Negative Stiffness Structures Research Articles

Modelling and Investigation of a Driver Seat Suspension with Negative Stiffness Structure

Modelling and Investigation of a Driver Seat Suspension with Negative Stiffness Structure

Simultaneous vibration isolation and energy harvesting via a new negative stiffness system with inertial amplifier

The negative stiffness system provides significant vibration isolation. The conversion of mechanical energy from structural vibrations into electrical energy is an effective method of energy harvesting. In this paper, a new negative stiffness system (NSS) with inertial amplifier for vibration isolation and energy harvesting is established, whose main purpose is to achieve good vibration isolation effect while the system can achieve the purpose of energy harvesting. Inertial amplifiers are used to improve the dynamic effective mass of the system, thereby reducing the natural frequency of the system. Using the multi-scale method, the amplitude-frequency response equation of the system is derived and the amplitude-frequency characteristic curve is plotted. The Lyapunov exponent, the root mean square of the voltage of the piezoelectric system and the basin of attraction are introduced to analyze the energy harvesting performance of the system. Numerical results show that the inertial amplifier improves the vibration isolation capacity of the negative stiffness structure in the low-frequency band. There is a correlation between the basin of attraction, the Lyapunov exponent, and the root mean square of voltage.

Bifurcation and dynamic analysis of quasi-zero stiffness isolator with asymmetric stiffness and mismatched load based on X-shaped negative stiffness structure

Bifurcation and dynamic analysis of quasi-zero stiffness isolator with asymmetric stiffness and mismatched load based on X-shaped negative stiffness structure

A self-recoverable negative stiffness metamaterial with enhanced bearing and energy dissipation capacity

Because of their desirable properties, mechanical metamaterials have drawn increasing attention. Negative stiffness (NS) metamaterials can be used as reusable energy dissipation devices, but they usually have low bearing capacity. In this study, a self-recoverable NS structure with enhanced bearing and energy dissipation capacity was proposed. It breaks free from the size limitations of curved beams or thin rods, and can have high bearing and energy dissipation capacity through the mutual extrusion and friction between the snap plug and the layered snap groove. The mechanical properties of the proposed NS structure were studied by finite element analysis and experiments. The reusability of the structure was verified by cyclic loading experiments. The results show that compared with the traditional curved beam NS structure and the previously self-recoverable NS structure, the bearing and energy dissipation capacity of the proposed structure have been greatly improved.

Bio-inspired quasi-zero stiffness vibration isolator with quasilinear negative stiffness in full stroke

Simpler structure, better adaptability to variable loads, and wider linear stable region have always been pursued by nonlinear quasi zero stiffness (QZS) isolator. Inspired by the balancing and stabilizing effect of the leg and wing in the take-off and landing of birds, this paper proposes a novel bio-inspired QZS vibration isolator (BI-QZSVI). The BI-QZSVI is composed of two primary components: the legged negative stiffness structure, which comprises a two-link mechanism and a set of oblique springs, and a pair of vertical springs that imitate wings. A static model is established based on the virtual work principle, the nonlinear dynamic model is then constructed using Lagrangian equations, and an analytical solution is derived through implementation of the harmonic balance method. An experimental platform is established to verify the effectiveness of the theoretical results. The results reveal that the proposed isolator outperforms existing typical isolators by offering a larger quasi-zero stiffness region, as evidenced by the two proposed range and linearity indexes. The unique structure effectively tackles geometric nonlinearity to establish a linear relationship between the load and stiffness. Notably, the negative stiffness of the isolator exhibits exceptional linearity throughout the entire stroke, ensuring a broad stability region even under high excitation levels. Furthermore, the isolator demonstrates remarkable efficacy in reducing vibrations with frequencies exceeding 3 Hz. Overall, the proposed isolator is an efficient low-frequency isolator with simple structure, strong adaptability, and wide linear range.

Characteristic analysis of bionic-induced structures with negative stiffness inspired by the growth and deformation differences of branches

Negative stiffness (NS) structures with curved beams easily experience beam fracture in small-scale designs, limiting their repeatability and energy absorption. The induced energy absorption structure (IEAS), which achieves negative stiffness by altering load transfer paths, is designed inspired by the growth and deformation of tree branches. By means of the variation method of geometric parameters, a unique asymmetric buckling deformation mode is realized in IEAS. The NS and energy absorption characteristics in IEAS are analyzed based on load distribution and major principal strain theory. Compression results demonstrate that the asymmetric buckling mode exhibits higher energy absorption and specific energy absorption compared to symmetric linear buckling, effectively improving structural toughness. Through gradient analysis of geometric parameters and comprehensive analysis of induced structure layouts, the asymmetric buckling mode is successfully implemented in multi-layer IEAS. The multi-layer IESA exhibits excellent ability of energy absorption and toughness, making it have potential applications in areas that require small-sized designs with high energy absorption capabilities.

