Design and experiments of a quasi–zero-stiffness isolator with a noncircular cam-based negative-stiffness mechanism

2020 ◽  
Vol 26 (21-22) ◽  
pp. 1935-1947
Author(s):  
Ming Li ◽  
Wei Cheng ◽  
Ruili Xie
Keyword(s):  
Harmonic Balance ◽  
Experimental Studies ◽  
Approximation Error ◽  
Low Frequency ◽  
Harmonic Balance Method ◽  
Negative Stiffness ◽  
Restoring Force ◽  
Stiffness Characteristic ◽  
Physical Prototype ◽  
Negative Stiffness Mechanism

This article presents a quasi–zero-stiffness isolator with a cam-based negative-stiffness mechanism, where the cam has a user-defined noncircular profile to generate negative stiffness to counterbalance the positive stiffness of the vertical spring and yield the quasi–zero-stiffness characteristic around the equilibrium position. Unlike previous studies, the proposed quasi–zero-stiffness isolator has the preferable feature that the desired cubic restoring force can be directly obtained through the well-designed profile of the cam in the negative-stiffness mechanism with the friction considered during the model design, rather than through the Taylor expansion and friction-ignoring assumption, which can avoid the approximation error between the theoretical design and the specific realization. The pure-cubic nonlinear differential equation of motion of the quasi–zero-stiffness isolator is derived and solved with the harmonic balance method, followed by the discussion of the relevant dynamic characteristics. Experimental studies are carried out based on the physical prototype of the quasi–zero-stiffness isolator. The results show that the quasi–zero-stiffness isolator can greatly extend the isolation frequency bandwidth and has a much lower resonance peak. In the low-frequency band, the quasi–zero-stiffness isolator greatly outperforms the corresponding linear system but is equivalent or even inferior in the high-frequency range with the increase of excitation force.

Design and analysis of a vibration isolation system with cam–roller–spring–rod mechanism

2021 ◽  
pp. 107754632110005
Author(s):  
Yonglei Zhang ◽  
Guo Wei ◽  
Hao Wen ◽  
Dongping Jin ◽  
Haiyan Hu
Keyword(s):  
Vibration Isolation ◽  
Dynamic Stiffness ◽  
Experimental Studies ◽  
Excitation Amplitude ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Stiffness Characteristic ◽  
Negative Stiffness Mechanism ◽  
Isolation Systems ◽  
Vibration Isolation Performance

The vibration isolation system using a pair of oblique springs or a spring-rod mechanism as a negative stiffness mechanism exhibits a high-static low-dynamic stiffness characteristic and a nonlinear jump phenomenon when the system damping is light and the excitation amplitude is large. It is possible to remove the jump via adjusting the end trajectories of the above springs or rods. To realize this idea, the article presents a vibration isolation system with a cam–roller–spring–rod mechanism and gives the detailed numerical and experimental studies on the effects of the above mechanism on the vibration isolation performance. The comparative studies demonstrate that the vibration isolation system proposed works well and outperforms some other vibration isolation systems.

scholarly journals An Air Spring Vibration Isolator Based on a Negative-Stiffness Structure for Vehicle Seat

2021 ◽  
Vol 11 (23) ◽  
pp. 11539
Author(s):  
Cong Hung Nguyen ◽  
Cong Minh Ho ◽  
Kyoung Kwan Ahn
Keyword(s):  
Vibration Isolation ◽  
Dynamic Stiffness ◽  
Low Frequency ◽  
Negative Stiffness ◽  
Vibration Isolator ◽  
Air Spring ◽  
Nonlinear Force ◽  
Mechanical Spring ◽  
Negative Stiffness Mechanism ◽  
Vehicle Seat

This research introduces an air spring vibration isolator system (ASVIS) based on a negative-stiffness structure (NSS) to improve the vehicle seat’s vibration isolation performance at low excitation frequencies. The main feature of the ASVIS consists of two symmetric bellows-type air springs which were designed on the basis of a negative stiffness mechanism. In addition, a crisscross structure with two straight bars was also used as the supporting legs to provide the nonlinear characteristics with NSS. Moreover, instead of using a vertical mechanical spring, a sleeve-type air spring was employed to provide positive stiffness. As a result, as the weight of the driver varies, the dynamic stiffness of the ASVIS can be easily adjusted and controlled. Next, the effects of the dimension parameters on the nonlinear force and nonlinear stiffness of ASVIS were analyzed. A design process for the ASVIS is provided based on the analytical results in order to achieve high static–low dynamic stiffness. Finally, numerical simulations were performed to evaluate the effectiveness of the ASVIS. The results obtained in this paper show that the values of the seat displacement of the ASVIS with NSS were reduced by 77.16% in comparison with those obtained with the traditional air spring isolator without NSS, which indicates that the design of the ASVIS isolator with NSS allows the effective isolation of vibrations in the low-frequency region.

