Magnetic Negative Stiffness Research Articles

A new magnetic negative stiffness mechanism: A case study of Fast Steering Mirror for quasi-zero stiffness vibration isolation

Quasi-Zero Stiffness (QZS) is essential for low-frequency passive vibration isolation, with the negative stiffness mechanism (NSM) being pivotal for achieving QZS. Mechanical spring-based NSMs often face issues like contact friction, parasitic high-frequency modes, and stiffness nonlinearity. This paper presents a new magnetic NSM designed to overcome these challenges effectively. The mechanism is applied to a Fast Steering Mirror (FSM) as a case study, enhancing its vibration isolation performance. Initially, a torque model for the magnetic NSM is established, exploring the impact of various structural dimensions on torque and nonlinear issues. The magnetic NSM features adjustable negative stiffness and a large, adjustable linear working range. Experiments were designed to validate the principle of the magnetic NSM and its effect on the QZS FSM’s vibration isolation performance. The experimental results confirm the accuracy of the magnetic NSM principle. The QZS FSM stiffness is significantly reduced to quasi-zero stiffness, resulting in a decrease of the resonance peak from 20.1 to −12.8 dB and lowering the minimum suppressible vibration frequency from 54.63 to 3.44 Hz, thereby enhancing the vibration isolation performance of the QZS FSM.

Youla-Parameterized Adaptive Switched Control of a Magnetic Negative Stiffness Isolator

Youla-Parameterized Adaptive Switched Control of a Magnetic Negative Stiffness Isolator

Performance enhanced magnetic negative stiffness eddy-current damper: Numerical simulation and experimental investigation

Passive negative stiffness dampers (NSDs) possess significant advantages and promising application prospects in the field of structural vibration control. NSDs with high energy dissipation capability are desired to satisfy the vibration mitigation requirements for large-scale engineering structures, such as high-rise buildings and long-span bridges. However, in practical applications, due to the constraints of mounting space and additional weight, the negative stiffness and damping coefficient of existing NSDs are generally not very large and with poor adjustability. To overcome these limitations, this study develops a novel magnetic negative stiffness eddy-current damper (MNSECD) with enhanced overall performance. This damper consists of a magnetic negative stiffness system (MNSS), a multi-layer-plate-type eddy-current damping system (ECDS) in parallel, and a bidirectional ball screw transmission system. Firstly, different magnetic arrays are designed to optimize the magnetic fields of the MNSECD, and to enhance its magnetic negative stiffness and eddy-current damping without adding extra dimensions and weight. Subsequently, the electromagnetic finite-element models (FEMs) of the MNSECD are established to precisely simulate its magnetic negative stiffness and eddy-current damping forces, and these models are further utilized to elucidate the enhancement mechanism of different magnetic arrays. Finally, based on the numerical simulation results, the best performing magnetic array is selected respectively for the ECDS and MNSS systems to carry out experimental studies on a small-scale prototype. Numerical and experimental results indicate that the selected magnetic array for the MNSS proves highly effective in enhancing the magnetic negative stiffness of the MNSECD, while the selected magnetic array for the ECDS also demonstrates superior effectiveness in enhancing the eddy-current damping of the damper. These findings suggest that the novel MNSECD can be readily used in the vibration control of large-scale engineering structures.

Nonlinear wire rope isolator with magnetic negative stiffness

The high-static-low-dynamic-stiffness (HSLDS) isolators have been widely employed to achieve low-frequency vibration isolation. However, traditional HSLDS isolators are prone to nonlinear jump phenomena due to the introduction of nonlinear stiffness characteristics, which will cause the performance deterioration under high excitation levels. To overcome this issue, inspired by the dry friction characteristic of wire ropes, the wire ropes are employed to design HSLDS isolators to suppress nonlinear jump phenomenon by introducing hysteretic damping in this paper. Therefore, a nonlinear wire rope isolator with magnetic negative stiffness is proposed to achieve HSLDS with hysteretic damping. The elastic force of wire rope and the magnetic force are modeled to obtain nonlinear restoring force, and then the dynamic model of the proposed isolator is established to investigate isolation performance. The equivalent beam element method is proposed to model wire ropes for obtaining dynamic characteristics by considering tensile and bending stiffnesses. Then, numerical simulation is performed to investigate the isolation performance of the wire rope isolators with different magnetic negative stiffnesses, and demonstrates that the proposed isolator can work in a higher excitation level than the isolator without dry friction of wire ropes. Moreover, experiments are carried out to show that the onset isolation frequency of the proposed isolator can be reduced by 66.7% compared with the wire rope isolator without magnetic negative stiffness. Therefore, it is demonstrated that the proposed wire rope isolator with magnetic negative stiffness has the preferable performance in low frequency isolation, and can improve the adaptability under a higher excitation level.

