The Effect of Stiffness and Loading Deviations in a Nonlinear Isolator Having Quasi Zero Stiffness and Geometrically Nonlinear Damping

2017 ◽  
Author(s):  
Ata Donmez ◽  
Ender Cigeroglu ◽  
Gokhan O. Ozgen
Keyword(s):  
Vibration Isolation ◽  
Dynamic Stiffness ◽  
Nonlinear Differential Equations ◽  
Harmonic Balance Method ◽  
Nonlinear Damping ◽  
Geometrically Nonlinear ◽  
Algebraic Equations ◽  
Isolation System ◽  
Highly Nonlinear ◽  
Isolation Performance

Static deflections due to static loadings limit the isolation performance of linear vibration isolation systems. Therefore, quasi-zero stiffness (QZS) mechanisms, i.e. nonlinear isolators with high static and low dynamic stiffness characteristic, are used to decrease the natural frequency of the isolation structure and improve the isolation performance of the system while having the same loading capacity. However, the resulting system is highly nonlinear and unstable solutions may as well occur. Although increasing the amount of linear viscous damping in the system reduces the nonlinearity, it has adverse effect on the isolation region. Geometrically nonlinear damping is effective when the response of the isolation system increases; hence, isolation region is unaffected. Combination of position depended nonlinear damping and QZS mechanism eliminates highly input depended response of QZS mechanism. In this study, a single degree of freedom system with a nonlinear isolator having QZS mechanism and geometrically nonlinear damping is considered. The nonlinear differential equations of motion of the isolation system are converted into a set of nonlinear algebraic equations by using harmonic balance method, which are solved by using Newton’s method with arc-length continuation. Several case studies are performed and the effect of stiffness and loading deviations on the isolation performance is studied.

scholarly journals High-Efficiency Vibration Isolation for a Three-Phase Power Transformer by a Quasi-Zero-Stiffness Isolator

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Hao Cao ◽  
Yaopeng Chang ◽  
Jiaxi Zhou ◽  
Xuhui Zhao ◽  
Ling Lu ◽  
...  
Keyword(s):  
Vibration Isolation ◽  
High Efficiency ◽  
Power Transformer ◽  
Dynamic Stiffness ◽  
Harmonic Balance Method ◽  
Isolation System ◽  
Three Phase ◽  
Engineering Practices ◽  
Vibration Isolation Performance ◽  
Isolation Performance

The vibrations generated by a three-phase power transformer reduce the comfort of residents and the service life of surrounding equipment. To resolve this tough issue, a quasi-zero-stiffness (QZS) isolator for the transformer is proposed. This paper is devoted to developing a QZS isolator in a simple way for engineering practices. The vertical springs are used to support the heavy weight of the transformer, while the oblique springs are employed to fulfill negative stiffness to neutralize the positive stiffness of the vertical spring. Hence, a combination of the vertical and oblique spring can yield high static but low dynamic stiffness, and the vibration isolation efficiency can be improved substantially. The dynamic analysis for the QZS vibration isolation system is conducted by the harmonic balance method, and the vibration isolation performance is estimated. Finally, the prototype of the QZS isolator is manufactured, and then the vibration isolation performance is tested comparing with the linear isolator under real power loading conditions. The experimental results show that the QZS isolator prominently outperforms the existing linear isolator. This is the first time to devise a QZS isolator for three-phase power transformers with heavy payloads in engineering practices.

Sources and Propagation of Nonlinearity in a Vibration Isolator With Geometrically Nonlinear Damping

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
J. C. Carranza ◽  
M. J. Brennan ◽  
B. Tang
Keyword(s):  
Vibration Isolation ◽  
Nonlinear Behavior ◽  
High Amplitude ◽  
Nonlinear Damping ◽  
Single Frequency ◽  
Geometrically Nonlinear ◽  
Harmonic Force ◽  
Isolation System ◽  
Linear Spring ◽  
Harmonic Components

In this paper, the behavior of a single degree-of-freedom (SDOF) passive vibration isolation system with geometrically nonlinear damping is investigated, and its displacement and force transmissibilities are compared with that of a linear system. The nonlinear system is composed of a linear spring and a linear viscous damper which are connected to a mass so that the damper is perpendicular to the spring. The system is excited by a harmonic force applied to the mass or a displacement of the base in the direction of the spring. The transmissibilities of the nonlinear isolation system are calculated using analytical expressions for small amplitudes of excitation and by using numerical simulations for high amplitude of excitation. When excited with a harmonic force, the forces transmitted through the spring and the damper are analyzed separately by decomposing the forces in terms of their harmonics. This enables the effects of these elements to be studied and to determine how they contribute individually to the nonlinear behavior of the system as a whole. For single frequency excitation, it is shown that the nonlinear damper causes distortion of the velocity of the suspended mass by generating higher harmonic components, and this combines with the time-varying nature of the damping in the system to severely distort the force transmitted though the damper. The distortion of the force transmitted through the spring is much smaller than that through the damper.

