Nonlinear Design of a Passive Vibration Isolator: Influence of Multi-Axial Stiffness

2019 ◽  
Author(s):  
Sudhir Kaul
Keyword(s):  
Dynamic Response ◽  
Dynamic Stiffness ◽  
Harmonic Balance Method ◽  
Axial Stiffness ◽  
Vibration Isolators ◽  
Trade Offs ◽  
Nonlinear Design ◽  
Integration Test ◽  
Voigt Model ◽  
Isolation Systems

Abstract Passive vibration isolators are widely used in multiple engineering applications to reduce resonance peaks or to mitigate transmissibility in the presence of internal or external sources of dynamic excitation. The design of a linear passive isolator involves multiple trade-offs. In the literature, different design configurations with nonlinearities have been investigated to limit some of these trade-offs. These include designs with quasi-zero stiffness (QZS) or high-static-low-dynamic stiffness (HSLDS) characteristics. This study investigates three viscoelastic models that incorporate stiffness nonlinearity along the non-isolating axes in order to exhibit more control over the dynamic response of the isolated system and possibly mitigate some of the design trade-offs. The dynamic response of these three models is compared to an existing HSLDS model in the literature. The three models investigated in this study are as follows: Kelvin-Voigt (or Voigt), Zener, and Generalized Maxwell (or Maxwell Ladder). These three models have been commonly used in the literature for vibration analysis of passive isolators. Two methods have been used for analysis, namely the Harmonic Balance Method (HBM) and explicit numerical integration. Test results from a previous study have been used for model characterization of all the models. It is observed that the modified Kelvin-Voigt model is analogous to the HSLDS model from the literature. For the isolator parameters used in this study, it is observed that the Kelvin-Voigt model with stiffness nonlinearity is able to exhibit characteristics similar to the HSLDS design, this includes the jump phenomenon as well as the hardening behavior. In general, all three models demonstrate that stiffness nonlinearity results in a reduction in peak transmissibility as well as an enhancement of the isolation bandwidth. The findings of this study could be useful in the design of passive isolation systems for products with significantly different multi-axial requirements with various design constraints.

Influence of Fractional Damping and Time Delay on Maxwell-Voigt Model for Vibration Isolation

2016 ◽  
Author(s):  
Sudhir Kaul
Keyword(s):  
Time Delay ◽  
Dynamic Characteristics ◽  
Vibration Isolation ◽  
Model Parameters ◽  
Fractional Damping ◽  
Vibration Isolators ◽  
Multiple Parameters ◽  
Realistic Representation ◽  
Voigt Model ◽  
Isolation Systems

Models of vibration isolators are very commonly used for the design and analysis of isolation systems. Accurate isolator modeling is critical for a successful prediction of the dynamic characteristics of isolated systems. Isolators exhibit a complex behavior that depends on multiple parameters such as frequency, displacement amplitude, temperature and loading conditions. Therefore, it is important to choose a model that is accurate while adequately representing the relationships with relevant parameters. Recent literature has indicated some inherent advantages of fractional derivatives that can be exploited in the modeling of elastomeric isolators. Furthermore, time delay of damping is also seen to provide a realistic representation of damping. This paper examines the Maxwell-Voigt model with fractional damping and a time delay. This model is compared with the conventional Maxwell-Voigt model (without time delay or fractional damping) and the Voigt model in order to comprehend the influence of fractional damping and time delay on dynamic characteristics. Multiple simulations are performed after identifying model parameters from the data collected for a passive elastomeric isolator. The analysis results are compared and it is observed that the Voigt model is highly sensitive to fractional damping as well as time delay.

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 Using Waveguides to Model the Dynamic Stiffness of Pre-Compressed Natural Rubber Vibration Isolators

Polymers ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 1703
Author(s):  
Michael Coja ◽  
Leif Kari
Keyword(s):  
Natural Rubber ◽  
Dynamic Stiffness ◽  
Low Frequency ◽  
Complex Problem ◽  
Wide Frequency Range ◽  
Vibration Isolators ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Frequency Magnitude ◽  
Good Agreement

