Negative Stiffness Mechanism 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.

An approach for realizing lightweight quasi-zero stiffness isolators via lever amplification

Quasi-zero stiffness (QZS) vibration isolators exhibit excellent performance in low-frequency vibration isolation but require the negative stiffness to be consistent or close to the positive stiffness, which may lead to an excessively large volume or weight of the negative stiffness mechanism. In this paper, a lightweight QZS (L-QZS) vibration isolator using the lever amplification mechanism is developed, theoretically investigated, and experimentally verified. The negative stiffness can be amplified by one order of magnitude through the amplification effect of the lever structure, enabling a lower negative stiffness to compensate for the positive stiffness. Meanwhile, the lever increases the inertia effect of the negative stiffness structure, leading to an increase in the system’s effective mass and further reducing the resonance frequency. Results indicate that with a small negative stiffness, the isolation bandwidth of L-QZS isolators is significantly enlarged. The transmissibility at high frequencies of the L-QZS isolator tends to a certain value, which is mainly determined by the lever ratio and the tip mass of the lever. Furthermore, the negative stiffness can be controlled by adjusting the lever ratio, providing a viable method for matching various positive stiffnesses in engineering applications.

Low-frequency multiple topological interface modes in metamaterial beams with quasi-zero-stiffness resonators

To achieve multiple low-frequency topological interface modes (TIMs) while maintaining lightweight and load-bearing capacities in metamaterial beams, we propose novel topological beams equipped with double quasi-zero-stiffness (QZS) resonators. Following the introduction of the negative stiffness (NS) mechanism, we derived the dispersion relations of the topological beams with double QZS resonators using the transfer matrix method (TMM), and performed comparative and parametric analyses of stiffness ratio on folded Dirac cones (DCs) and locally resonant band gaps (LRBGs). Thanks to the NS mechanism and the double degrees of freedom (DOFs) in the QZS resonators, we can realize double low-frequency DCs (< 500 Hz) in metamaterial beams. It is notable that adjusting the stiffness of oblique springs can tune the resonators’ effective stiffness, implying that we can custom the frequency of DCs and LRBGs by adjusting the QZS resonator. By altering the distance between two QZS resonators, we obtain two topologically distinct unit cells. Transmission simulations confirm the presence of multiple low-frequency TIMs at the interface between these two domains. We also find that the effect of mass and geometric defects at various positions on TIMs is minimal. The proposed metamaterial beams could inspire innovative low-frequency vibration energy harvesters and lightweight topological devices.

Development and experimental study of disc spring-based negative-positive-uncoupled stiffness devices for structural multi-level seismic fortification

To achieve the structural multi-level seismic fortification objectives, this paper proposes a novel negative-positive-uncoupled stiffness device (NPUSD) based on combined disc springs with multi-linear elasticity characteristics. This device allows for independent variations in the negative stiffness range under small deformations and the positive stiffness range under large deformations. It primarily utilizes the negative stiffness mechanism for seismic mitigation during medium and small seismic events referring to existing research on traditional negative stiffness devices (NSDs) while providing positive stiffness to prevent collapse during major seismic events. The configuration and working principle of the NPUSD are discussed. By replacing the preloaded linear elastic spring of traditional NSDs with multi-linear elastic spring, the NPUSD can effectively and conveniently achieve stiffnesses decoupling. A design algorithm based on the successive area equivalence principle for the multi-linear elastic spring is proposed. Finally, based on a 56-story steel core-outrigger structure, a comparison between NSDs and NPUSDs is made under the four seismic intensity levels. Results show that the novel NPUSDs contribute to achieving structural multi-level seismic fortification objectives.

Semi-active control of the electromagnetic negative stiffness mechanism in a double-layer vibration isolator

Semi-active control of the electromagnetic negative stiffness mechanism in a double-layer vibration isolator

Bandgap characteristics of a hybrid multi-resonator elastic metamaterial with negative stiffness mechanism and its application to mitigate seismic response of building structures