scholarly journals An Asymmetric Quasi-zero Stiffness Vibration Isolator with Long Stroke and Large Bearing Capacity

2021 ◽  
Author(s):  
Xinghua Zhou ◽  
Dingxuan Zhao ◽  
Xiao Sun ◽  
Xiao Yang ◽  
Jianhai Zhang ◽  
...  
Keyword(s):  
Bearing Capacity ◽  
Vibration Isolation ◽  
Geometrical Nonlinearity ◽  
Harmonic Balance Method ◽  
Nonlinear Damping ◽  
Vibration Isolator ◽  
Plate Spring ◽  
Supporting Force ◽  
Vibration Isolation Performance ◽  
Isolation Performance

Abstract A novel passive asymmetric quasi-zero stiffness vibration isolator (AQZS-VI) comprising two linear springs acting in parallel with one negative stiffness element (NSE) is proposed, of which the NSE is mainly constructed by the combination of cantilever plate spring and L-shaped lever (CPS-LSL). The static model of the isolator is deduced considering the geometrical nonlinearity of the NSE and the bending deformation of plate spring. The nonlinear stiffness properties of the CPS-LSL and the AQZS-VI, as well as the nonlinear damping properties of the AQZS-VI are discussed. The absolute displacement transmissibility of the AQZS-VI under base displacement excitation is obtained using Harmonic Balance Method, and the effects of different excitation amplitudes and damping factors on the vibration isolation performance are analyzed. Better than other quasi-zero stiffness vibration isolators (QZS-VI) whose NSEs do not provide supporting force at zero stiffness point, the NSE of the AQZS-VI provides more supporting force than the parallel connected linear springs, which is very beneficial for improving the bearing capacity of the isolator. Compared with a typical symmetric QZS-VI with same damping property, the AQZS-VI has longer stroke with low stiffness and lower peak value of displacement transmissibility. The prototype experiments indicate that the AQZS-VI outperforms the linear counterpart with much smaller starting frequency of vibration isolation and lower displacement transmissibility. The proposed AQZS-VI has great potential for applying in various engineering practices with superior vibration isolation performance.

Displacement transmissibility evaluation of vibration isolation system employing nonlinear-damping and nonlinear-stiffness elements

2017 ◽  
Vol 24 (18) ◽  
pp. 4247-4259 ◽  
Author(s):  
S M Mahdi Mofidian ◽  
Hamzeh Bardaweel
Keyword(s):  
Numerical Simulation ◽  
Vibration Isolation ◽  
Harmonic Balance Method ◽  
Nonlinear Damping ◽  
Resonant Peak ◽  
Engineering Practice ◽  
Nonlinear Stiffness ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Isolation Systems

Undesired oscillations commonly encountered in engineering practice can be harmful to structures and machinery. Vibration isolation systems are used to attenuate undesired oscillations. Recently, there has been growing interest in nonlinear approaches towards vibration isolation systems design. This work is focused on investigating the effect of nonlinear cubic viscous damping in a vibration isolation system consisting of a magnetic spring with a positive nonlinear stiffness, and a mechanical oblique spring with geometric nonlinear negative stiffness. Dynamic model of the vibration isolation system is obtained and the harmonic balance method (HBM) is used to solve the governing dynamic equation. Additionally, fourth order Runge–Kutta numerical simulation is used to obtain displacement transmissibility of the system under investigation. Results obtained from numerical simulation are in good agreement with those obtained using HBM. Results show that introducing nonlinear damping improves the performance of the vibration isolation system. Nonlinear damping purposefully introduced into the described vibration isolation system appears to eliminate undesired frequency jump phenomena traditionally encountered in quasi-zero-stiffness vibration isolation systems. Compared to its rival linear vibration isolation system, the described nonlinear system transmits less vibrations around resonant peak. At lower frequencies, both nonlinear and linear isolation systems show comparable transmissibility characteristics.

