the LRSM are very sensitive to the height of the structure. The increase of the height of the LRSM can move the first band gap to the low frequency, and the total bandwidth increases, which is mainly caused by the increase of the equivalent mass of the system with the increase of the height of the structure. Further, it is verified that LRSM can effectively attenuate seismic surface waves of 0.1–20 Hz, and its maximum amplitude attenuation can exceed 85%. The novel periodic structure proposed in this paper can provide new options for the fields of earthquake and low-frequency vibration reduction.

Low-Frequency Vibration Control of Metro Slab Track Based on Locally Resonant Theory

Vibration control has always been one of the research hotspots in the field of urban metro system. Due to the unsatisfactory application effect of traditional vibration damping technology in practice, a novel method, based on the locally resonant theory, was introduced into metro vibration damping system to improve the low-frequency vibration reduction effect. Meanwhile, the new metro vibration reduction slab track was designed. Furthermore, the coupled model of the metro vehicle-slab track was established and verified, and the reduction effect of the new metro slab track on low-frequency vibration under the action of metro vehicles was analyzed. Results show that: 1) The new vibration reduction slab track is really in control of the low-frequency vibration (50–100 Hz), and the attenuation effect can reach 10 dB; 2) The new slab track has multiple low-frequency vibration band gaps, which can achieve multi-frequency vibration reduction; 3) The new slab track can reduce the vibration acceleration of the track, which can improve the comfort level of the vehicle. Therefore, the local resonance theory enriches the existing metro vibration reduction design theory and provides a method for the design of the metro vibration control.

Multiscale modeling and design of lattice truss core sandwich metastructures for broadband low-frequency vibration reduction

Lattice truss core sandwich structures are advanced lightweight structures that have broad application prospects in many fields, but the attenuation of low-frequency vibrations in these structures is still challenging. To achieve broadband low-frequency vibration reduction in lattice truss core sandwich structures, we propose a design of multiscale lattice truss core sandwich metastructures which exhibit a coupling effect of local resonance and Bragg scattering mechanisms. For ease of analysis and design of such multiscale metastructures, we develop an efficient semi-analytical multiscale modeling method based on a combination of the dynamic homogenization method and the spectral element method. The multiscale modeling method is verified by comparing it with the conventional finite element method, and it is further employed to design multiscale metastructures. Numerical and experimental results demonstrate that the low-frequency bandgap and vibration reduction band can be greatly broadened via an appropriate multiscale design. Specifically, a typical multiscale finite metastructure, fabricated by embedding only three identical local resonators, achieves a significant vibration reduction within the super-wide low-frequency range of 295–905.4 Hz. The normalized vibration reduction bandwidth is as large as 1.02, which is much broader than that of a conventional equi-scale metastructure designed with the same added resonator mass ratio.

A Review of Bioinspired Vibration Control Technology

Due to huge demand in engineering, vibration control technology and related studies have always been at the frontiers of research. Although traditional vibration control methods are stable and reliable, they have obvious shortcomings. Through evolution and natural selection, certain body-parts of animals in the natural world have been cleverly constructed and well designed. This provides a steady stream of inspiration for the design of vibration control equipment. The prime objective of this review is to highlight recent advances in the bionic design of vibration control devices. Current bionic vibration control devices were classified, and their bionic principles were briefly described. One kind was the bionic device based on the brain structure of the woodpecker, which is mostly used to reduce vibration at high frequencies. Another kind of bionic device was based on animal leg structure and showed outstanding performance in low frequency vibration reduction. Finally, we briefly listed the problems that need to be solved in current bionic vibration control technology and gave recommendations for future research direction.

Low frequency vibration reduction method for floating slab tracks based on tuned viscous mass damper

Low frequency vibration reduction method for floating slab tracks based on tuned viscous mass damper

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.

Theoretical analysis and experimental research on multi-layer elastic damping track structure

The increase of axle load and train speed would cause intense wheelrail interactions, and lead to potential vibration related problems in train operation. For the low-frequency vibration reduction of a track system, a multi-layer track structure was proposed and analyzed theoretically and experimentally. Firstly, the analytical solution was derived theoretically, and followed by a parametric analysis to verify the vibration reduction performance. Then, a finite element simulation is carried out to highlight the influence of the tuned slab damper. Finally, the vibration and noise tests are performed to verify the results of the analytical solution and finite element simulation. As the finite element simulation indicates, after installation of the tuned slab damper, the peak reaction force of the foundation can be reduced by 60%, and the peak value of the vertical vibration acceleration would decrease by 50%. The vibration test results show that the insertion losses for the total vibration levels are 13.3 dB in the vertical direction and 21.7 dB in the transverse direction. The noise test results show that the data of each measurement point is smoother and smaller, and the noise in the generating position and propagation path can be reduced by 1.9 dB–5.5 dB.

