Analytical modeling of piezoelectric meta-beams with unidirectional circuit for broadband vibration attenuation

Broadband vibration attenuation is a challenging task in engineering since it is difficult to achieve low-frequency and broadband vibration control simultaneously.To solve this problem,this paper designs a piezoelectric meta-beam with unidirectional electric circuits,exhibiting promising broadband attenuation capabilities.An analytical model in a closed form for achieving the solution of unidirectional vibration transmission of the designed meta-beam is developed based on the state-space transfer function method.The method can analyze the forward and backward vibration transmission of the piezoelectric meta-beam in a unified manner,providing reliable dynamics solutions of the beam.The analytical results indicate that the meta-beam effectively reduces the unidirectional vibration across a broad low-frequency range,which is also verified by the solutions obtained from finite element analyses.The designed meta-beam and the proposed analytical method facilitate a comprehensive investigation into the distinctive unidirectional transmission behavior and superb broadband vibration attenuation performance.

Vibration attenuation of meta-mortar with spring-mass resonators

Metamaterial based on local resonance has excellent vibration attenuation ability in low frequency.In this research,an attempt was performed to make meta-mortar with spring-mass resonators to attenuate vibration and shock hazards.Single-spring-mass resonators and dual-spring-mass resonators were designed and made using lead or aluminum blocks and SWPB springs encased by PMMA(polymethyl methacrylate)or aluminum frames.These resonators were placed into mortar blocks to make metamortar specimens.Vibration attenuation effect was investigated by sweeping vibration with frequency from 50 Hz to 2000 Hz.All these meta-mortar blocks exhibit excellent vibration attenuation ability in the designed band gaps.With dual-spring-mass resonators,meta-mortar blocks have two distinct vibration attenuation bands.

Suppression of low-frequency ultrasound broadband vibration using star-shaped single-phase metamaterials

In order to suppress the low-frequency ultrasound vibration in the broadband range of 20 k Hz—100 k Hz,this paper proposes and discusses an acoustic metamaterial with low-frequency ultrasound vibration attenuation properties,which is configured by hybrid arc and sharp-angle convergent star-shaped lattices.The effect of the dispersion relation and the bandgap characteristic for the scatterers in star-shaped are simulated and analyzed.The target bandgap width is extended by optimizing the geometry parameters of arc and sharp-angle convergent lattices.The proposed metamaterial configured by optimized hybrid lattices exhibits remarkable broad bandgap characteristics by bandgap complementarity,and the simulation results verify a 99%vibration attenuation amplitude can be obtained in the frequency of20 k Hz—100 k Hz.After the fabrication of the proposed hybrid configurational star-shaped metamaterial by 3D printing technique,the transmission loss experiments are performed,and the experimental results indicate that the fabricated metamaterial has the characteristics of broadband vibration attenuation and an amplitude greater than 85%attenuation for the target frequency.These results demonstrate that the hybrid configurational star-shaped metamaterials can effectively widen the bandgap and realize high efficiency attenuation,which has capability for the vibration attenuation in the application of highprecise equipment.

Optimal design for rubber concrete layered periodic foundations based on the analytical approximations of band gaps and mapping relations

The seismic performance of rubber concrete-layered periodic foundations are significantly influenced by their design,in which the band gaps play a paramount role.Aiming at providing better designs for these foundations,this study first proposes and validates the analytical formulas to approximate the bounds of the first few band gaps.In addition,the mapping relations linking the frequencies of different band gaps are presented.Furthermore,an optimal design method for these foundations is developed,which is validated through an engineering example.It is demonstrated that ensuring the superstructure’s resonance zones are completely covered by the corresponding periodic foundation’s band gaps can achieve satisfactory vibration attenuation effects,which is a good strategy for the design of rubber concrete layered periodic foundations.

Parameter-dependent vibration-attenuation controller design for electro-hydraulic actuated linear structural systems

The problem of robust active vibration control for a class of electro-hydraulic actuated structural systems with time-delay in the control input channel and parameter uncertainties appearing in all the mass, damping and stiffness matrices is investigated in this paper. First, by introducing a linear varying parameter, the nonlinear system is described as a linear parameter varying （LPV） model. Second, based on this LPV model, an LMI-based condition for the system to be asymptotically stabilized is deduced. By solving these LMIs, a parameter-dependent controller is established for the closed- loop system to be stable with a prescribed level of disturbance attenuation. The condition is also extended to the uncertain case. Finally, some numerical simulations demonstrate the satisfying performance of the proposed controller.

