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.

scholarly journals Displacement Transmissibility Characteristics of Harmonically Base Excited Damper Isolators with Mixed Viscous Damping

2013 ◽  
Vol 20 (5) ◽  
pp. 921-931 ◽  
Author(s):  
Xiaojuan Sun ◽  
Jianrun Zhang
Keyword(s):  
Damping Ratio ◽  
Harmonic Balance Method ◽  
Nonlinear Damping ◽  
Viscous Damping ◽  
Damping Force ◽  
Response Characteristics ◽  
Damping Characteristics ◽  
Linear Damping ◽  
Frequency Ratios ◽  
Good Agreement

The viscous damping force in the mixed form asfd(x˙)=c1x˙+c2|x˙|x˙can well describe damping characteristics of isolators and dampers in many cases. In this paper, performance characteristics of single-degree-of-freedom (SDOF) linear-stiffness isolators with mixed and piecewise mixed viscous damping are analytically examined under harmonic base excitation. Based on the first-order harmonic balance method (HBM), both relative and absolute displacement transmissibility expressions with the equivalent linear damping coefficient (ELDC) are given. And the analytical calculations show good agreement with the numerical results. Also, the influence of nonlinear damping on the response characteristics is investigated by comparing the transmissibility of linear and nonlinear systems. The resonant frequency always shifts to a lower value as the nonlinear damping component of the forcefd(x˙)=c1x˙+c2|x˙|x˙becomes stronger, and when the damping ratio in the corresponding linear model is relatively high, the relative transmissibility decreases at frequencies higher than the resonance frequency of the corresponding linear damping system and the absolute one increases for the frequency ratios above2. Finally, the displacement transmissibility of a nonlinear isolator with piecewise mixed viscous damping is discussed and the process shows research similarity with the non-piecewise case.

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.

Study on Design Method for Magneto-Rheological Fluid Damper Based on Squeeze Mode and Experimental Tests

2011 ◽  
Vol 199-200 ◽  
pp. 97-101 ◽  
Author(s):  
Chang Rong Liao ◽  
Li Juan Fu ◽  
Ying Yang
Keyword(s):  
Analytical Method ◽  
Vibration Isolation ◽  
Squeeze Flow ◽  
Damping Force ◽  
Mr Fluid ◽  
Isolation System ◽  
Technical Requirements ◽  
Fluid Damper ◽  
Magneto Rheological ◽  
Mr Fluid Damper

A Magneto-rheological(MR) fluid damper based on squeeze model is put forward. The squeeze flow differential equation is obtained. Navier slip condition is considered on two boundary surfaces and compatible condition is established. The radial velocity profile and the radial pressure distributions are derived respectively. The mathematical expression of damping force is devloped. In order to verify rationality of analytical method, MR fluid damper based on squeeze mode is designed and fabricated according to technical requirements of engine vibration isolation system. The experimental damping forces from MTS870 Electro-hydraulic Servo with sine wave excitation show that analytical method proposed in this paper is feasible and has the reference value to design MR fluid damper based on squeeze mode.

Experimental Investigation on Damping Characteristics in Pump-Sand Box-Isolation System

2014 ◽  
Vol 1051 ◽  
pp. 906-909
Author(s):  
Xiang Jun Kong ◽  
Chong Zheng Chen
Keyword(s):  
Particle Size ◽  
Vibration Isolation ◽  
Influence Factor ◽  
Damping Ratio ◽  
Particle Packing ◽  
Initial Displacement ◽  
Isolation System ◽  
Damping Characteristics ◽  
Sand Box ◽  
Particle Damping

Sand is used in the pump-sand box-isolation system, studying the initial displacement, particle size and packing rate how to affect the damping ratio by free vibration experiments. The result shows that the initial displacement of the system has less effect on damping ratio, the particle packing rate is a significant influence factor of damping ratio, selecting the appropriate particle packing rate can get the maximum damping ratio, reducing the particle size can increase the system damping ratio, but the damping ratio no longer obviously changes when the particle size of is less than 1.5mm. In general, the packing rate needs to be controlled at below 70% in metal spring or rubber isolator system. This result can provide the basis for the design of particle damping vibration isolation system.