scholarly journals A Novel Sensor Prototype with Enhanced and Adaptive Sensitivity Based on Negative Stiffness Mechanism

Sensors ◽  
2020 ◽  
Vol 20 (16) ◽  
pp. 4644
Author(s):  
Lijun Liu ◽  
Yongzhong Nie ◽  
Ying Lei
Keyword(s):  
Low Frequency ◽  
High Sensitivity ◽  
Negative Stiffness ◽  
Micro Electro Mechanical Systems ◽  
Enhanced Sensitivity ◽  
Landslide Hazards ◽  
Negative Stiffness Mechanism ◽  
Low Sensitivity ◽  
Electric Filed ◽  
Design And Manufacture

Loess–mudstone/soil-rock interfacial landslide is one of the prominent landslide hazards that occurs in soil rock contacting zones. It is necessary to develop sensors with high sensitivity to weak and low frequency vibrations for the early warning of such interfacial landslides. In this paper, a novel monitoring sensor prototype with enhanced and adaptive sensitivity is developed for this purpose. The novelty of the sensitive sensor is based on the variable capacitances and negative stiffness mechanism due to the electric filed forces on the vibrating plate. Owing to the feedback control of adjustable electrostatic field by an embedded micro controller, the sensor has adaptive amplification characteristics with high sensitivity to weak and low frequency input and low sensitivity to high input. The design and manufacture of the proposed sensor prototype by Micro-Electro-Mechanical Systems (MEMS) with proper packaging are introduced. Post-signal processing is also presented. Some preliminary testing of the prototype and experimental monitoring of sand interfacial slide which mimics soil–rock interfacial landslide were performed to demonstrate the performance of the developed sensor prototype with adaptive amplification and enhanced sensitivity.

Non-resonant response of the novel airborne photoelectric quasi-zero stiffness platform with friction damping

2020 ◽  
Vol 64 (1-4) ◽  
pp. 315-324
Author(s):  
Guangxu Dong ◽  
Chicheng Ma ◽  
Feng Zhang ◽  
Yajun Luo ◽  
Chuanxing Bi
Keyword(s):  
Current Model ◽  
Excitation Frequency ◽  
Low Frequency ◽  
Harmonic Balance Method ◽  
Negative Stiffness ◽  
The Novel ◽  
Friction Damping ◽  
Improve Measurement ◽  
Photoelectric System ◽  
Isolation Performance

To suppress the low frequency vibrations of airborne photoelectric system and improve measurement accuracy, a novel passive airborne photoelectric quasi-zero stiffness platform (APQZSP), which is composed of upper/bottom planes, anti-shaking structure and six quasi-zero stiffness (QZS) legs, is designed. The QZS leg is constructed by connecting the folded beam spring with magnetic negative stiffness spring (MNSS) in parallel. According to current model, the magnetic force and negative stiffness of MNSS are derived. As the friction damping is introduced with anti-shaking structure, the isolation performance of the platform under friction damping is investigated based on harmonic balance method. Then the effect of damping and excitation on the isolation performance is analyzed. The results indicate that with the QZS technology, the resonant frequency of the platform is reduced and the low frequency vibrations can be effectively isolated with APQZSP. Moreover, the friction damping can maintain the displacement transmissibility at unity as long as the excitation frequency is lower than the break-loose frequency, and then the resonance can be avoided.

Subharmonic-Response Computation and Stability Analysis for a Nonlinear Oscillator Using a Split-Frequency Harmonic Balance Method

2006 ◽  
Vol 1 (3) ◽  
pp. 221-229 ◽  
Author(s):  
J. F. Dunne
Keyword(s):  
Stability Analysis ◽  
High Frequency ◽  
Harmonic Balance ◽  
Low Frequency ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Equation Error ◽  
Subharmonic Response ◽  
Split Frequency ◽  
Frequency Harmonic