Magnetic Negative Stiffness Devices for Vibration Isolation Systems: A State-of-the-Art Review from Theoretical Models to Engineering Applications

Magnetic Negative Stiffness Devices for Vibration Isolation Systems: A State-of-the-Art Review from Theoretical Models to Engineering Applications

The vibration isolation proprieties of an X-shaped structure with enhanced high-static and low-dynamic stiffness via torsional magnetic negative stiffness mechanism

The vibration isolation proprieties of an X-shaped structure with enhanced high-static and low-dynamic stiffness via torsional magnetic negative stiffness mechanism

A creative wide-frequency and large-amplitude vibration isolator design method based on magnetic negative stiffness and displacement amplification mechanism

Negative stiffness vibration isolation devices have attracted significant attention and research interest for their ability to enhance the low-frequency vibration isolation performance of passive vibration isolators. However, their narrow linear negative stiffness region has hindered their broader application. To address this limitation, a novel design method for vibration isolators is proposed, integrating the permanent magnetic negative stiffness device (NSD) with the displacement amplification mechanism (DAM). The paper begins by presenting a specific vibration isolator design method and analyzing the kinematic relationship. Next, a single-degree-of-freedom (SDOF) nonlinear equivalent model of the vibration isolator is established using the pseudo-rigid-body model (PRBM) approach. Numerical simulations are then conducted to obtain the transmissibility of the isolator. Furthermore, two isolators—one with the displacement amplification effect and another without—are manufactured, and experimental investigations are carried out. The experimental results confirm that the incorporation of the displacement amplification mechanism effectively expands the linear negative stiffness region of the negative stiffness magnet pair, enabling wide-frequency and large-amplitude vibration isolation. Notably, these experimental findings align well with the simulation results. In summary, this paper proposes a creative design method for wide frequency and large amplitude vibration isolators, and proves it through theoretical analysis and experimental validation.

Circular Halbach negative stiffness isolating from torsional vibration: Design, modeling and experiments

Excessive torsional vibration is detrimental to the operation performance of key mechanical equipment. To attenuate low-frequency torsional vibration in high payload occasions, the negative stiffness isolator has been widely employed. However, due to the space constraints of compact rotating machinery, it is difficult to promote negative stiffness for counteracting high positive stiffness. Therefore, a circular Halbach torsion negative stiffness isolator is proposed to provide high torsional magnetic negative stiffness for low-frequency isolation. The semi-analytical expressions of tangential-tangential coupling and tangential-radial coupling for tile magnets are derived to calculate the magnetic torque and the torsional stiffness of circular magnetic arrays, and then the influences of structural parameters on magnetic negative stiffness are investigated. The simulation results show that the circular Halbach array has the much higher magnetic stiffness than the circular traditional array. The dynamic responses of the proposed torsional isolator are analyzed based on harmonic balance method. Moreover, experimental results show that the onset isolation frequencies of circular Halbach isolator and circular traditional isolator can be decreased by 32.57% and 17.90% respectively compared with the linear isolator. Therefore, it is demonstrated that the proposed circular Halbach isolator has a preferable performance for low frequency torsional isolation.