Theoretical analysis on ground vibration attenuation using sub-track asphalt layer in high-speed rails

Using a finite element method （FEM） program, a Portland cement concrete slab trackbed （So）, and a sub- track asphalt roadbed （RAC-S） were modeled under high- speed train loads to analyze their responses to ground vibration attenuation, by considering 10, 15, 20, 25, and 30 thick sub-track asphalt layer replaced on the top of the upper subgrade. FEM results show that the vibration amplitude of RAC-S is at least three times lower than the vibration for So. The maximum vibration amplitude of RAC-S is linearly increased with train speed. The vertical acceleration is found to be reduced by more than 10 % when the asphalt layer thickness is increased from 10 to 20 cm. However, the reduction in vertical acceleration is only about 1% when the thickness of the asphalt layer changes from 20 to 30 cm. The vibration level is slightly lower if the asphalt layer has higher resilient modulus in the seasons of autumn or winter. This theoretical analysis indicates that a railway substructure that consists of a 10-20 cm thick high modulus asphalt layer located at the top of trackbed shows a good performance in ground vibration control for high-speed rails.

Design and Verification of High Attenuation Vibration Isolation Damper in Remote Sensing Satellite Transport

To solve the safe horizontal transportation by rail&road of remote sensing satellite problem in the process of unpredictable dynamic load,a high attenuation vibration isolation damper(hereinafter referred to as vibration isolation damper)was developed.By simulation analysis and transportation test using satellite structural model and engineering prototype,validity and reliability of the vibration isolation damper was verified,which can meet the requirements of vibration and shock from various transportation conditions.

Characteristics of Vibrational Wave Propagation and Attenuation in Submarine Fluid-Filled Pipelines

As an important part of lifeline engineering in the development and utilization of marine resources, the submarine fluid-filled pipeline is a complex coupling system which is subjected to both internal and external flow fields. By utilizing Kennard＇s shell equations and combining with Helmholtz equations of flow field, the coupling equations of submarine fluid-filled pipeline for n=0 axisymmetrical wave motion are set up. Analytical expressions of wave speed are obtained for both s=1 and s=2 waves, which correspond to a fluid-dominated wave and an axial shell wave, respectively. The numerical results for wave speed and wave attenuation are obtained and discussed subsequently. It shows that the frequency depends on phase velocity, and the attenuation of this mode depends strongly on material parameters of the pipe and the internal and the external fluid fields. The characteristics of PVC pipe are studied for a comparison. The effects of shell thickness/radius ratio and density of the contained fluid on the model are also discussed. The study provides a theoretical basis and helps to accurately predict the situation of submarine pipelines, which also has practical application prospect in the field of pipeline leakage detection.

A novel method for vibration signal transmission and attenuation analysis in complex planetary gearboxes

Planetary gearboxes play a crucial role in altering rotary speed and transmitting power in large machines like wind turbines and sophisticated vehicles. There are many nonlinear interfaces, such as splines, bearings, and gear pairs, in planetary gearboxes, and the resulting vibration signal transmission and attenuation mechanisms are still unknown. In this study, a novel method for quantitatively analyzing the transmission and attenuation of vibration signals is proposed. A multibody dynamic model of the planetary gearbox considering nonlinear gear meshing is presented and experimentally validated. To avoid the interference of foundation vibration on the transmission of the fault signal, the fault impact factor(FIF) is used to describe the intensity of the failure, which aligns well with the experimental signals. Based on the FIF, the vibration signal attenuation of nonlinear interfaces such as splines, bearings, and gear meshing interfaces is quantitatively evaluated. To clarify the transfer paths of fault vibration signals inside the gearbox, the transfer path area method(TPAM) based on FIF is proposed. According to the simulated results,the primary transfer paths of fault vibration signals within the gearbox have been identified, which is of great help in understanding the transmission and attenuation of vibration signals in planetary gearboxes.

A Review on Methods for Determining the Vibratory Damping Ratio

This article aims to popularize the methods for determining the vibratory damping ratio, to explain the various mathematical and physical theorems related to the establishment of literal expressions. Vibration damping is an essential parameter to reduce the dynamic responses of structures. The study aimed at its determination is necessary and essential for the safeguard of buildings and human lives during the earthquake. Among the main methods studied in this article, the free vibration attenuation method seems to be easy to implement but requires a state-of-the-art device to capture the responses. In addition to this device, the other methods require other equipment for the vibration of the system and the transformation of the responses in the frequency domain.