A waveguide model for a pre-compressed cylindrical natural rubber vibration isolator is developed within a wide frequency range—20 to 2000 Hz—and for a wide pre-compression domain—from vanishing to the maximum in service, that is 20%. The problems of simultaneously modeling the pre-compression and frequency dependence are solved by applying a transformation of the pre-compressed isolator into a globally equivalent linearized, homogeneous, and isotropic form, thereby reducing the original, mathematically arduous, and complex problem into a vastly simpler assignment while using a straightforward waveguide approach to satisfy the boundary conditions by mode-matching. A fractional standard linear solid is applied as the visco-elastic natural rubber model while using a Mittag–Leffler function as the stress relaxation function. The dynamic stiffness is found to depend strongly on the frequency and pre-compression. The former is resulting in resonance phenomena such as peaks and troughs, while the latter exhibits a low-frequency magnitude stiffness increase in addition to peak and trough shifts with increased pre-compressions. Good agreement with nonlinear finite element results is obtained for the considered frequency and pre-compression range in contrast to the results of standard waveguide approaches.

Design of a Miniaturized Pneumatic Vibration Isolator With High-Static-Low-Dynamic Stiffness

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Yuhu Shan ◽  
Wenjiang Wu ◽  
Xuedong Chen
Keyword(s):  
Vibration Isolation ◽  
Dynamic Stiffness ◽  
Structure Design ◽  
Negative Stiffness ◽  
Vibration Isolator ◽  
Load Bearing Capacity ◽  
Compact Structure ◽  
Chamber Volume ◽  
Isolation Systems ◽  
Magnetic Rings

In the ultraprecision vibration isolation systems, it is desirable for the isolator to have a larger load bearing capacity and a broader isolation bandwidth simultaneously. Generally, pneumatic spring can bear large load and achieve relatively low natural frequency by enlarging its chamber volume. However, the oversized isolator is inconvenient to use and might cause instability. To reduce the size, a miniaturized pneumatic vibration isolator (MPVI) with high-static-low-dynamic stiffness (HSLDS) is developed in this paper. The volume of proposed isolator is minimized by a compact structure design that combines two magnetic rings in parallel with the pneumatic spring. The two magnetic rings are arranged in the repulsive configuration and can be mounted into the chamber to provide the negative stiffness. Then dynamic model of the developed MPVI is built and the isolation performances are analyzed. Finally, experiments on the isolator with and without the magnetic rings are conducted. The final experimental results are consistent with the dynamical model and verify the effectiveness of the developed vibration isolator.

scholarly journals Influence of the use of spring vibration isolators in the construction of track pavement for damping vibrations from the track

2018 ◽  
Vol 2018 (5) ◽  
pp. 1-9
Author(s):  
Ewelina Kwiatkowska ◽  
Wiesław Fiebig
Keyword(s):  
Noise Reduction ◽  
Vibration Isolation ◽  
New Technology ◽  
Track Structure ◽  
Vibration Isolators ◽  
Isolation Systems ◽  
Tuning Frequency ◽  
Mass Spring ◽  
Lower Frequencies

The paper presents tuned track bed vibration isolation systems used for the railway and tramway lines. The presented solution based on mass spring systems and is effective especially at lower frequencies. The tuning frequency of such systems is mostly in the range 5 to 8 Hz. With measures based on spring elements elaborated by GERB company the significant vibration and noise reduction coming from the railways and tramways can be achieved. This new technology in Poland can be used during the track structure modernization as well as in the new projects, in which the track bed vibration isolation is required.

scholarly journals Tailoring of Composite Links for Optimal Damped Elasto-Dynamic Performance

1989 ◽  
Author(s):  
D. A. Saravanos ◽  
C. C. Chamis
Keyword(s):  
Optimal Design ◽  
Dynamic Stiffness ◽  
Dynamic Performance ◽  
Performance Criteria ◽  
Modal Damping ◽  
Trade Offs ◽  
Design Variables ◽  
Material Systems ◽  
Structural Composite ◽  
Selective Minimization

Abstract A method is developed for the optimal design of composite links based on dynamic performance criteria directly related to structural modal damping and dynamic stiffness. An integrated mechanics theory correlates structural composite damping to the parameters of basic composite material systems, laminate parameters, link shape, and modal deformations. The inclusion of modal properties allows the selective minimization of vibrations associated with specific modes. Ply angles and fiber volumes are tailored to obtain optimal combinations of damping and stiffness. Applications to simple composite links indicate wide margins for trade-offs and illustrate the importance of various design variables to the optimal design.