Analysis of negative stiffness structures with B-spline curved beams

With unique mechanical properties, negative stiffness (NS) structures have presented significant advantages in energy absorption. In recent years, NS structures consisting of periodically arranged curved beams have attracted comprehensive attention. However, the curved beams of the current report mainly focus on geometrical parameters in specific configurations, and the variety of the reported geometrical configurations of the flexible beams is relatively limited. In this paper, a B-spline curved beam design method is proposed. A static analysis model of a B-spline curved beam is developed to investigate the force-displacement relations of curved beams in different configurations. The configuration for the B-spline curved beam is obtained, and the relation between the geometric parameters and the mechanical properties of the B-spline curved beam is discussed. Then the mechanical properties of NS structures with periodically arranged B-spline curved beams are analyzed by the finite element method, and the experiments verified the correctness of the simulation method. Finally, the force-displacement relation and energy-absorption properties of gradient NS structures with B-spline curved beams are discussed. The results indicate that the NS structure with B-spline curved beams has repeatability and effective energy absorption properties. The deformation form of the NS structure can be modulated by gradient NS design, and the energy absorption properties of the NS structure can be improved effectively. The research can provide a reference for the design of NS structures.

Load-adaptive quasi-zero stiffness vibration isolation via dual electromagnetic stiffness regulation

Conventional quasi-zero stiffness (QZS) isolators are sensitive to load variation, especially the load mismatch can severely degrade low-frequency vibration isolation performance. Herein, a load-adaptative electromagnetic QZS vibration isolator (LEQVI) is proposed. The stiffness nonlinearization for QZS characteristic is achieved by exploiting a nonlinear positive stiffness structure (a cylindrical coil and a magnet in the face-to-face configuration) to modulate a negative stiffness structure (a conical coil and a magnet in the nested configuration). Static modeling and tests reveal that the rated load of the LEQVI can be flexibly and linearly adjusted by regulating the excitation current. Dynamic modeling found that the load mismatch can narrow the vibration isolation bandwidth and deteriorate the vibration attenuation effect. A sliding mode control law considering input saturation is developed to adapt to unknown loads. Simulations and dynamic experiments are conducted to evaluate the vibration isolation performance and verify the effectiveness of the load-adaptive controller. The results demonstrate that the LEQVI can realize a wide vibration isolation band and effective vibration attenuation under various loads via dual electromagnetic stiffness regulation. The proposed LEQVI provides a novel perspective for designing load-insensitive QZS isolators and holds great promise in facilitating future engineering applications of QZS isolators.

A new design of seat suspension using different models of negative stiffness structure

Three models of seat suspension using the negative stiffness structure including steel springs (SS), roller springs (RS), and tuned mass damper (TMD) are proposed and studied to improve the driver's seat ride comfort. Based on the dynamic models of the SS, RS, and TMD, their isolation efficiency and driver’s ride comfort are evaluated via two indexes of the root mean square displacement and acceleration of the seat (zws and aws) under two excitations of the random road surface and bumpy road surface. The results show that under the random road surface, the zws and aws with the seat's RS are reduced by 10.31 % and 20.32 % in comparison with the seat’s SS; whereas the zws and aws with the seat's TMD are smaller than that of the seat's RS by 19.15 % and 26.13 %; and the seat’s SS by 27.49 % and 41.15 %, respectively. Besides, the seat's displacement and acceleration responses with the seat’s TMD are also lower than that of both the SS and RS under the bumpy road surface. Therefore, the structure of the TMD should be designed and added to the seat suspension to enhance the driver’s seat ride comfort.