SEMI ACTIVE VIBRATION CONTROL BASED ON A VIBRATION ABSORBER WITH ADJUSTABLE CLEARANCE

Presented in this paper is a semi active vibration control strategy based on the vibration absorber with adjustable clearance in elastic component. The control law of the clearance for alleviating the vibration of primary system is derived by means of harmonic balancing technique so that the working frequency of the vibration absorber can trace the frequency variation of the harmonic excitation. The efficacy of the strategy is demonstrated by numerical simulations for attenuating the steady state vibration of a SDOF system and a 2 DOF system, which are under the harmonic excitation with slowly varied frequency in a wide range.

Resonance response of fluid-conveying pipe with asymmetric elastic supports coupled to lever-type nonlinear energy sink

This paper studies the vibration absorber for a fluid-conveying pipe,where the lever-type nonlinear energy sink(LNES)and spring supports are coupled to the asymmetric ends of the system.The pseudo-arc-length method integrated with the harmonic balance method is used to investigate the steady-state responses analytically.Meanwhile,the numerical solution of the fluid-conveying pipe is calculated with the Runge-Kutta method.Moreover,a special response,called the collapsible closed detached response(CCDR),is first observed when the vibration response of mechanical structures is studied.Then,the relationship between the CCDR and the main structure primary response(PR)is obtained.In addition,the closed detached response(CDR)is also observed to research the resonance response of the fluid-conveying pipe.The appearance of either the CCDR or the CDR does affect the resonance attenuation.Furthermore,the mentioned two phenomena underline that the trend of vibration responses under external excitation goes continuous and gradual.Besides,the main advantage of the LNES is presented by contrasting the LNES with the nonlinear energy sink(NES)coupled to the same pipe system.It is found that the LNES can reduce the resonance response amplitude by 91.33%.

Preparation and Properties of Epoxy Piezoelectric Vibration Reduction Composites

The epoxy resin (E-51) was used as polymer matrix,conductive carbon black (CB) as conductive filler,and PZT was used to prepare a composite by curing.The effects of PZT and CB content on the properties of PZT/ CB/ EP piezoelectric composite were studied.When the PZT content reaches 40 wt%,the optimized vibration attenuation properties of PZT/CB/EP materials could be achieved with a loss factor of 0.9 from room temperature to 60 ℃.With the increase of PZT content,the bending strength of PZT/CB/EP piezoelectric composite vibration reduction material firstly increased from 45 MPa to 65 MPa and then decreased to 38 MPa.At room temperature,the dielectric constant increased from 7 to 50,and the dielectric loss increased from 0.1 to 0.5.

Reasons and laws of ground vibration amplification induced by vertical dynamic load

The phenomenon of ground vibration amplification caused by railway traffic was found and proved. In order to study the reasons which cause the amplification, a drop-weight test was performed. Then, the model for both homogeneous and layered soil subjected to a harmonic vertical load was built. With the help of this model, displacement Green's function was calculated and the propagation laws of ground vibration responses were discussed. Results show that: 1) When applying a harmonic load on the half-space surface, the amplitude of ground vibrations attenuate with fluctuation, which is caused by the superposition of bulk and Rayleigh waves. 2) Vibration amplification can be enlarged under the conditions of embedded source and the soil layers. 3) In practice, the fluctuant attenuation should be paid attention to especially for the vibration receivers who are sensitive to single low frequencies(<10 Hz). Moreover, for the case of embedded loads, it should also be paid attention to that the receivers are located at the place where the horizontal distance is similar to embedded depth, usually 10 to 30 m for metro lines.

PARAMETRIC MATCHING SELECTION OF MULTI-MEDIUM COUPLING SHOCK ABSORBER

To achieve the dual demand of resisting violent impact and attenuating vibration in vibration-impact-safety of protection for precision equipment such as MEMS packaging system, a theo- retical mathematical model of multi-medium coupling shock absorber is presented. The coupling of quadratic damping, linear damping, Coulomb damping and nonlinear spring are considered in the model. The approximate theoretical calculating formulae are deduced by introducing transformation-tactics. The contrasts between the analytical results and numerical integration results are developed. The resisting impact characteristics of the model are also analyzed in progress. In the meantime, the optimum model of the parameters matching selection for design of the shock absorber is built. The example design is illustrated to confirm the validity of the modeling method and the theoretical solution.