scholarly journals Numerical Analysis on the Ground Vibration Isolation of Duxseal

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
M. Gao ◽  
S. P. Tian ◽  
R. He ◽  
Y. Wang ◽  
Q. S. Chen
Keyword(s):  
Vibration Isolation ◽  
Damping Ratio ◽  
Free Field ◽  
Three Dimensional ◽  
Ground Vibration ◽  
Vibration Source ◽  
Isolation System ◽  
Vertical Excitation ◽  
Thin Layer Method ◽  
Active Vibration

A new kind of vibration screening material, Duxseal, with a high damping ratio is proposed to be used as an active vibration barrier in the free field. To investigate the influence of width, thickness, and embedded depth of using Duxseal on vibration reduction, numerical studies are performed using a three-dimensional (3D) semianalytical boundary element method (BEM) combined with a thin-layer method (TLM). The isolation effectiveness of Duxseal in ground vibration is also compared with the traditional wave impeding block (WIB). The numerical results show that Duxseal performed exceedingly well in screening ground vibrations in the free field. The effectiveness of the vibration isolation increases with the increase in the width, thickness, and embedded depth of the Duxseal material, within a certain range, under harmonic vertical excitation. In addition, Duxseal is much more effective for isolating ground vibration than the traditional WIB. The performance of Duxseal in isolating ground vibration is relatively stable along the distance away from the vibration source, while the amplitude attenuation ratio bounces upward when the distance away from the vibration source increases for the WIB isolation system.

Modeling and Control of Magnetorheological Dampers for Vibration Isolation

2003 ◽  
Author(s):  
A. Narimani ◽  
M. F. Golnaraghi
Keyword(s):  
Vibration Isolation ◽  
Mr Damper ◽  
Damping Force ◽  
Isolation System ◽  
Modeling And Control ◽  
Quarter Car Model ◽  
Car Model ◽  
Quarter Car ◽  
Set Up ◽  
And Control

Semi-active isolators offer significant improvement in performance over passive isolators. These systems benefit from the advantages of active systems with the reliability of the passive systems. In this work we study a vibration isolation system with a magnetorheological (MR) damper. The experimental investigation of the mechanical properties of a commercially available linear MR damper (RD-1005-3) was conducted next. The mathematical Bouc-Wen model was adopted to predict the performance of MR damper. In addition, a modified Bingham model has been developed to characterize the damper behavior more accurately and efficiently. The measured hysteresis characteristics of field-dependent damping forces are compared with the simulation results from the described mathematical models. The accuracy of a damping-force controller using the proposed method is also demonstrated experimentally. Finally, a scaled quarter car model is set up to study the performance of the control strategy. The experimental results show that with the semi-active control the vibration of the quarter car model is well controlled.

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.

Force transmissibility of floating raft systems with quasi-zero-stiffness isolators

2017 ◽  
Vol 24 (16) ◽  
pp. 3608-3616 ◽  
Author(s):  
Li Yingli ◽  
Xu Daolin
Keyword(s):  
Vibration Isolation ◽  
Damping Ratio ◽  
Low Frequency ◽  
Frequency Region ◽  
Mass Ratio ◽  
Isolation System ◽  
Floating Raft ◽  
Highly Nonlinear ◽  
Vibration Attenuation ◽  
Force Transmissibility

In view of the excellent performance of a single quasi-zero-stiffness (QZS) device in vibration attenuation, this paper presents a study on a vibration isolation floating raft system constructed with a double-layer QZS mechanism. A QZS device is a typical nonlinear isolator, hence the floating raft system is a coupled highly nonlinear isolation system. To understand the behaviors and its performance in vibration attenuation, an analytical approach is developed to describe the characteristics including the mathematical relationship between amplitude–frequency, force transmissibility, and the effects of the mass ratio and damping ratios on attenuation performance. The outcomes show that the two-degree-of-freedom QZS–QZS system is superior for vibration isolation when compared to the traditional linear system and the two other types of QZS systems. The effective vibration isolation frequency region of the QZS–QZS system is expanded to the low-frequency region by 72%. The QZS system is sensitive to the damping ratio, which decreases the resonance peak significantly. The mass ratio is a crucial design parameter in low-frequency vibration isolation design.