Shock Isolation of an Orthogonal Six-DOFs Platform With High-Static-Low-Dynamic Stiffness

Abstract A novel approach to enhance the shock vibration environment of multi-directions using a high-static-low-dynamic stiffness supported orthogonal six-degrees-of-freedom (DOFs) nonlinear vibration isolation (OSNVI) system is presented in this paper. By combining spring positive stiffness and magnetic negative stiffness, the proposed system achieves high-static-low-dynamic stiffness. Under the multi-directions half-sine vibration, the dynamic equation of the OSNVI is obtained. Both dynamic and static analysis methods are utilized to explore the effect of various parameters on the shock isolation performance of the OSNVI from both the time and frequency domains. The results indicate that the proposed OSNVI can efficiently suppress multi-direction shocks at the cost of only one second. Although a nonlinear jump is usually not expected, the nonlinear jump of the OSNVI could improve the load capacity by increasing the spring stiffness without changing the shock isolation frequency band. Finally, a shock experiment is employed through a three-axis shaker platform to validate the shock isolation performance of the orthogonal six-DOF nonlinear vibration isolator. The proposed OSNVI provides a promising approach to suppress the multi-directional shock vibrations.

Analysis of driving stability and smoothness based on magnetic negative stiffness suspension for cars

Existing economy vehicles mostly use inexpensive passive suspensions, which struggle to fulfil the driving performance needs of people because of their fixed damping stiffness. This paper proposes to build magnetic suspensions by integrating inexpensive negative stiffness magnetic springs and passive suspensions to improve the suspension performance of such cars. Based on the constructed magnetic suspension model, simulations were conducted to investigate and analyse its stability and smoothness in various aspects. Finally, the performance was verified using experiments. The results demonstrate that adding magnetic springs in passive suspensions enables the total stiffness of the suspension to vary adaptively, enhancing the car’s driving stability. Furthermore, it also reduces the car body acceleration, the resonance interval of the suspension system and its displacement transmissibility, further improving the car’s ride smoothness. These performance benefits increase with increasing road excitation, and their role is more pronounced in off-road vehicles. This magnetic suspension system provides novel ideas for the further design of passive suspensions and lays the foundation for the future development of variable stiffness suspensions.

Analysis and experiment of a novel compact magnetic spring with high linear negative stiffness

Improving the isolation performance of vibration isolators by introducing magnetic negative stiffness mechanisms (NSMs) has attracted extensive attention in recent years. Nevertheless, common magnetic NSMs are always accompanied by nonlinear stiffness, resulting in degradation of isolation performance and system instability when subjected to excitations with large amplitude. To improve the stiffness linearity and working range of magnetic NSMs in a limited space, a novel compact magnetic spring with high linear negative stiffness (CMS-HLNS) is proposed in this paper. The CMS-HLNS consists of two sets of permanent magnets (PMs) arranged in an alternate manner, which has both high linearity and high negative stiffness properties. A simplified analytical stiffness model of the CMS-HLNS is deduced based on the magnetic charge method. The effects of design parameters on the stiffness characteristics of the CMS-HLNS are investigated. Finally, experimental prototypes are constructed to verify the feasibility of the analytical model and the superior vibration isolation performance when introducing the CMS-HLNS. The experimental results demonstrate that the CMS-HLNS can achieve linear negative stiffness in a large working range under the constraint of space and is suitable for (ultra-) low-frequency isolation under excitations with large amplitude. It’s believed that the magnetic spring proposed in this paper can be applied as an innovative technology in engineering practice, and its good linearity and compact structure make it extremely adaptable.

A magnetic negative stiffness eddy-current inertial mass damper for cable vibration mitigation

Previous studies have shown superior control performance in mitigating vibrations of stay cables by using passive control devices such as negative stiffness dampers (NSDs) and inertial mass dampers (IMDs). Integrating the advantages of the two dampers, we propose a novel passive control device termed magnetic negative stiffness eddy-current inertial mass damper (MNS-ECIMD) for cable vibration mitigation. A mechanical model of the MNS-ECIMD is proposed and validated against dynamic test data of a small-scale prototype. A parametric analysis is conducted based on the finite difference model of the cable-damper system to investigate the effects of the magnetic negative stiffness coefficient, inertance coefficient, and eddy-current damping coefficient of the MNS-ECIMD on cable vibration mitigation performance. The MNS-ECIMD performance is further validated using a small-scale cable test, of which the results illustrate its superior performance for the first two modes compared with the ECIMD. A simple parameter optimization procedure is then presented for cable multi-mode vibration control, which is then demonstrated via numerical simulation of a 306 m-long stay cable of Stonecutter Bridge in Hong Kong. Numerical results illustrate that the MNS-ECIMD significantly outperforms conventional viscous dampers and the ECIMD for cable multi-mode vibration control, owing to the additional negative stiffness effect.