Seismic metamaterials have attracted extensive attention due to their unique ability to attenuate the transmission of elastic waves in their frequency bandgaps. However, generating a metamaterial with a low-frequency and wide bandgap remains challenging. Previous studies have shown that negative stiffness mechanisms can lower the frequency range of bandgaps while employing a multi-resonator technique can broaden the width of bandgaps. In this study, by combining these two techniques, a negative stiffness enhanced multi-resonator elastic metamaterial (NMEM) is first proposed. The feasibility of NMEM is validated by comparing the theoretical dispersion relation and the transmission spectra of a finite cell model. The results demonstrate that low-frequency and wide bandgaps can be realized by NMEM. To further widen the bandgap, a hybrid NMEM is proposed by connecting multiple types of cells in series. The proposed hybrid NMEM consists of two types of cells, one with a single resonator and another with two resonators, which merge individual bandgaps into a continuous and wider bandgap. The proposed hybrid NMEM is then adopted as a meta-basement for a case building to demonstrate its effectiveness in mitigating seismic responses. The results show that the seismic responses of the building with the hybrid meta-basement are considerably reduced than those of the building with the conventional basement. However, the hybrid meta-basement may lead to larger structural displacement response when the dominant frequency of ground motion is outside the designed bandgap.

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

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

Double roller negative stiffness mechanism seat suspension optimization design and vibration analysis

To further improve the vibration isolation performance of automobile seat suspension and the riding comfort of automobiles, this paper uses the double roller negative stiffness mechanism (NSM) to calculate the seat suspension with quasi-zero stiffness (QZS) characteristics. The influence of the structural parameters on the QZS characteristics is simulated and analyzed, and the structural parameters are optimized by the orthogonal design method. The effectiveness of the optimization was verified by analyzing the dynamic response of the seat suspension system. The results show that the natural frequency of the vibration isolation system of the seat suspension decreases, the vibration isolation band widens after the introduction of the double roller NSM, and the vibration isolation effect is improved under low-frequency excitation.

Design of low-frequency circular metastructure isolators with high-load-bearing capacity

Traditional vibration isolation structures cannot work effectively for low-frequency vibration under heavy loads, due to the inherent contradiction between the high-static and low-dynamic stiffness of these structures. Although the challenge can be effectively addressed by introducing a negative stiffness mechanism, the existing structures inevitably have complex configurations. Metastructures, a class of man-made structures with both extraordinary mechanical properties and simple configurations, provide a new insight for low-frequency vibration isolation technology. In this paper, circular metastructure isolators consisting of some simple beams are designed for low-frequency vibration, including a single-layer isolator and a double-layer isolator, and their static and dynamic characteristics are studied, respectively. For the static characteristic, the force–displacement and stiffness–displacement curves are obtained by finite element simulation; for the dynamic characteristic, the vibration transmissibility curves are obtained analytically and numerically. The result shows that the circular nonlinear single-layer isolator has excellent low-frequency isolation performance, and the isolation frequency band will decrease about 20 Hz when the isolated mass is fixed at 1.535 kg, compared with a similar circular linear isolator. These static and dynamic properties are well verified through experiments. Our work provides an innovative approach for the low-frequency vibration isolation and has wide potential applications in aeronautics.

A compliant constant-force mechanism with sub-Newton force and millimeter stroke output

Force control technology plays a pivotal role in manipulating vulnerable objects. This paper presents a new compliant mechanism with constant-force output characteristics, which can prevent force damage due to displacement overshoot. Due to its unique passive structure, it is exempted from intricate sensors and complicated controllers. The quasi-static constant-force mechanism is obtained by the parallel combination of positive- and negative-stiffness mechanisms. Such a straightforward method facilitates a rapid development and implementation process. The procedures of architectural arrangement selection, theoretical model establishment, parameter sensitivity evaluation, and multi-objective structural optimization are carried out to achieve specified constant-force characteristics. Moreover, the prototype fabrication and performance testing of a constant-force mechanism have been performed. The results demonstrate that the mechanism delivers a constant output force of 339 mN in the motion range of 1.84 mm. The constant-force feature is solely governed by the actuating displacement and is independent of driving speed and acceleration. The promising application of the constant-force mechanism has been demonstrated by manipulating small force-sensitive objects such as biological eggs.

A customizable cam-typed bistable nonlinear energy sink

A novel cam-typed bistable nonlinear energy sink (CBNES) is first proposed in this paper. The CBNES achieves a customized design of the ideal configuration of BNES by introducing a cam-roller-spring negative stiffness mechanism (CRS-NSM). The design criteria for continuous and smooth bistable cam profiles are studied, and the extreme values of dimensionless stiffness and pre-compression are predicted. Furthermore, the periodic and quasi-periodic dynamics of the system are studied by using the complexification-averaging (CA-X) method. By combining Slow Invariant Manifold (SIM) and phase trajectory, the energy dissipations of different response types of the CBNES are predicted. The SMR and chaotic response have the best and lowest targeted energy transfer (TET) efficiency, respectively. The saddle-node (S-N) and Holf bifurcation characteristics of the periodic fixed points are analyzed to predict the possibility of SMR occurrence. The analysis of the amplitude frequency curve with the variation of system parameters indicates that weak negative stiffness and intermediate cubic stiffness are more beneficial to vibration suppression. The highlight is that the excitation thresholds of SMR are predicted by using analytical and numerical methods, and the influences of system parameters on the thresholds are analyzed. The deviation between the analytical and numerical results will decrease with increasing damping. Finally, the correctness of the analytical results is verified through a series of fixed-frequency experiments. The proposed CBNES provides a valuable potential solution for designing efficient and robust mechanical BNES physical implementations.