A Novel Application of Multi-Resonant Dissipative Elastic Metahousing for Bearings

Bearing as an important machine element is widely used for industrial and automotive applications.At certain operational speed,bearings induce disturbing vibrations and noises that affect machine service life,productivity and passenger comfort in case of vehicle applications.Dissipative elastic metamaterials have caught considerable attention of scientific community due to their effective medium properties and peculiar dynamic characteristics including frequency bandgaps that can be effectively applied to attenuate and control undesirable vibration and noises.Although a substantial amount of theoretical work for effective medium characteristics and dynamic properties of acoustic/elastic metamaterials has been reported,the practical design and application of these composite structures for real-life engineering problems still remain unexplored.The present study intends to investigate a potential application of dissipative elastic metamaterials in controlling the bearing-generated vibration and noises over an ultrawide frequency range.The study is based on a simple analytical model together with rigorous finite element numerical simulations.It has been established that the dissipative characteristic of resonant system caused by larger material mismatch broadens the local resonance bandgaps beyond the bounding resonance frequency at the cost of wave transmission.In order to achieve broadband vibration and noise control,multi-resonant composite structures are embedded inside the bearing housing in five different layers.The reported results revealed the presence of broadband wave attenuation zone distributed from 3 to 52 kHz with consideration of material damping.The bearing-generated vibration and noises lying inside the wave attenuation zone will be mitigated.This feasibility study provides a new concept for the design and application of acoustic/elastic metamaterials in the bearing industry to improve machine service life and to enhance productivity and passenger comfort.

Control performance simulation and tests for Microgravity Active vibration Isolation System onboard the Tianzhou-1 cargo spacecraft

The Microgravity Active vibration Isolation System(MAIS),which was onboard China’s first cargo-spacecraft Tianzhou-1 launched on April 20,2017,aims to provide high-level microgravity at an order of 10^(-5)–10^(-6)g for specific scientific experiments.MAIS is mainly composed of a stator and a floater,and payloads are mounted on the floater.Sensing relative motion with respect to the stator fixed on the spacecraft,the floater is isolated from vibration on the stator via control forces and torques generated by electromagnetic actuators.This isolation results in a high-level microgravity environment.Before MAIS was launched into space,its control performance had been simulated on computers and tested by air-bearing platform levitation and aircraft parabolic flight.This article first presents an overview of the MAIS’s hardware system,particularly system structure,measurement sensors,and control actuators.Its system dynamics,state estimation,and control laws are then discussed,followed by the results of computer simulation and engineering tests,including the test of the six-degree-of-freedom motion by aircraft parabolic flight.Simulation and test results verify the accuracy of the control strategy design,effectiveness of the control algorithms,and performance of the entire control system,paving the way for operation of MAIS in space.This article also presents the steps recommended for the control performance simulation and tests of MAIS-like devices.These devices are expected to be used on China’s Space Station for various scientific experiments that require a high-level microgravity environment.

Intrinsic physical relationships between rotor modal shapes and instantaneous vibrational energy flow transmission characteristics:Theoretical and numerical analysis and application

The modal vibration of the rotor is the main cause of excessive vibration of the aeroengine overall structure.To attenuate the vibration of the rotor under different modal shapes from the perspective of energy control,the intrinsic physical relationships between rotor modal shapes and instantaneous vibrational energy flow transmission characteristics is derived from the general equation of motion base on the structural intensity method.A dual-rotor-support-casing coupling model subjected to the rotor unbalanced forces is established by the finite element method in this paper.The transmission,conversion and balance relationships of the vibrational energy flow for the rotors in the first-order bending modal shape,the conical whirling modal shape and the translational modal shape are analyzed,respectively.The results show that the vibrational energy flow transmitted to the structure can be converted into the strain energy,the kinetic energy and the energy dissipated by the damping of the structure.The vibrational energy flow transmission characteristics of rotors with different modal shapes are quite different.Especially for the first-order bending modal shape,the vibrational energy flow and the strain energy are transmitted and converted to each other in the middle part of the rotor shaft,resulting in large deformation at this part.To attenuate this harmful vibration,the influences of grooving on the shaft on the first-order bending vibration are studied from the perspective of transmission control of vibrational energy flow.This study can provide theoretical references and guidance for the vibration attenuation of the rotors in different modal shapes from a more essential perspective.