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.

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.

A model for the vibrator–ground coupling vibration and the dynamic responses under excitation of sweep signal

2019 ◽  
Vol 22 (8) ◽  
pp. 1855-1866 ◽  
Author(s):  
Gang Li ◽  
Zhi-Qiang Huang ◽  
Zhang-Hua Lian ◽  
Lei Hao
Keyword(s):  
Dynamic Stiffness ◽  
Low Frequency ◽  
Dynamic Responses ◽  
Coupling Vibration ◽  
Lower Velocity ◽  
Dynamic Damping ◽  
Velocity Response ◽  
Cell Test ◽  
Three Stages ◽  
Good Agreement

To analyze the behavior of the vibrator–ground coupling vibration, a model containing equivalent dynamic stiffness and equivalent dynamic damping to describe the interaction between the vibrator and the ground is established based on half-space theory. According to load cell test, this model shows a good agreement with the experimental data. Dynamic responses of the structure are analyzed on displacement, velocity, acceleration, and ground force. Results show that the stroke and pump displacement are main constraints that limit the bandwidth of vibrator toward low frequency, and the stroke of conventional vibrator is not long enough to achieve lower frequency. Analysis of velocity response indicates that with the increase of frequency, a larger mass results in a lower velocity under external force. The influence of the ground acting on the baseplate is limited, and the acceleration of the baseplate is determined by its own mass beyond 80 Hz. Analysis of ground force shows that the response of the structure can be divided into three stages. The reaction mass, the baseplate, and the ground play different roles in dominating the ground force at different frequency bands.

scholarly journals Dynamically variable negative stiffness structures

2016 ◽  
Vol 2 (2) ◽  
pp. e1500778 ◽  
Author(s):  
Christopher B. Churchill ◽  
David W. Shahan ◽  
Sloan P. Smith ◽  
Andrew C. Keefe ◽  
Geoffrey P. McKnight
Keyword(s):  
Vibration Isolation ◽  
Dynamic Stiffness ◽  
Low Frequency ◽  
Variable Stiffness ◽  
Negative Stiffness ◽  
Load Bearing ◽  
Vibration Isolators ◽  
Wide Range ◽  
Engineered Systems ◽  
Tunable Stiffness

Variable stiffness structures that enable a wide range of efficient load-bearing and dexterous activity are ubiquitous in mammalian musculoskeletal systems but are rare in engineered systems because of their complexity, power, and cost. We present a new negative stiffness–based load-bearing structure with dynamically tunable stiffness. Negative stiffness, traditionally used to achieve novel response from passive structures, is a powerful tool to achieve dynamic stiffness changes when configured with an active component. Using relatively simple hardware and low-power, low-frequency actuation, we show an assembly capable of fast (<10 ms) and useful (>100×) dynamic stiffness control. This approach mitigates limitations of conventional tunable stiffness structures that exhibit either small (<30%) stiffness change, high friction, poor load/torque transmission at low stiffness, or high power active control at the frequencies of interest. We experimentally demonstrate actively tunable vibration isolation and stiffness tuning independent of supported loads, enhancing applications such as humanoid robotic limbs and lightweight adaptive vibration isolators.

Audible-frequency stiffness of a primary suspension isolator on a high-speed tilting bogie

2003 ◽  
Vol 217 (1) ◽  
pp. 47-62 ◽  
Author(s):  
L Kari
Keyword(s):  
High Speed ◽  
Dynamic Stiffness ◽  
Low Frequency ◽  
Vertical Stiffness ◽  
Audible Frequency ◽  
Minimum Number ◽  
Shear Relaxation ◽  
Operator Kernel ◽  
Incompressible Rubber ◽  
Good Agreement

The preload-dependent dynamic stiffness of a primary suspension isolator on a high-speed tilting bogie is examined via measurements and modelling within an audible frequency range. The stiffness is found to depend strongly on both frequency and preload. The former displays some resonance phenomena, such as stiffness peaks and troughs, while the latter exhibits a steep low-frequency stiffness increase in addition to an anti-resonance peak shifting to a higher frequency with increased preload. The problems of simultaneously modelling the preload and frequency dependence are removed by adopting a frequency-dependent waveguide approach, assuming incompressible rubber with an Abel operator kernel as its shear relaxation function. The preload dependence is modelled by a non-linear shape factor based approach, using a globally equivalent preload configuration. All the translational stiffnesses are modelled, including the vertical, longitudinal and lateral directions, and the vertical stiffness results are compared to those of measurements in a specially designed test rig. Good agreement is obtained for a wide frequency domain-covering 100-600 Hz-using a minimum number of parameters and for a wide preload domain-from vanishing to the maximum in service, 90 kN.

Dynamic Stiffness Matrix of a Long Rubber Bush Mounting

2002 ◽  
Vol 75 (4) ◽  
pp. 747-770 ◽  
Author(s):  
L. Kari
Keyword(s):  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Low Frequency ◽  
Material Model ◽  
Incompressible Material ◽  
Noise Abatement ◽  
Arbitrary Boundary ◽  
Dynamic Stiffness Matrix ◽  
Minimum Number ◽  
Standard Linear Solid

Abstract The complete blocked dynamic stiffness matrix of a long rubber bush mounting of particular interest for noise abatement is examined by an analytical model, where influences of audible frequencies, material properties, bush mounting length, and radius, are investigated. The model is based on the dispersion relation for an infinite, thick-walled cylinder with arbitrary boundary conditions at the radial inner and outer surfaces; yielding the sought stiffness matrix, including axial, torsional, radial, and tilting stiffness. A nearly incompressible material model is adopted, being elastic in dilatation while displaying viscoelasticity in deviation. The applied deviatoric Mittag-Leffler relaxation function is based on a fractional standard linear solid, the main advantage being the minimum number of parameters required to successfully model the rubber properties over a broad structure-borne sound frequency domain. The dynamic stiffness components display a strong frequency dependence at audible frequencies, resulting in acoustical resonance phenomena, such as stiffness peaks and troughs. The low-frequency stiffness asymptotes of the presented model are shown to agree with those of static theories.