A split-frequency harmonic balance method (SF-HBM) is developed to obtain subharmonic responses of a nonlinear single-degree-of-freedom oscillator driven by periodic excitation. This method is capable of generating highly accurate periodic solutions involving a large number of solution harmonics. Responses at the excitation period, or corresponding multiples (such as period 2 and period 3), can be readily obtained with this method, either in isolation or as combinations. To achieve this, the oscillator equation error is first expressed in terms of two Mickens functions, where the assumed Fourier series solution is split into two groups, nominally associated with low-frequency or high-frequency harmonics. The number of low-frequency harmonics remains small compared to the number of high-frequency harmonics. By exploiting a convergence property of the equation-error functions, accurate low-frequency harmonics can be obtained in a new iterative scheme using a conventional harmonic balance method, in a separate step from obtaining the high-frequency harmonics. The algebraic equations (needed in the HBM part of the method) are generated wholly numerically via a fast Fourier transform, using a discrete-time formulation to include inexpansible nonlinearities. A nonlinear forced-response stability analysis is adapted for use with solutions obtained with this SF-HBM. Period-3 subharmonic responses are obtained for an oscillator with power-law nonlinear stiffness. The paper shows that for this type of oscillator, two qualitatively different period-3 subharmonic response branches can be obtained across a broad frequency range. Stability analysis reveals, however, that for an increasingly stiff model, neither of these subharmonic branches are stable.

The design of negative stiffness spring for precision vibration isolation using axially magnetized permanent magnet rings

2019 ◽  
Vol 25 (19-20) ◽  
pp. 2667-2677 ◽  
Author(s):  
Zhenhua Zhou ◽  
Shuhan Chen ◽  
Dun Xia ◽  
Jianjun He ◽  
Peng Zhang
Keyword(s):  
Vibration Isolation ◽  
Dynamic Stiffness ◽  
Low Frequency ◽  
Design Procedure ◽  
Air Gap ◽  
Negative Stiffness ◽  
Linear Component ◽  
Vibration Isolator ◽  
Stiffness Characteristic ◽  
Isolation Performance

A negative stiffness element is always employed to generate high-static–low-dynamic stiffness characteristic of the vibration isolator, reduce the resonance frequency of the isolator, and improve the vibration isolation performance under low and ultra-low frequency excitation. In this paper, a new compact negative stiffness permanent magnetic spring (NSPMS) that is composed of two axial-magnetized permanent magnetic rings is proposed. An analytical expression of magnetic negative stiffness of the NSPMS is deduced by using the Coulombian model. After analyzing the effect of air-gap width, air-gap position, height difference between the inner ring and outer ring on the negative stiffness characteristic, a design procedure is proposed to realize the negative stiffness characteristic with a global minimum linear component and uniformity stiffness near the equilibrium position. Finally, an experimental prototype is developed to validate the effectiveness of the NSPMS. The experimental results show that combining a vibration isolator with the NSPMS in parallel can lower the natural frequency and improve the isolation performance of the isolator.

Analysis of Large-Amplitude Oscillations in Triple-Well Non-Natural Systems

2019 ◽  
Vol 14 (9) ◽  
Author(s):  
S. K. Lai ◽  
X. Yang ◽  
F. B. Gao
Keyword(s):  
Large Amplitude ◽  
Harmonic Balance ◽  
Structural Engineering ◽  
Equilibrium Points ◽  
Harmonic Balance Method ◽  
Integral Form ◽  
Homoclinic Orbits ◽  
Algebraic Equations ◽  
Restoring Force ◽  
Linear Algebraic Equations

In this paper, the large-amplitude oscillation of a triple-well non-natural system, covering both qualitative and quantitative analysis, is investigated. The nonlinear system is governed by a quadratic velocity term and an odd-parity restoring force having cubic and quintic nonlinearities. Many mathematical models in mechanical and structural engineering applications can give rise to this nonlinear problem. In terms of qualitative analysis, the equilibrium points and its trajectories due to the change of the governing parameters are studied. It is interesting that there exist heteroclinic and homoclinic orbits under different equilibrium states. By adjusting the parameter values, the dynamic behavior of this conservative system is shifted accordingly. As exact solutions for this problem expressed in terms of an integral form must be solved numerically, an analytical approximation method can be used to construct accurate solutions to the oscillation around the stable equilibrium points of this system. This method is based on the harmonic balance method incorporated with Newton's method, in which a series of linear algebraic equations can be derived to replace coupled and complicated nonlinear algebraic equations. According to this harmonic balance-based approach, only the use of Fourier series expansions of known functions is required. Accurate analytical approximate solutions can be derived using lower order harmonic balance procedures. The proposed analytical method can offer good agreement with the corresponding numerical results for the whole range of oscillation amplitudes.

scholarly journals Design and Characteristics Analysis of a Nonlinear Isolator Using a Curved-Mount-Spring-Roller Mechanism as Negative Stiffness Element