Integrated vibration isolation and actuation via dual nonlinear stiffness regulation

Integrating vibration isolation and actuation is superior, enabling enhanced vibration isolation performance while attaining controllable load position and attitude. Herein, a novel actuatable quasi-zero stiffness (QZS) vibration isolator (AQVI) is proposed and systematically investigated. The stiffness nonlinearization for QZS is fulfilled by paralleling nonlinear electromagnetic negative and positive stiffness structures. This configuration gives rise to an interesting behavior, that is, the rated load and equilibrium position are tailorable via dual nonlinear stiffness regulation, rendering the load actuatable without a trade-off with the QZS characteristic. The comprehensive static investigation is implemented to fully reveal and verify the dual nonlinear stiffness regulation mechanism. Dynamic governing equations are derived and solved in the cases of dwell and actuation, and it is found that the AQVI is capable of isolating broadband vibrations and tracking prescribed trajectories. Finally, an experimental apparatus is built to evaluate the vibration isolation performance and examine the effectiveness of the load actuation. The sweep excitation test demonstrates that the AQVI has good vibration isolation performance, exemplified by a low resonant frequency of 2.5 Hz and a small isolation starting frequency of 3.6 Hz. The load actuation test validates that the AQVI under open-loop control is competent to actuate the load following the desired trajectory while retaining excellent vibration attenuation. The proposed AQVI provides a novel paradigm for devising QZS isolators that are insensitive to the load and working point, shedding promising light on applications requiring integrated vibration isolation and actuation.

An energy dissipation metamaterial based on Coulomb friction and vibration

Compared with traditional energy dissipation structures, negative stiffness metamaterials can repeatedly dissipate energy without incurring irreversible plastic deformation. The existing negative stiffness structures are generally multistable, and their energy dissipation mechanism is either through internal component vibration or friction. In this paper, a self-recoverable negative stiffness structure was proposed which can dissipate energy through both vibration and Coulomb friction. The structure consists of an external I-shaped structure and a buckle-like structure composed of a plug and cantilever beams inside. The proposed structure achieves monostable characteristics by utilizing the concept of self-contact. To investigate the mechanical properties, quasi-static loading-unloading experiments were performed and verified using finite element simulation. The energy dissipated in the proposed structure by vibration and friction was quantified theoretically. The influence of geometric parameters on energy dissipation was studied using simulation and analytical methods. This type of metamaterial has the potential to be employed in the production of multi-functional metamaterial structures such as deformable robots or reusable bumpers.

Optimal Design and Dynamic Analysis of a New Quasi-Zero-Stiffness Isolation Device

Compared with the linear isolation system, the quasi-zero-stiffness (QZS) nonlinear isolation system has the characteristics of high static stiffness and low dynamic stiffness, which has better low-frequency vibration isolation performance. However, most of the existing QZS isolators only consider the quasi-zero-stiffness characteristic at the static equilibrium position achieved by the parallel connection of positive and negative stiffness structures. To optimize the isolation performance of the QZS system, a new isolation device based on the parallel connection of oblique springs and vertical springs was proposed. The device can not only achieve quasi-zero-stiffness at the static equilibrium position but also expand the interval of quasi-zero-stiffness through parameter optimization design to optimize the stiffness characteristics of the QZS system, thus effectively improving the vibration isolation performance. The QZS nonlinear systems with the optimal parameters were analyzed dynamically, and the nonlinear motion equations were approximately solved based on the fifth-order polynomials fitted by the restoring force curves. A prototype was further designed and fabricated to compare and analyze the vibration isolation performance of the QZS system and the equivalent linear system through a shaking table test.

Research on hierarchical cylindrical negative stiffness structures’ energy absorption characteristics

Negative stiffness (NS) structures possess distinctive mechanical properties and exhibit promising potential for diverse applications. In this paper, we presented an innovative hierarchical design to further enhance the capabilities of NS structures. The dynamic and static performance of the normal and hierarchical cylindrical NS structures were investigated and compared with experiments and numerical simulation. The results demonstrated that the hierarchical structures displayed superior cushioning performance relative to the traditional one. The presented approach offers a novel method to enhance cylindrical NS structures and serves as a valuable reference for future research in this field.

A novel reinforced cylindrical negative stiffness metamaterial for shock isolation: Analysis and application

Negative stiffness (NS) metamaterials have been widely studied in the fields of shock isolation and energy absorption due to their special properties. For various application scenarios, many types of NS metamaterials have been proposed, such as 2D honeycomb, 3D cube, hollow cylinder. However, when installation space is limited, the hollow cylindrical NS metamaterials may not achieve buffering effect due to its weak stiffness. In this paper, a cylindrical negative stiffness structure with inner hollow parts filled by inclined beam elements is proposed, which can obtain enhanced stiffness and energy absorption by improving space utilization. Theoretical analysis, numerical simulation and experimental validation were carried out to study the quasi-static and dynamic mechanical properties of the structure. Finally, the structure was applied as a cushion in a non-pyrotechnic separator, which could achieve good cushion performance. This work is expected to provide more potential for the applications of cylindrical negative stiffness structures.