Low-frequency vibration suppression of metastructure beam with high-static–low-dynamic stiffness resonators employing magnetic spring

The low/ultra-low-frequency structural vibrations exist widely in some engineering structures, for example, aerospace, naval, and building structures and so on. They could seriously affect the working performance and even cause the destruction of these engineering structures. In order to restrain the low/ultra-low-frequency structural vibration, a locally resonant (LR) metastructure beam equipped with high-static–low-dynamic stiffness (HSLDS) resonators employing negative stiffness magnetic spring is proposed. The analytical model of magnetic negative stiffness spring is firstly derived and the design method of HSLDS resonators is presented based on parametric optimization. Then, the dynamic model of the LR metastructure beam with HSLDS resonators is established using the wave finite element method. The effects of the number of local resonator units on low-frequency band gap are analyzed. Finally, the low-frequency vibration control performance of LR metastructure beam is validated experimentally. The experimental result is in agreement with the theoretical analysis, which demonstrates that the HSLDS resonators are conductive to suppress vibration of the metastructure beam in the low-frequency region (f < 10 Hz). The results also showed that the more the HSLDS resonators are used, the better the vibration suppression effect is.

Research on design and characteristic of a new type of air suspension system with magnetic negative quasi-zero stiffness

This paper designs a quasi-zero stiffness suspension with an air spring and a magnetic spring in parallel to improve the vehicle ride comfort. The proposed new suspension does not change the overall layout of the air suspension or affect the handling stability, reducing the system’s natural frequency by a sound vibration isolation effect for a low-frequency vibration and finally improving ride comfort. The feasibility of quasi-zero stiffness suspension is verified by mathematical modeling of air spring and magnetic spring, and reasonable structural parameters are set for the simulation experiment. The 1/4 vehicle model with two degrees of freedom is built in MATLAB / Simulink. Select body acceleration, suspension working space, and tire dynamic load as evaluation indexes to test the comfort performance of the proposed suspension. The result shows that the proposed new suspension has a noticeable effect on reducing the acceleration of the vehicle body and significantly improves the vehicle ride comfort.

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

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

Genetic Optimization of Repulsive Magnetic Array Negative Stiffness Structure for High-Performance Precision Micro-vibration Isolation

Genetic Optimization of Repulsive Magnetic Array Negative Stiffness Structure for High-Performance Precision Micro-vibration Isolation

Low-frequency sound insulation performance of novel membrane acoustic metamaterial with dynamic negative stiffness

For improving the low-frequency sound insulation properties of membrane/plate structures, a new quasi-zero stiffness membrane acoustic metamaterial with dynamic magnetic negative stiffness is proposed. When the equivalent magnetic charge theory is used to investigate the dynamic magnetic negative stiffness, a theoretical model of proposed metamaterial with finite dimension is established based on the Galerkin method. Through a combination of theoretical analysis, numerical simulation and experimental measurement, the low-frequency (1–1000 Hz) sound insulation performance of the metamaterial is investigated from several perspectives, including structural modality, vibration mode, average velocity, phase curve, equivalent mass density, and equivalent spring-mass dynamics model. The results show that at a certain initial membrane tension, the decreasing of the magnetic gap or the increasing of the residual flux density can increase the dynamic magnetic negative stiffness. This in turn leads the peak frequency to decrease and the bandwidth of sound insulation to increase, thus achieving effective low-frequency sound insulation over a wide frequency band. Further, when the magnetic gap is larger than the second critical magnetic gap and smaller than the first critical magnetic gap, the first-order modal resonance of the metamaterial disappears, and the corresponding value of sound insulation valley increases significantly, thus demonstrating superior sound insulation effect in a wide frequency band. The proposed method of using dynamic magnetic negative stiffness to improve low-frequency sound insulation valleys due to modal resonance provides useful theoretical guidance for designing membrane/plate type low-frequency sound insulation metamaterials.