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Han Junshu ◽  
Meng Lingshuai ◽  
Sun Jinggong
Keyword(s):  
Damping Ratio ◽  
Harmonic Balance Method ◽  
Excitation Amplitude ◽  
Negative Stiffness ◽  
Response Curves ◽  
Restoring Force ◽  
Characteristics Analysis ◽  
Stiffness Softening ◽  
Isolation Performance ◽  
Cubic Stiffness

The characteristics of a passive nonlinear isolator are developed by combining a curved-mount-spring-roller mechanism as a negative stiffness corrector in parallel with a vertical linear spring. The static characteristics of the isolator are presented, and the configurative parameters are optimized to achieve a wider displacement range at the equilibrium position where the isolator has a low stiffness and the stiffness changes slightly. The restoring force of the isolator is approximated using a Taylor expansion to a cubic stiffness. Considering the overload and underload conditions, a dynamic equation is established as a Helmholtz-Duffing equation, and the resonance response of the nonlinear system is determined by employing the harmonic balance method (HBM). The frequency response curves (FRCs) are obtained for displacement excitations. The absolute displacement and acceleration transmissibility are defined and investigated to evaluate the performance of the nonlinear isolator, and they are compared with an equivalent linear isolator that can support the same mass with the same static deflection as the proposed isolator. The effects of the amplitude of the excitation, the offset displacement, and the damping ratio on the dynamic characteristics and the transmissibility performance are considered, and experiments are carried out to verify the above analysis. The results show that the overload and underload system can outperform the counterparts with the linear stiffness, softening stiffness, softening-hardening stiffness, and hardening stiffness with the magnitude of the excitation amplitude, and that its isolation performance is generally better than that of a linear system. The transmissibility, response, and resonance frequency of the system are affected by the excitation amplitude, offset displacement, cubic stiffness, and damping ratio. To obtain a better isolation performance, an appropriate mass, not-too-large amplitude, and larger damper are necessary for the proposed isolator.

scholarly journals Experimental Characterization of Friction in a Negative Stiffness Nonlinear Oscillator

Vibration ◽  
2020 ◽  
Vol 3 (2) ◽  
pp. 132-148
Author(s):  
Dario Anastasio ◽  
Stefano Marchesiello
Keyword(s):  
Dynamical Behavior ◽  
Harmonic Balance Method ◽  
Nonlinear Behavior ◽  
Nonlinear Damping ◽  
Negative Stiffness ◽  
Experimental Characterization ◽  
Restoring Force ◽  
Wide Range ◽  
Energy Dissipated

Nonlinear dissipative phenomena are common features of many dynamical systems and engineering applications, and their experimental characterization has always been a challenge among the research community. Within the wide range of nonlinear damping mechanisms, friction is surely one of the most common, and with a high impact on the dynamical behavior of structures. In this paper, the nonlinear identification of friction in a negative stiffness oscillator is pursued. The structure exhibits a strong nonlinear behavior, mainly due to its polynomial elastic restoring force with a negative stiffness region. This leads to an asymmetric double-well potential with two stable equilibrium positions, and the possibility of switching between them in a chaotic way. Friction plays a crucial role in this context, as it derives from the continuous sliding between the central guide and the moving mass. The system is driven through harmonic tests with several input amplitudes, in order to estimate the variations in the energy dissipated per cycle. The identification of the frictional behavior is then pursed by minimizing the errors between the experimental measurements and the model predictions, using the harmonic balance method in conjunction with a continuation technique on the forcing amplitudes.

Nonlinear Dynamics in Drilling and Boring Operations Assisted by Low Frequency Vibration

2007 ◽  
Author(s):  
George F. Moraru
Keyword(s):  
Nonlinear Dynamics ◽  
Harmonic Balance ◽  
Low Frequency ◽  
Harmonic Balance Method ◽  
Nonlinear Behavior ◽  
Drilling Process ◽  
Process Damping ◽  
Regenerative Effect ◽  
Low Frequency Vibration ◽  
Machining System

The nonlinear dynamics of the drilling process assisted by self-excited axial vibrations is analyzed. Models are developed and discussed, including regenerative effect and various phenomena contributing to the process damping in drilling and boring operations. Stability and bifurcation analysis, using several assumptions on the damping in the cutting process, are carried out using linear analysis tools or simulations. A simple predictive model based on a harmonic balance method is presented. Behavior charts are constructed using simulations. Hypothesis on the nature of the process damping and nonlinear behavior of the machining system are proved by experiments. A possible application to the gundrilling boring process in aircraft drilling and assembly process is presented.

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