On the Effects of Mistuning a Force-Excited System Containing a Quasi-Zero-Stiffness Vibration Isolator

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Ali Abolfathi ◽  
M. J. Brennan ◽  
T. P. Waters ◽  
B. Tang
Keyword(s):  
Vibration Isolation ◽  
Dynamic Stiffness ◽  
Low Frequency ◽  
Vibration Isolator ◽  
Linear Vibration ◽  
Vibration Isolators ◽  
Zero Dynamic ◽  
Low Frequency Vibration ◽  
Excited System ◽  
Better Than

Nonlinear isolators with high-static-low-dynamic-stiffness have received considerable attention in the recent literature due to their performance benefits compared to linear vibration isolators. A quasi-zero-stiffness (QZS) isolator is a particular case of this type of isolator, which has a zero dynamic stiffness at the static equilibrium position. These types of isolators can be used to achieve very low frequency vibration isolation, but a drawback is that they have purely hardening stiffness behavior. If something occurs to destroy the symmetry of the system, for example, by an additional static load being applied to the isolator during operation, or by the incorrect mass being suspended on the isolator, then the isolator behavior will change dramatically. The question is whether this will be detrimental to the performance of the isolator and this is addressed in this paper. The analysis in this paper shows that although the asymmetry will degrade the performance of the isolator compared to the perfectly tuned case, it will still perform better than the corresponding linear isolator provided that the amplitude of excitation is not too large.

Control Concepts for a Vibration Absorber With an Adaptive Joint Connection

2014 ◽  
Author(s):  
Pascal Reuss ◽  
Lothar Gaul
Keyword(s):  
Harmonic Balance ◽  
Frictional Contact ◽  
Normal Force ◽  
Dynamic Stiffness ◽  
Control Variable ◽  
Harmonic Balance Method ◽  
Direct Control ◽  
Additional Degree ◽  
Nonlinear Relation ◽  
Joint Connection

The use of absorbers to reduce vibrations of machines is common in industry and can be found in various applications. In most cases passive absorbers are used to cancel one particular eigenfrequency. The disadvantage of this solution is that due to the introduction of an additional degree-of-freedom two resonance peaks occur next to the absorbed eigenfrequency. Given the case that the machine operates in a wider frequency band these two eigenfrequencies could be excited and feature similarly high amplitudes. To address this concern, in the present case an adaptive absorber is used, which is able to adjust its eigenfrequency to the actually excited frequency. Therefore, the anti-resonance can be shifted such that a full cancellation of the resonance is possible. The absorber consists of a mass and two springs. One spring is fixed to the mass permanently and the second can be coupled to the system by an adaptive joint connection. The normal force in the frictional contact serves as control variable to achieve adaptivity of the dynamic eigenfrequency of the absorber. Two control concepts are presented. Both concepts include isolated curves characterizing the nonlinear relation between the dynamic stiffness and the related normal force based on simulations using the Harmonic Balance Method. Due to the isolation of the nonlinearity, linear control concepts like LQR can be applied, which is done in the present case. Furthermore, a direct control of the eigenfrequency is done. The adaptive absorber is applied to a simplified machine tool carriage.

Analysis for Dynamic Response of Buried Steel Pipeline in Cross-Anisotropic Layered Soils

2020 ◽  
Vol 20 (07) ◽  
pp. 2071006
Author(s):  
Jin Zhang ◽  
Zejun Han ◽  
Hongyuan Fang ◽  
Linqing Yang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Response ◽  
Dynamic Stiffness ◽  
Engineering Practice ◽  
Layered Soils ◽  
Buried Pipeline ◽  
Network Systems ◽  
The Time Domain ◽  
Element Method

The interaction between underground pipelines and soils is crucial to the design and maintenance of underground pipeline network systems. In this paper, the dynamic stiffness matrix in the frequency-domain of the buried pipeline is obtained by the improved scaled boundary finite element method (SBFEM) coupled with the finite element method (FEM) at the interface between the far and near fields. A new coordinate transformation together with a scaled line is introduced in the improved SBFEM. Combined with the mixed variable algorithm, the time-domain solution of the buried pipeline under dynamic loads is then obtained. The accuracy of the proposed algorithm was verified by numerical examples. A parametric study is performed to assess the influence of the anisotropic characteristics of the layered soils on the dynamic response of the pipeline, the result of which provides a reliable basis for engineering practice. The results show that these parameters have a significant impact on the pipeline. The understanding of this impact can contribute to the design, construction, and maintenance of the corresponding engineering projects.

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