Low-frequency sound insulation performance of novel membrane acoustic metamaterial with dynamic negative stiffness

For improving the low-frequency sound insulation properties of membrane/plate structures, a new quasi-zero stiffness membrane acoustic metamaterial with dynamic magnetic negative stiffness is proposed. Upon applying the equivalent magnetic charge theory to derive the dynamic magnetic negative stiffness, a theoretical model of proposed metamaterial with finite dimensions is established based on the Galerkin method. Through a combination of theoretical analysis, numerical simulation and experimental measurement, the low-frequency (1—1000 Hz) sound insulation performance of the metamaterial is investigated from several perspectives, including structural modality, vibration mode, average velocity, phase curve, equivalent mass density, and equivalent spring-mass dynamics model. Results show that, at a certain initial membrane tension, decreasing the magnetic gap or increasing the residual flux density can increase the dynamic magnetic negative stiffness. This in turn leads to decreased peak frequency and enlarged bandwidth of sound insulation, thus achieving effective low-frequency sound insulation over a wide frequency band. Further, when the magnetic gap is larger than the second critical magnetic gap and smaller than the first critical magnetic gap, the first-order modal resonance of the metamaterial disappears, and the corresponding value of sound insulation valley increases significantly, thus demonstrating superior sound insulation effect with wide frequency band. The proposed method of using dynamic magnetic negative stiffness to improve low-frequency sound insulation valleys due to modal resonance provides useful theoretical guidance for designing membrane/plate type low-frequency sound insulation metamaterials.

Analysis and design of a novel arrayed magnetic spring with high negative stiffness for low-frequency vibration isolation

Paralleling magnetic negative stiffness mechanism (NSM) with positive stiffness serves as an effective way to resolve the inherent contradiction between high load capacity and ultra-low frequency vibration isolation ability. Nevertheless, the stiffness nonlinearity and oversize of common magnetic NSMs restrict their further applications. In this paper, a novel compact arrayed-magnetic-spring with negative stiffness (AMS-NS) is proposed. The AMS-NS, which consists of cuboidal magnets arranged as a rectangular array, possesses high negative stiffness density and ameliorative nonlinearity. An analytical model of the AMS-NS is established based on the magnetic charge model and validated by static experiments. Parametric studies are conducted to provide guidelines for the optimal design of the AMS-NS. In addition, the nonlinear displacement transmissibility of an isolator with the AMS-NS and positive stiffness in parallel (APSP) is derived utilizing the harmonic balance method, and effect of stiffness characteristic of the AMS-NS on the isolation performance are furtherly investigated. Finally, dynamic experiments were conducted on a prototype with APSP, the results demonstrated that the proposed AMS-NS has high negative stiffness density and can effectively reduce the resonance frequency to broaden the vibration isolation band; and the analytical results showed good agreements with the experimental results.

High-performance semiactive secondary suspension of high-speed trains using negative stiffness and magnetorheological dampers

With increasing transportation speed, the excessive vibrations of high-speed trains (HSTs) have become a critical issue to be solved. This study presents an innovative semiactive suspension system consisting of a magnetorheological (MR) damper in parallel with a magnetic negative stiffness (NS) element. The proposed semiactive dampers, called MRNS dampers, are integrated into the secondary suspension of an HST to improve riding comfort. The MRNS design can effectively enhance the vibration mitigation performance of semiactive MR dampers and compensate for the performance gap between traditional semiactive MR dampers and active controllers (e.g. linear quadratic regulator (LQR)). The effects of the NS coefficient and control force weight coefficient are presented, and the optimal selections of these parameters are discussed with respect to the control performance and force tracking errors of the MRNS controller. Results indicate that the MRNS damper can satisfactorily emulate LQR force trajectories. Hence, the semiactive MRNS controller can achieve vibration suppression performance comparable to that of an active LQR controller.