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

Design and Testing of a New Microinjector With Capacitive Force Sensor for Biological Microinjection

Microinjection with force sensing plays an important role in delivering foreign materials into biological entities. In this paper, a new force-sensing microinjector with compliant mechanism is presented. It provides a high sensitivity of force sensing by offering a small stiffness in the direction of microinjection. Meanwhile, it enables a sufficient load-bearing capability thanks to a large stiffness in the lateral direction. The small stiffness is realized by the combination of a positive-stiffness mechanism and a negative-stiffness mechanism, rather than a zero-stiffness mechanism. A custom-made capacitive force sensor based on tilted micropillar array is introduced to measure the microinjection force based on the microinjector’s output displacement. Moreover, a prototype has been fabricated for experimental testing. Experimental results show that the sensitivity of the proposed design has been improved by two-fold over previous work. The developed microinjector has been applied to successfully detect the microinjection force during the injection of zebrafish larvae, which renders a promising solution for regulating the microinjection force. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Force-assisted microinjection can provide force feedback, which is desirable to protect biological samples from excessive force and to judge successful penetration. Currently, most existing force sensor-based microinjectors can only puncture biological samples, rather than injecting materials, mainly due to the inability of bearing the weight of linker for the injection needle and actuator. In this work, a new microinjector with capacitive force sensor is presented for microinjection of zebrafish larvae. Based on the combination of a positive-stiffness mechanism and a negative-stiffness mechanism, a small-stiffness mechanism is introduced to design the microinjector. It simultaneously provides large axial sensitivity and large lateral loading ability. Moreover, a capacitive force sensor based on tilted micropillar array is devised to measure the microinjection force based on the overall displacement of the microinjector. For fixing zebrafhish larvae, a micro-array petri dish is fabricated by silicon wafer mould. Experimental results show that the microinjector is capable of delivering foreign materials and detecting the microinjection force, which is beneficial to the microinjection operation.

Low-frequency vibration isolation via new wide range zero-stiffness isolator with multiple negative stiffness mechanisms

Low-frequency vibration isolation via new wide range zero-stiffness isolator with multiple negative stiffness mechanisms

Non-contact electromagnetic controlled metamaterial beams for low-frequency vibration suppression

To address the challenge of suppressing extremely-low frequency vibration and noise in precision instruments and equipment, a novel non-contact metamaterial beams is proposed in this paper. The resonators of the metamaterial beams integrate negative stiffness mechanism and electromagnetic damping tuning system. Based on the magnetic dipole theory and the electromagnetic induction law, the mechanical model of magnetic resonator is established. The band structure and transmission spectrum of the metamaterial beams are obtained by transfer matrix method. Besides, the results of numerical simulations are used to verify the accuracy of theoretical results. The result shows that the negative stiffness can be controlled by nonlinear magnetic force among the magnets. Based on this mechanism, the bandgap frequency can be reduced to a minimum of 50Hz. Then, the method of combining electromagnetic damping and negative impedance circuit is proposed to form a tuning system which can reduce the initial frequency of the bandgap to 4Hz. Interestingly, the proposed bandgap control mechanism achieves the extremely-low bandgap while broadens the bandwidth relatively, which overcomes the deficiency of traditional quasi-zero-stiffness metamaterials that reduce the bandgap frequency while causing the bandwidth to narrow. This study is expected to provide valuable ideas for the application of metamaterials in the field of low-frequency vibration and noise reduction.

Research on a Novel CRSM for a Type of QZS Vibration Isolator

Quasi-zero stiffness is usually abbreviated as QZS. This kind of QZS isolator has a negative stiffness mechanism, which is usually a spring mechanism (NSSM), thus possessing excellent isolation performance. However, it is prone to instability under low-frequency and large amplitude excitation. In response to this situation, a novel type of cam and roller spring mechanism (CRSM) is designed. This mechanism is composed of an arc-shaped groove, a rolling element, a spring, and a sliding pair. Use the combination of CRSM and NSSM to improve the stability of QZS isolators and prevent instability. Under two typical excitations, simulation tests in SIMULINK are conducted to analyze the vibration attenuation performance of the improved isolator and the role of CRSM in improving stability. The conclusion is that CRSM can greatly improve stability without reducing vibration damping performance.