A Nonlinear Viscoelastic Model for Polyester Mooring Line Analysis

2011 ◽  
Author(s):  
J. W. Kim ◽  
J. H. Kyoung ◽  
A. Sablok ◽  
K. Lambrakos
Keyword(s):  
Dynamic Stiffness ◽  
Relaxation Times ◽  
Viscoelastic Model ◽  
Line Tension ◽  
Mooring Line ◽  
Prony Series ◽  
Nonlinear Viscoelastic ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Nonlinear Viscoelastic Model

A viscoelastic model considering multiple relaxation times and nonlinearity in dynamic stiffness has been developed. The model is based on the Maxwell-Wiechert model, which is an extension of an earlier model based on the standard linear solid (SLS) model. The time-dependent elastic modulus of polyester rope is represented by a 4-term Prony series (MW4 model). Relaxation times and coefficients of the Prony series have been determined from test data of dynamic stiffness at different loading periods. Nonlinearity in dynamic stiffness is considered by iteratively adjusting the dynamic stiffness of polyester rope based on the calculated mean load on the rope. The developed model has been applied in the global performance analysis of a Spar platform moored in deep water. Platform offset and mooring-line tension comparisons between the SLS and the MW4 models are given for intact and broken mooring-line cases.

scholarly journals Optimal fluid passageway design methodology for hydraulic engine mounts considering both low and high frequency performances

2019 ◽  
Vol 25 (21-22) ◽  
pp. 2749-2757
Author(s):  
Yuan Li ◽  
Jason Zheng Jiang ◽  
Simon A Neild
Keyword(s):  
High Frequency ◽  
Dynamic Stiffness ◽  
Low Frequency ◽  
Relative Displacement ◽  
Wide Frequency Range ◽  
Performance Criteria ◽  
Frequency Model ◽  
Engine Mounts ◽  
Engine Mount ◽  
And Performance

This paper investigates the potential for improving the performance of hydraulic engine mounts through fluid passageway designs. In previous studies, a few simple inertia track designs have been investigated with moderate improvements obtained. However, there are countless alternative design possibilities existing; while analyzing each one of them in turn is impracticable. To this end, this paper introduces a systematic methodology to optimize fluid passageway designs in a hydraulic engine mount. First, beneficial fluid passageway configurations are systematically identified using a linearized low-frequency model that captures the relative displacement transmissibility. A nonlinear model is then used to fine-tune the fluid passageway designs for the low-frequency transmissibility improvement, and also for the assessment of high-frequency dynamic stiffness performance. The obtained beneficial designs present performance advantages over a wide frequency range. The design approach introduced in this study is directly applicable to other engine mount models and performance criteria.

A Triboelastic Model for the Cyclic Mechanical Behavior of Filled Vulcanizates

1995 ◽  
Vol 68 (4) ◽  
pp. 660-670 ◽  
Author(s):  
V. A. Coveney ◽  
D. E. Johnson ◽  
D. M. Turner
Keyword(s):  
Natural Rubber ◽  
Mechanical Behavior ◽  
Material Behavior ◽  
Computationally Efficient ◽  
Complex Deformation ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Basic Equations ◽  
Efficient Approximation ◽  
Natural Rubber Vulcanizates

Abstract Aspects of the mechanical behavior of filled vulcanizates are reviewed with reference to existing mathematical models. The basic equations of the triboelastic theory, previously described by Turner, are derived. A standard triboelastic solid (STS) three parameter model, analogous to the standard linear solid, is described and a computationally efficient approximation developed. Comparisons are made between the predictions of the STS model and the behavior of testpieces of heavily filled natural rubber vulcanizates when subjected to simple and to complex deformation histories at various frequencies; the model is found to give a satisfactory representation of material behavior. Limitations of the STS model are also discussed.

Linear Viscoelastic Creep Model for the Contact of Nominal Flat Surfaces Based on Fractal Geometry: Standard Linear Solid (SLS) Material

2007 ◽  
Vol 129 (3) ◽  
pp. 461-466 ◽  
Author(s):  
Osama M. Abuzeid ◽  
Peter Eberhard
Keyword(s):  
Constitutive Law ◽  
Creep Model ◽  
Viscoelastic Creep ◽  
Flat Surfaces ◽  
Proposed Model ◽  
Linear Viscoelastic ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Creep Force ◽  
Good Agreement

The objective of this study is to construct a continuous mathematical model that describes the frictionless contact between a nominally flat (rough) viscoelastic punch and a perfectly rigid foundation. The material’s behavior is modeled by assuming a complex viscoelastic constitutive law, the standard linear solid (SLS) law. The model aims at studying the normal compliance (approach) of the punch surface, which will be assumed to be quasistatic, as a function of the applied creep load. The roughness of the punch surface is assumed to be fractal in nature. The Cantor set theory is utilized to model the roughness of the punch surface. An asymptotic power law is obtained, which associates the creep force applied and the approach of the fractal punch surface. This law is only valid if the approach is of the size of the surface roughness. The proposed model admits an analytical solution for the case when the deformation is linear viscoelastic. The modified analytical model shows a good agreement with experimental results available in the literature.

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