Negative Stiffness Mechanism on An Asymmetric Wave Energy Converter by Using A Weakly Nonlinear Potential Model

Salter's duck,an asymmetrical wave energy converter(WEC)device,showed high efficiency in extracting energy from 2D regular waves in the past;yet,challenges remain for fluctuating wave conditions.These can potentially be addressed by adopting a negative stiffness mechanism(NSM)in WEC devices to enhance system efficiency,even in highly nonlinear and steep 3D waves.A weakly nonlinear model was developed which incorporated a nonlinear restoring moment and NSM into the linear formulations and was applied to an asymmetric WEC using a time domain potential flow model.The model was initially validated by comparing it with published experimental and numerical computational fluid dynamics results.The current results were in good agreement with the published results.It was found that the energy extraction increased in the range of 6%to 17%during the evaluation of the effectiveness of the NSM in regular waves.Under irregular wave conditions,specifically at the design wave conditions for the selected test site,the energy extraction increased by 2.4%,with annual energy production increments of approximately 0.8MWh.The findings highlight the potential of NSM in enhancing the performance of asymmetric WEC devices,indicating more efficient energy extraction under various wave conditions.

Vertical seismic absorber utilizing inertance and negative stiffness implemented with gas springs

A novel implementation of negative stiffness elements(NSEs)is proposed,utilizing industrial grade nitrogen gas springs as pre-stressed stiffness elements in a configuration with lever arms.This NSE is combined with an inerter to form a stiff dynamic absorber(SDA)for vertical seismic protection of structures with base isolation.The SDA is optimized to minimize vertical accelerations while ensuring static structural integrity,excellent damping performance and containment of relative displacements.The introduction of gas springs in place of conventional linear springs addresses important practical limitations through features of non-linearity and industrial grade manufacturing.The proposed implementation is dimensioned for a 50-ton structure and evaluated numerically for 25 actual earthquake records,in comparison with a linear SDA model and an equivalent conventional damper(CD).Individual and averaged results of acceleration and displacement time histories demonstrate vastly superior response compared to CD regarding induced accelerations for similar displacements.Performance equivalency with the linear SDA model indicates the stability of the gas spring implementation while guaranteeing predictability,tested endurance,proper tolerances,and off-axis motion resistance without requiring additional guiding components,as opposed to conventional springs.These features render the proposed implementation a promising solution for the realization of NSEs in seismic protection.

Improving the performance of conventional base isolation systems by an external variable negative stiffness device under near-fault and long-period ground motions

Recent studies have shown that base-isolated objects with long fundamental natural periods are highly influenced by long-period earthquakes. These long-period waves result in large displacements for isolators, possibly leading to exceedance of the allowable displacement limits. Conventional isolation systems, in general, fail to resist such large displacements. This has prompted the need to modify conventional base isolation systems. The current work focuses on the development of an external device, comprising a unit of negative and positive springs, for improving the performance of conventional base isolation systems. This unit accelerates the change in the stiffness of the isolation system where the stiffness of the positive spring varies linearly in terms of the displacement response of the isolated objects. The target objects of the present study are small structures such as computer servers, sensitive instruments and machinery. Numerical studies show that the increase in the damping of the system and the slope of the linear function is effective in reducing the displacement response. An optimal range of damping values and slope, satisfying the stability condition and the allowable limits of both displacement and acceleration responses when the system is subjected to near-fault and long-period ground motions simultaneously, is proposed.

Dynamics of 1D mass–spring system with a negative stiffness spring realized by magnets: Theoretical and experimental study

Realization of negative stiffness （NS） in damping low frequency acoustic and mechanical vibration is relevant in engineering applications. In this work, assemblage of two repelling magnets was used to produce negative magnetic spring （NMS）. A mass-spring system with NMS is experimented where the free and forced vibrations of the system are examined. The anti-phase movement is observed due to the presence of proposed NMS, confirming the analytical solution. We further showed the dynamics of the system containing NS spring could also be derived from Hamilton＇s principle.

Design and evaluation of cab seat suspension system based on negative stiffness structure

To improve the vibration-isolation performance of cab seats,the optimization model of the seat suspension system of construction machinery cabs is proposed based on the negative stiffness structure.The negative stiffness nonlinear kinetic equation is established by designing the seat negative stiffness suspension structure(NSS).Using MATLAB,the different parameters of the suspension system and their influences on the dynamic stiffness are analyzed.The ideal configuration parameter range of the suspension system is obtained.Meanwhile,the optimization model of NSS is proposed,and the vibration transmissibility characteristics are simulated and analyzed by different methods.The results show that the displacement and acceleration amplitudes of the optimized seat suspension system are evidently reduced,and the four-time power vibration dose value and root mean square calculation values in the vertical vibration direction of the seat decrease by 86%and 87%,respectively.Seat effective amplitude transmissibility(SEAT)and the vibration transmissibility ratio values also decrease.Moreover,the peak frequencies of the vibration transmitted to the driver deviate from the key frequency values,which easily cause human discomfort.Thus,the design of the seat suspension system has no effect on the health condition of the driver after being vibrated.The findings also illustrate that the NSS suspension system has good vibration-isolation performance,and the driver's ride comfort is improved.