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.

High efficiency and wideband wave energy capture of a bistable wave energy converter with a displacement amplifier

Ocean wave energy is a kind of renewable energy with huge reserves, which can play an important role in the future construction of smart oceans. The low capture efficiency and narrow bandwidth of traditional wave energy capture devices seriously restrict the large-scale application of wave energy. To address these issues, a rack-pinion-lever-spring (RPLS) adaptive bistable Power Take-Off (PTO) mechanism with a time-varying potential barrier is proposed and applied to a point absorber wave energy converter (WEC). In the proposed nonlinear PTO system, a rack-pinion-lever (RPL) mechanism, as a displacement amplifier, has an effect on enhancing the poor amplitude sensitivity issue of the negative stiffness mechanism. Based on linear wave theory, a special nonlinear one-and-half-degree of freedom dynamic model is developed to describe the adaptive bistable wave energy converter (AB WEC). In comparison with the traditional bistable WEC (TB WEC) and equivalent linear WEC, the numerical results show that the AB WEC can greatly enhance the capture efficiency of lower frequency energy, especially at small wave excitations. The energy capture efficiency of the AB WEC is close to that of the TB WEC even at large wave amplitudes and is higher than that of the equivalent linear WEC. Finally, the wave energy capture characteristics of the three kinds of systems are studied based on the wave distribution diagram of a certain sea area in the South China Sea. The results show that the AB WEC has a large wave height adaptability in the low frequency region. The AB PTO mechanism with a displacement amplifier proposed in this paper can provide a technical reserve for the highly efficient and wide bandwidth capture of low frequency ocean wave energy.

Dual quasi-zero-stiffness dynamic vibration absorbers for double-low-frequency vibration suppression

Generally, a dynamic vibration absorber (DVA) is effective in suppressing single-frequency vibration, which would be unworkable for double-frequency vibration. This study introduces a dual quasi-zero-stiffness dynamic vibration absorber (DQZS-DVA) as a solution to this problem. Firstly, the DQZS-DVA with a pair of mutually exclusive permanent magnets as the negative stiffness mechanism (NSM) is designed, and its static characteristics are theoretically analyzed. Next, the Harmonic Balance Method (HBM) is used to derive an approximate analytical solution, and the effect of system parameters on the dynamic characteristics of the primary oscillator is discussed. In addition, the dynamic behavior of the primary oscillator under a random or impulse excitation is numerically analyzed. The results demonstrate that the DQZS-DVA exhibits excellent vibration suppression under double-low-frequency harmonic, random, and impulse excitations. The anti-resonance frequency of the system with the DQZS-DVA can be reduced by 50 % compared to the linear DVA. Furthermore, the system parameters of the DQZS-DVA are optimized using the fixed-points theory to further improve the vibration suppression performance. Finally, a prototype of the DQZS-DVA is manufactured, and verification experiments are conducted. The experimental results confirm that the DQZS-DVA can suppress vibrations with double low frequencies of 3.5 Hz and 7.0 Hz. More importantly, the design procedure of the DQZS-DVA should be a valuable guide for dealing with the scenario when the primary oscillator suffers from an excitation with three or more frequencies.

New low-frequency broadband metamaterials based on inerter and novel large-linear negative stiffness mechanism

Elastic metamaterials are recently emerging structural–functional materials, which provide a new way for the control of elastic waves. However, the current low-frequency broadband performance is yet to be further improved. Herein, a novel large-linear negative stiffness mechanism is first proposed, which is capable of generating constant negative stiffness; the influences of the relevant structural parameters are discussed, and a design method for this mechanism is also given. Subsequently, a new type of elastic metamaterial is designed by combining the inerter and the proposed negative stiffness mechanism; a parametric programming method with general characteristics is proposed to guide the selection of unit-cell parameters, and it is revealed that only at most one negative stiffness spring is allowed to exist in the system. Finally, the low-frequency broadband characteristics of the metamaterial are investigated. It is found that the proposed metamaterial can produce a basin-like attenuation band, i.e., the attenuation curve at the bottom of the attenuation band is a stable flat line; in a given frequency range, the introduction of negative stiffness can further increase the attenuation strength of the metamaterial basin-like band.