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.

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 Design, Experiment, and Improvement of a Quasi-Zero-Stiffness Vibration Isolation System

2020 ◽  
Vol 10 (7) ◽  
pp. 2273 ◽  
Author(s):  
Shuai Wang ◽  
Wenpen Xin ◽  
Yinghao Ning ◽  
Bing Li ◽  
Ying Hu
Keyword(s):  
Vibration Isolation ◽  
Damping Ratio ◽  
Excitation Amplitude ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Linear Spring ◽  
Isolation Effects ◽  
Magnetic Rings ◽  
The Relationship ◽  
Force Displacement

This paper proposes a new kind of quasi-zero-stiffness (QZS) isolation system that has the property of low-dynamic but high-static stiffness. The negative stiffness was produced using two magnetic rings, the magnetization of which is axial. First, the force–displacement characteristic of the two coupled magnetic rings was developed and the relationship between the parameters of the magnetic rings and the stiffness of the system was investigated. Then, the dynamic response of the QZS was analyzed. The force transmissibility of the system was calculated and the effects of the damping ratio and excitation amplitude on the isolation performance were investigated. The prototype of the QZS system was developed to verify the isolation effects of the system based on a comparison with a linear vibration isolation platform. Lastly, the improvement of the QZS system was conducted based on changing the heights of the ring magnets and designing a proper non-linear spring. The analysis shows the QZS system after improvement shows better isolation effects than that of the non-improved system.

scholarly journals H∞ active control of frequency-varying disturbances in a main engine on the floating raft vibration isolation system

2017 ◽  
Vol 37 (2) ◽  
pp. 199-215 ◽  
Author(s):  
Chunsheng Song ◽  
Yao Xiao ◽  
Chuanchao Yu ◽  
Wei Xu ◽  
Jinguang Zhang
Keyword(s):  
Numerical Simulation ◽  
Vibration Isolation ◽  
Control Method ◽  
Mimo System ◽  
Single Frequency ◽  
Isolation System ◽  
Floating Raft ◽  
Power Machinery ◽  
Simulation Results ◽  
Dominant Frequencies

Reducing the vibration of marine power machinery can improve warships' capabilities of concealment and reconnaissance. Being one of the most effective means to reduce mechanical vibrations, the active vibration control technology can overcome the poor effect in low frequency of traditional passive vibration isolation. As the vibrations arising from operation of marine power machinery are actually the frequency-varying disturbances, the H∞ control method is adopted to suppress frequency-varying disturbances. The H∞ control method can solve the stability problems caused by the uncertainty of the model and reshape the frequency response function of the closed loop system. Two-input two-output continuous transfer function models were identified by using the system identification method and are validated in frequency domain of which all values of best fit exceeds 89%. The method of selecting the weighting functions on the mixed sensitivity problem is studied. Besides, the H∞ controller is designed for a multiple input multiple output (MIMO) system to suppress the single-frequency-varying disturbance. The numerical simulation results show that the magnitudes of the error signals are reduced by more than 50%, and the amplitudes of the dominant frequencies are attenuated by more than 10 dB. Finally, the single excitation source dual-channel control experiments are conducted on the floating raft isolation system. The experiment results reveal that the root mean square values of the error signals under control have fallen by more 74% than that without control, and the amplitudes of the error signals in the dominant frequencies are attenuated above 13 dB. The experiment results and the numerical simulation results are basically in line, indicating a good vibration isolation effect.

Study on the Application of Magnetorheological Damper in Chaotic Vibration Control

2007 ◽  
Author(s):  
Shuyong Liu ◽  
Shijian Zhu ◽  
Xiang Yu ◽  
Jingjing Wang
Keyword(s):  
Nonlinear Vibration ◽  
Vibration Isolation ◽  
Harmonic Excitation ◽  
Magnetorheological Damper ◽  
Single Frequency ◽  
Control Line ◽  
Chaotic State ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Chaotic Vibration

The nonlinear vibration isolation system works in a chaotic state when its parameters are in chaotic range. Under single frequency harmonic excitation, the output of this system is broad spectrum response, and thus the chaotic vibration isolation system is applied to control line spectra of the warship water-born noise. The passive vibration isolation system, however, cannot change the parameters when the work condition of isolated equipments is varied, and it is difficult to ensure that the system is in chaotic state. In order to adjust the system parameter on line, the magnetorheological damper can be used to control chaos in nonlinear vibration isolation systems. The system model with magnetorheological damper is presented in this paper, and then the simulation is carried out. Results show that the magnetorheological damper can be used to reduce the amplitude of the chaotic vibration when voltage is applied to the MR. When the voltage is increased, the system can exhibit period behaviour. This is a new method for chaos control.

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.

scholarly journals Research and Analysis of Quasi-Zero-Stiffness Isolator with Geometric Nonlinear Damping

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Qingguo Meng ◽  
Xuefeng Yang ◽  
Wei Li ◽  
En Lu ◽  
Lianchao Sheng
Keyword(s):  
Vibration Isolation ◽  
Low Frequency ◽  
Harmonic Balance Method ◽  
Nonlinear Damping ◽  
Vibration Isolator ◽  
Rehabilitation Robots ◽  
Geometric Nonlinear ◽  
Low Frequency Vibration ◽  
Linear Spring ◽  
The Relationship

This paper presents a novel quasi-zero-stiffness (QZS) isolator designed by combining a tension spring with a vertical linear spring. In order to improve the performance of low-frequency vibration isolation, geometric nonlinear damping is proposed and applied to a quasi-zero-stiffness (QZS) vibration isolator. Through the study of static characteristics first, the relationship between force displacement and stiffness displacement of the vibration isolation mechanism is established; it is concluded that the parameters of the mechanism have the characteristics of quasi-zero stiffness at the equilibrium position. The solutions of the QZS system are obtained based on the harmonic balance method (HBM). Then, the force transmissibility of the QZS vibration isolator is analyzed. And the results indicate that increasing the nonlinear damping can effectively suppress the transmissibility compared with the nonlinear damping system. Finally, this system is innovative for low-frequency vibration isolation of rehabilitation robots and other applications.

Vibration Isolation With Nonlinear Damping

1971 ◽  
Vol 93 (2) ◽  
pp. 627-635 ◽  
Author(s):  
Jerome E. Ruzicka ◽  
Thomas F. Derby
Keyword(s):  
Relative Velocity ◽  
Vibration Isolation ◽  
Damping Ratio ◽  
Nonlinear Damping ◽  
System Response ◽  
Viscous Damping ◽  
Damping Force ◽  
Isolation System ◽  
Equivalent Viscous Damping ◽  
Arbitrary Power

This paper discusses the performance characteristics of single degree-of-freedom vibration isolation systems in which the isolator damping force is proportional to the relative velocity across the isolator raised to an arbitrary power. The concept of equivalent viscous damping is employed to develop a general equation for the equivalent viscous damping ratio which is used to determine approximate isolation system response parameters. A range of isolator damping nonlinearity is studied by varying the relative velocity exponent between 0.5 and 5 for a fixed value of damping. Detailed results for parametric variations in damping are presented for specific values of the relative velocity exponent that correspond to Coulomb, viscous, quadratic, and cubic damping mechanisms.

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