A quasi-zero stiffness energy harvesting isolator with triple negative stiffness

Vibration isolation for low frequency excitation and the power supply for low power monitoring sensors are important issues in bridge engineering.The main problem is how to effectively combine the vibration isolator with the energy harvester to form a multi-functional structure.In this paper,a system called quasi-zero stiffness energy harvesting isolator(QZS-EHI)with triple negative stiffness(TNS)is proposed.The TNS structure consists of linear springs,rigid links,sliders,and ring permanent magnets.Newton’s second law and Kirchhoff’s law construct dynamic equations of the QZS-EHI,and a comparison is made to contrast it with other QZS and linear isolators.The comparison field includes the QZS range,amplitude-frequency relationship,force transmissibility,and energy harvested power.The isolator can be applied to many engineering fields such as bridges,automobiles,and railway transportation.This paper selects bridge engineering as the main field for the dynamic analysis of this system.Considering the multi-span beam bridge,this paper compares different situations including the bridge with QZS-EHI support,with linear stiffness isolator support,and with single beam support.All results show that the QZS-EHI is not only better than the traditional isolator with linear stiffness under both harmonic and stochastic excitation,but also better than some QZS isolators with double or single negative stiffness in bridge vibration isolation and energy harvesting.Theoretical analysis is verified to correspond to the simulation analysis,which means the proposed QZS-EHI has practical application value.

High-static-low-dynamic stiffness isolator based on an electromagnetic negative stiffness spring with long linear stroke

Negative stiffness mechanisms can improve low-frequency vibration isolation performance and have been widely used in the vibration isolation of precision equipment. However, the negative stiffness mechanism usually introduces a nonlinear stiffness,resulting in a nonlinear response and worsening the vibration isolation performance, especially under large amplitude vibration.In this paper, an electromagnetic spring with linear negative stiffness(ESLNS) is proposed, in which the antagonistic ampere forces of the energized coils are used to generate negative stiffness within a long linear stroke. The magnetic field distribution is improved through the design of the magnetic circuit, thereby increasing the stiffness generation efficiency. The stiffness can be adjusted bidirectionally by current within the range of positive and negative stiffness. An electromagnetic stiffness model was established based on the equivalent magnetic circuit method. Experimental measurements verified the accuracy of the model and proved the linearity of the electromagnetic spring. A vibration isolator with high static and low dynamic stiffness(HSLDS) based on the ESLNS is designed and tested. The experimental results prove that the introduction of the ESLNS can effectively expand the isolation frequency band without changing the equilibrium position. Moreover, the vibration isolator with ESLNS does not produce nonlinear response. The proposed electromagnetic spring with linear negative stiffness extends the application range of HSLDS isolators to a large amplitude vibration environment.

Design of a combined magnetic negative stiffness mechanism with high linearity in a wide working region

Combining magnetic negative stiffness mechanism(NSM) in parallel with positive stiffness has been considered to be an effective approach to realize the quasi-zero stiffness(QZS) characteristic,thus resolving the contradiction between high load capacity and(ultra-) low-frequency vibration isolation capability.However,the remarkable stiffness nonlinearity of common magnetic NSMs restricts the displacement region with reliable negative stiffness,resulting in considerable nonlinear behavior,poor vibration attenuation performance,and probable instability under large amplitude vibrations.A novel combined negative stiffness mechanism(CNSM) with attractive magnetic NSM(ANSM) and repulsive magnetic NSM(RNSM) in parallel is proposed in this paper.The stiffness nonlinearities of the ANSM and RNSM in the CNSM are counteracted through the parallel configuration such that the displacement region with reliable linear stiffness of the CNSM is widened by several times.An analytical model of the CNSM is established by the magnetic charge model and verified by simulation on ANSYS Maxwell.Parametric studies are then conducted to investigate the effects of design parameters on the stiffness characteristic,providing guidelines for the optimal design of the CNSM.Meanwhile,the stiffness and nonlinearity of the CNSM are compared with that of a single ANSM and RNSM.Static and dynamic experiments are finally conducted on the proposed test prototypes.Experimental results demonstrated the validity of the established model and the effectiveness of the CNSM in generating high linear stiffness within a wide displacement region and lowering the resonance frequency.Thus,the proposed CNSM can be applied in(ultra-) low-frequency vibration isolation under large amplitude excitations.

Stability Analysis of a Force-Aided Lever Actuation System for Dry Clutches with Negative Stiffness Element

A force-aided lever with a preload spring is not only force-saving but also energy-saving. Therefore, it has great potential to be applied to dry clutch actuations. However, the negative stiffness of the clutch diaphragm spring introduces unstable dynamics which becomes more intensive due to the preload spring. In order to explore the intensified unstability, this paper builds dynamic models for the rotating lever coupling a negative stiffness diaphragm spring and a preload spring. The stability analysis using the Routh-Huiwitz criterion shows that the open-loop system can never be stable due to the negative stiffness. Even if the diaphragm spring stiffness is positive, the system is still unstable when the preload of the spring exceeds an upper limit. A proportionalintegral-derivative(PID) closed-loop scheme addressing this problem is designed to stabilize the system. The stability analysis for the closed-loop system shows that stable region emerges in spite of the negative stiffness; the more the negative stiffness is, the less the allowed preload is. Further, the influences of the dimensions and PID parameters on the stability condition are investigated. Finally, the transient dynamic responses of the system subjected to disturbance are compared between the unstable open-loop and stabilized closed-loop systems.