Investigation of Damping Nonlinearity in Duffing-Type Vibration Isolation System With Geometric and Magnetic Stiffness Nonlinearities

2017 ◽  
Author(s):  
S. M. Mahdi Mofidian ◽  
Hamzeh Bardaweel
Keyword(s):  
Resonant Frequency ◽  
Dynamic Behavior ◽  
Vibration Isolation ◽  
Harmonic Balance Method ◽  
Nonlinear Damping ◽  
Resonant Peak ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Magnetic Stiffness ◽  
Sinusoidal Input

In this work, the effect of nonlinear damping in presence of geometric nonlinearities and magnetic stiffness nonlinearities in vibration isolation system is investigated. The dynamic behavior of the isolation system design is modeled. Harmonic Balance Method (HBM) is used to investigate the dynamic behavior of the vibration isolation system in response to sinusoidal input waveform. Results obtained using the HBM are compared to the results from numerical simulation attained using Runge-kutta method. Results show that introducing nonlinear viscous damping into the vibration isolation system suppresses frequency jump phenomena observed in Duffing-type vibration isolation systems. Additionally, results show that nonlinear damping can suppress transmissibility around resonant peak. For frequencies lower than resonant frequency the effect of nonlinear damping is minimum compared to a linear isolation system. Beyond resonant frequency higher nonlinear damping may slightly alter transmissibility of the isolation system.

An hourglass-type electromagnetic isolator with negative resistance electromagnetic shunt circuit

2020 ◽  
Vol 64 (1-4) ◽  
pp. 549-556
Author(s):  
Yajun Luo ◽  
Linwei Ji ◽  
Yahong Zhang ◽  
Minglong Xu ◽  
Xinong Zhang
Keyword(s):  
Vibration Isolation ◽  
Electromechanical Coupling ◽  
Coupling Effect ◽  
Negative Resistance ◽  
Isolation System ◽  
Amplitude Vibration ◽  
Vibration Responses ◽  
The Stability ◽  
Isolation Performance ◽  
Shunt Circuit

The present work proposed an hourglass-type electromagnetic isolator with negative resistance (NR) shunt circuit to achieve the effective suppression of the micro-amplitude vibration response in various advanced instruments and equipment. By innovatively design of combining the displacement amplifier and the NR electromagnetic shunt circuit, the current new type of vibration isolator not only can effectively solve the problem of micro-amplitude vibration control, but also has significant electromechanical coupling effect, to obtain excellent vibration isolation performance. The design of the isolator and motion relationship is presented firstly. The electromechanical coupling dynamic model of the isolator is also given. Moreover, the optimal design of the NR electromagnetic shunt circuit and the stability analysis of the vibration isolation system are carried out. Finally, the simulation results about the transfer function and vibration responses demonstrated that the isolator has a significant isolation performance.

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 Analysis and design of the power law damping based on the nonlinear vessel isolation system

2018 ◽  
Vol 10 (12) ◽  
pp. 168781401881719 ◽  
Author(s):  
You Wang ◽  
Xinghua Zhu ◽  
Rong Zheng ◽  
Zhe Tang ◽  
Bingbing Chen
Keyword(s):  
Resonant Frequency ◽  
Working Conditions ◽  
Power Law ◽  
Nonlinear Damping ◽  
Frequency Region ◽  
Isolation System ◽  
Analysis And Design ◽  
Force Transmissibility ◽  
Isolation Systems ◽  
Isolation Performance

In this study, the applications of the cubic power law damping in vessel isolation systems are investigated. The isolation performance is assessed using the force transmissibility of the vessel isolation system, which is simplified as a multiple-degree-of-freedom system with two parallel freedoms. The force transmissibilities of different working conditions faced in practice are discussed by applying the cubic power law damping on different positions of the vessel isolation system. Numerical results indicate that by adding the cubic power law damping to an appropriate position, the isolation system can not only suppress the force transmissibility over the resonant frequency region but also keep the force transmissibility unaffected at the nonresonant frequency region. Moreover, the design of the nonlinear vessel isolation system is discussed by finding the optimal nonlinear damping of the isolation system.

The Research on Robust LQ Control Applied to Uncertain Vibration Isolation System

2010 ◽  
Vol 34-35 ◽  
pp. 1289-1293
Author(s):  
Qiang Hong Zeng ◽  
Qi Wei He ◽  
Jing Jun Lou
Keyword(s):  
Optimal Control ◽  
Transfer Function ◽  
Vibration Isolation ◽  
Multi Objective Optimization ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Robust Optimal Control ◽  
Result Show ◽  
Isolation Performance ◽  
Lq Control

Synthesized considering several performance target, robust optimal control was applied to uncertain double layer vibration isolation system then the transfer function was got between input disturbance and out performance. By analyzing the amplitude-frequency characteristics of transfer function, the result show that the robust LQ control can successfully improve the isolation performance of uncertain hybrid vibration isolation system, realize the multi-objective optimization.

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