A Bidirectional-Controllable Magnetorheological Energy Absorber for Shock and Vibration Isolation Systems

2012 ◽  
Author(s):  
Xian-Xu Bai ◽  
Norman M. Wereley ◽  
Wei Hu ◽  
Dai-Hua Wang
Keyword(s):  
Mechanical Model ◽  
Vibration Isolation ◽  
Dynamic Force ◽  
Damping Force ◽  
Isolation System ◽  
Isolation Systems ◽  
Force Range ◽  
Fail Safe ◽  
Safe Performance ◽  
Vibration Isolation Performance

Semi-active shock and vibration isolation systems using magnetorheological energy absorbers (MREAs) require minimization of the field-off damping force at high speed. This is because the viscous damping force for high shaft speed become excessive. This implies that the controllable dynamic force range, defined as the ratio of the field-on damping force to the field-off damping force, is dramatically reduced. In addition, fail-safe MREA performance, if power were to be lost, is of great importance to shock and vibration isolation systems. A key design goal is to minimize field-off damping force while maximizing MREA dynamic force, while maintaining fail-safe performance. This study presents the principle of a bidirectional-controllable MREA that can produce large damping force and dynamic force range, as well as excellent fail-safe performance. The bidirectional-controllable MREA is configured and its hydro-mechanical model is theoretically constructed. From the hydro-mechanical model, the mathematical model for the MREA is established using a Bingham-plastic nonlinear fluid model. The characteristics of the MREA are theoretically evaluated and compared with those of a conventional flow-mode MREA with an identical volume. In order to investigate the feasibility and capability of the bidirectional-controllable MREA in the context of the semi-active shock and vibration isolation systems, a mechanical model of a single-degree-of-freedom (SDOF) isolation system using a bidirectional-controllable MREA is constructed and the governing equation for the SDOF isolation system is derived. A skyhook control algorithm is utilized to improve the shock and vibration isolation performance of the isolation systems. Simulated vibration isolation performance using bidirectional-controllable and conventional MREAs under shock loads due to vertical impulses (the initial velocity is as high as 10 m/s), and sinusoidal vibrations, are evaluated, compared, and analyzed.

An efficient method for estimating the damping ratio of a vibration isolation system

2020 ◽  
Vol 21 (1) ◽  
pp. 103 ◽  
Author(s):  
Qiang Yu ◽  
Dengfeng Xu ◽  
Yu Zhu ◽  
Gaofeng Guan
Keyword(s):  
Efficient Method ◽  
Vibration Isolation ◽  
Damping Ratio ◽  
Resonance Peak ◽  
Estimation Methods ◽  
Mathematical Relationship ◽  
Isolation System ◽  
Vibration Isolation System ◽  
At Resonance ◽  
Practical Engineering

As the damping ratio determines the response of a vibration isolation system at resonance, it is very necessary to estimate the damping ratio quickly and economically for an evaluation of the effectiveness to adjust the damping in practical engineering applications. An efficient method named the “ζ-Tr” method with the characteristics of simple operation and a high accuracy is introduced to estimate the damping ratio in this paper. According to the transmissibility curve, the specific mathematical relationship in which the value of the resonance peak corresponds to the value of the damping ratio is analysed theoretically. In this case, the recognition of the resonance peak can be used to directly estimate the damping ratio without an approximation or simplification. The “ζ-Tr” method is faster, more accurate and less costly than other estimation methods. Finally, the correctness of the “ζ-Tr” method is verified by a simulation and an experiment.

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