A piecewise negative stiffness mechanism and its application in dynamic vibration absorber

A new type of piecewise negative stiffness(NS)mechanism is designed and the relationship between the force and displacement is studied.At first,the prototype of the piecewise NS mechanism is established,and the stiffness characteristic of this mechanism is analyzed.Then,the piecewise NS mechanism is applied to dynamic vibration absorber(DVA)system to establish a dynamic model with the piecewise linearity.The differential motion equations are derived according to Newton's law of mechanics.The approximate analytical solution and the amplitude frequency curve of the system with the piecewise NS are obtained by means of the averaging method.The correctness of the analytical solution is proved by comparing with the numerical solution.In the end,the comparisons with two other traditional DVAs show that the system in this paper has better vibration reduction effect under the condition of harmonic excitation and random excitation.

Modeling and Analysis of Novel Integrated Radial Hybrid Magnetic Bearing for Magnetic Bearing Reaction Wheel

Conventional ball bearing reaction wheel used to control the attitude of spacecraft can＇t absorb the centrifugal force caused by imbalance of the wheel rotor,and there will be a torque spike at zero speed,which seriously influences the accuracy and stability of spacecraft attitude control.Compared with traditional ball-bearing wheel,noncontact and no lubrication are the remarkable features of the magnetic bearing reaction wheel,and which can solve the high precision problems of wheel.In general,two radial magnetic bearings are needed in magnetic bearing wheel,and the design results in a relatively large axial dimension and smaller momentum-to-mass ratios.In this paper,a new type of magnetic bearing reaction wheel（MBRW） is introduced for satellite attitude control,and a novel integrated radial hybrid magnetic bearing（RHMB） with permanent magnet bias is designed to reduce the mass and minimize the size of the MBRW,etc.The equivalent magnetic circuit model for the RHMB is presented and a solution is found.The stiffness model is also presented,including current stiffness,position negative stiffness,as well as tilting current stiffness,tilting angular position negative stiffness,force and moment equilibrium equations.The design parameters of the RHMB are given according to the requirement of the MBRW with angular momentum of 30 N ？ m ？ s when the rotation speed of rotor reaches to 5 kr/min.The nonlinearity of the RHMB is shown by using the characteristic curves of force-control current-position,current stiffness,position stiffness,moment-control current-angular displacement,tilting current stiffness and tilting angular position stiffness considering all the rotor position within the clearance space and the control current.The proposed research ensures the performance of the radial magnetic bearing with permanent magnet bias,and provides theory basis for design of the magnetic bearing wheel.

Comparison of the vibration isolation performance of a seat suspension with various design modes

Three design modes of seat suspension,i.e.,negative stiffness elements(NSEs),damping elements(DEs),and negative stiffness-damping elements(NSDEs),are proposed to evaluate the ride performance of a vehicle.Based on a dynamic model of a seat suspension and indexes of the root mean square deformation and acceleration of the seat suspension(x RMS)and driver s seat(a RMS),the influence of the design parameters of the NSEs,DEs,and NSDEs on the driver s ride comfort is evaluated.A genetic algorithm is then applied to optimize the parameters of the NSEs,DEs,and NSDEs.The study results indicate that the design parameters of the NSEs and NSDEs remarkably influence x RMS and a RMS,whereas those of the DEs insignificantly influence x RMS and a RMS.Based on the optimal results of the NSEs,DEs,and NSDEs,the damping force of the DEs is 98.3%lower than the restoring force of the NSEs.Therefore,the DEs are ineffective in decreasing x RMS and a RMS.Conversely,the NSEs combined with the damping coefficient of the seat suspension strongly reduce x RMS and a RMS.Consequently,the NSEs can be added to the seat suspension,and the damping coefficient of the seat suspension can also be optimized or controlled to further enhance the vehicle s ride performance.

Nonlinear response of a multidirectional negative-stiffness isolation system via semirecursive multibody dynamic approach

This paper investigates an innovative negative-stiffness device(NSD)that modifies the apparent stiffness of the supported structure for seismic isolation.The NSD comprises a lower base on the bottom and a cap on the top,together with a connecting rod,vertical movable wall,and compressed elastic spring,as well as circumferentially arranged,pretensioned external ropes,and inclined shape memory wires.This configuration can deliver negative stiffness and energy dissipation in any direction within the horizontal plane.A numerical model of the device is developed through a two-step semirecursive method to obtain the force–displacement characteristic relationship.Such a model is first validated through comparison with the results obtained via the commercial software ADAMS.Finally,a large parametric study is performed to assess the role and the influence of each design variable on the overall response of the proposed device.Useful guidelines are drawn from this analysis to guide the system design and optimization.