Parameters optimization of three-element dynamic vibration absorber with inerter and grounded stiffness

Improving the control performance of dynamic vibration absorbers has recently been effective by introducing a grounded negative stiffness device. However, the negative stiffness structure is unstable and difficult to achieve in engineering practice , and its major drawback is that it amplif ies the vibration response of the primary system at low frequency region. Meanwhile, some mechanical devices can be combined to make the DVA work even better with a grounded positive stiffness. For this purpose, this paper combines for the first time the control effect of the inerter device and grounded positive stiffness into a three-element DVA model in order to better improve vibration reduction of an undamped primary system under excitation. First, the dynamic equation of motion of the system is written according to Newton ’s second law. Then, the steady-state displacement response of the primary system under harmonic excitation is calculated. In order to minimize the resonant response of the primary system around its natural frequency, the extended fixed point theory is applied. Thus, the optimized parameters such as the tuning frequency ratio, the stiffness ratio , and the approximate damping ratio are determined as a function of mass ratio and inerter – mass ratio. From the results analysis, it was found that the inerter – mass ratio has a better working range to guarantee the stability of the coupled system. Then , study on the effect of inerter – mass ratio on the primary system response is carried out. It can be seen that increasing the inerter – mass ratio in the optimal working range can reduce the response of the primary system beyond its uncontrolled static response. However, it is necessary to avoid the situation where the inerter – mass ratio is very large because it can lead to unrealistic optimal parameters. Finally, comparison with other DVA models is show n under harmonic and random excitation of the primary system. It is found that the proposed DVA model in this paper has high control performance and can be used in many engineering practice s .

Negative-Stiffness Structure Vibration-Isolation Design and Impedance Control for a Lower Limb Exoskeleton Robot

The series elastic actuator (SEA) is generally used as the torque source of the exoskeleton robot for human–robot interaction (HRI). In this paper, an impedance control method for lower limb exoskeleton robots driven by SEA is presented. First, considering the low-frequency vibrations generated by the lower limb exoskeleton robot during walking, the displacement generated by the robot is regarded as an external disturbance to the SEA motor. An SEA structure with negative stiffness structure (NSS) is designed to achieve vibration isolation in the low-frequency excitation region. Second, the dynamics model of the SEA-driven exoskeleton robot system is proposed, and the impedance control strategy is integrated into the proposed system. In addition, the numerical responses of the vibration-isolation system in both time and frequency domains are given, and the designed NSS is designed to achieve vibration isolation. The amplitude-frequency responses of the system are obtained. The harmonic balance (HB) method is used to give the analytical solution of the designed negative-stiffness isolation system, and the effects of different characteristic parameters on the isolation system are analyzed. Moreover, the stability of the SEA-driven exoskeleton impedance control system is demonstrated using the Lyapunov method. Finally, numerical simulations are carried out in order to show the effectiveness of the control method.

Improving Ride Comfort of a Soil Compactor based on the NSS Embedded into the Seat's Semiactive Suspension

Three dynamic models (1-D, 2-D, and 3-D) of a soil compactor are established to research the vehicle's ride comfort via numerical simulation and experiment. Based on the efficiency of the semi-active control (SAC) of the Fuzzy-PID controller and the negative stiffness structure (NSS), a new suspension of the driver's seat equipped with the SAC and NSS is proposed to further improve the soil compactor's ride comfort under the various working conditions of the vehicle on the elastoplastic soil ground. The reduction of the root-mean-square seat acceleration (a_ws) in the time domain and the power-spectral-density seat acceleration (PSD) in the frequency domain is chosen as the objective function. The study indicates that the seat's acceleration response in the time domain with the 1-D, 2-D, and 3-D models of the soil compactor is similar. However, the a_ws and maximum PSD acceleration of the driver's seat with the 1-D model are higher than that of the 3-D model by 35.9% and 58.5%, while the acceleration response and PSD acceleration of the driver's seat with the simulation of the 3-D model are similar to the experiment. Therefore, the different dynamic models of the vehicle remarkably affect the investigation result. With the driver's seat suspension equipped with the SAC and NSS, the $a_{ws$ and maximum PSD acceleration of the driver's seat are strongly decreased by 80.1% and 87.6% compared to the seat's passive suspension without the SAC and NSS. Additionally, these values are also lower than that of oth the SAC and NSS under various simulation conditions. Consequently, the driver's seat suspension equipped with the SAC and NSS could be used to further improve the ride comfort of the soil compactor.