Vibration response analysis of floating slab track supported by nonlinear quasi-zero-stiffness vibration isolators

To improve the low-frequency vibration reduction effect of a steel spring floating slab track (FST), nonlinear quasi-zero-stiffness (QZS) vibration isolators composed of positive stiffness elements (PSEs) and negative stiffness elements (NSEs) were used to support the FST. First, considering the mechanical characteristics of the nonlinear QZS vibration isolators and the dynamic displacement limit (3 mm) of the FST, the feasible parameter groups were studied with the nonlinear stiffness variation range and bearing capacity as evaluation indices. A vertical vehicle-quasi-zero-stiffness floating slab track (QZS-FST) coupled dynamic model was then established. To obtain a reasonable nonlinear stiffness within a few millimeters, the original length of the NSEs must be analyzed first, because it chiefly determines the stiffness nonlinearity level. The compression length of the NSEs at the equilibrium position must be determined to obtain the low stiffness of the floating slab without vehicle load. Meanwhile, to meet the dynamic displacement limit of the FST, the PSE stiffness must be increased to obtain a higher stiffness at the critical dynamic displacement. Various stiffness groups for the PSEs and NSEs can provide the same dynamic bearing capacity and yet have a significantly different vibration reduction effect. Excessive stiffness nonlinearity levels cannot effectively improve the vibration reduction effect at the natural frequency. Furthermore, they also significantly amplify the vibrations above the natural frequency. In this paper, the vertical vibration acceleration level (VAL) of the floating slab and the supporting force of the FST can be decreased by 6.9 dB and 55%, respectively, at the resonance frequency.

Isolating low-frequency vibration via lightweight embedded metastructures

Load-bearing lightweight structures, such as lattice structures, are commonly used in various engineering fields, but often suffer from environmental low-frequency vibration which is difficult to suppress. The emerging field of metastructure offers a practical solution for the low-frequency vibration reduction without introducing extra isolators that have gigantic size and heavy weight. In this research, 3D printed subwavelength-scale microstructures are embedded into a honeycomb beam to form a lightweight metastructure which can suppress vibrations with different polarizations at targeted frequencies. Moreover, by simply rotating the fabricated resonators from the horizontal embedment into the vertical embedment, the bandgaps as well as the vibration isolations can be easily switched for different vibration sources. The multi-polarization vibration isolations have also been demonstrated with strategically positioned resonators following interval and segment arrangements. Finally, metastructures with geometrically optimized microstructures as well as quasi-zero dynamic stiffness microstructures are designed to achieve an even lower frequency isolation with unaltered lightweight advantages.

Study on the vibration attenuation property of one finite and hybrid piezoelectric phononic crystal beam

In this paper, a theoretical method is proposed to effectively improve the vibration attenuation characteristics of a finite hybrid piezoelectric phononic crystal (PC) beam utilizing the non-uniform distribution of shunting circuits. Considering the damping of resonators, the vibration transmissibility method (TM) for the finite electromechanical system is derived based on the Timoshenko beam theory. Numerical results are validated by the finite element method (FEM). Subsequently, a comprehensive study is conducted to investigate the influences of the structural and electrical parameters on the vibration attenuation property of the uniform PC. Furthermore, the organized disorder of the shunting circuits is introduced into the system. Combining with various types of non-uniform circuit configurations, the variation of the vibration attenuation is also examined. It is demonstrated that the hybrid PCs offer more tunable mechanisms to design target band-gaps, compared with the purely mechanical and piezoelectric PCs. The low-frequency vibration reduction over a broadband range could be achieved through the selective coupling ways of the mechanical local resonant band-gap (LRG), electromechanical LRG and Bragg band-gap (BG). It is expected to enhance the vibration attenuation and availability of hybrid PCs using the suitable distribution of shunting circuits in practice.