Dynamics and Stability of Magnetic-Air Hybrid Quasi-Zero Stiffness Vibration Isolation System

With the improvement of machining accuracy, external low frequency vibration has become one of the most important factors affecting the performance of equipment. The theory of quasi-zero stiffness vibration isolation shows favorable low frequency vibration isolation effect. However, the theory, mechanical properties and dynamics of the system still need to be studied and expanded. Based on our previous research on the structure of a magnetic-air hybrid quasi-zero stiffness vibration isolation system, the nonlinear mechanical expression of positive and negative stiffness structure has been analyzed in this paper, to improve application of the system and provide a theoretical basis for sequential studies of active control. To provide the judgment criteria and basis for the application of quasi-zero stiffness, a more accurate quasi-zero stiffness mechanical model was to be established, and the judgement criterion and stability of quasi-zero stiffness was to be discussed and analyzed. Then, the dynamical model based on external low frequency vibration was developed, to investigate the stability and natural frequency. At the same time, the influence of different feedback parameters on the amplitude frequency characteristics has been discussed, which provides a basis for the future study of active control. Finally, we carried out simulation and experimental analysis to verify the stiffness of high static and low dynamic and the low frequency vibration isolation effect of the vibration isolation system.

A negative stiffness structure with multi-stable characteristic

This work proposes a straw-shaped structure (SS) inspired by the folds of straw. Two samples named SSⅠ and SSⅡ with 5 and 5.5 layers of conical structures, respectively, are prepared using selective laser sintering (SLS) technology. SSⅠ and SSⅡ can spontaneously recover to their original shapes after compression experiments. With the thickness of 0.6 and 3.0 mm for the upper and lower parts of cells, the peak and valley forces of SSII (SS-3.0-0.6) during compression and tension alternate periodically. The first and second valley forces of SS-3.0-0.6 are −16.1 and −20.2 N during compression, and its second, fifth and fourth peak forces are 30.2, 4.3 and 0.8 N during tension. SS-3.0-0.6 exhibits significant NS and multi-stable properties in both compression and tension, and it is easier to be stretched than compressed. The deformation mode of the folded structure is similar to stacked porcelain bowls. Through a reasonable design of geometric parameters, the folding order and deformation mode as well as the number of stable state of the SSII models can be customized. In addition, the potential applications of SSs are also discussed, and this work provides a valuable reference for the study of NS structures.

3D printed negative stiffness meta-structures with superior energy absorption and super-elastic shape-recovery features

The aim of this paper is to create novel 3D cubic negative stiffness (NS) structures (NSSs) with superior mechanical performances such as high energy absorption, shape recovery, super-elasticity, and reversibility. The conceptual design is based on an understanding of geometrical influences, non-linear buckling-type instability, snap-through mechanism, elasto-plastic deformation growth and plastic hinges. A finite element (FE) based computational model with an elasto-plastic material behavior is developed to design and analyze NSSs, saving time, material, and energy consumption. Material samples and meta-structures are 3D printed by selective laser sintering printing method. Material properties are determined via mechanical testing revealing that the printing process does not introduce much anisotropy into the fabricated parts. Experimental tests are then conducted to study the behavior of novel designs under loading–unloading cycles verifying the accuracy of the computational model. A good correlation is observed between experimental and numerical data revealing the high accuracy of the FE modeling. The structural model is then implemented to digitally design and test NSSs. Effects of the geometrical parameters of the negative stiffness members under three cyclic loading are investigated, and their implications on the non-linear mechanical behavior of NSSs under cyclic loading are put into evidence, and pertinent conclusions are outlined. In addition, the dissipated energy and loss factor values of the designed structures are studied and the proposed unit cell is presented for the energy absorbing systems. The results show that the structural and geometry of energy absorbers are key parameters to improve the energy absorption capability of the designed structures. This paper is likely to fill a gap in the state-of-the-art NS meta-structures and provide guidelines that would be instrumental in the design of NSS with superior energy absorption, super-elasticity and reversibility features.