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Wang, B. & Kari, L. (2019). A nonlinear constitutive model by spring, fractional derivative and modified bounding surface model to represent the amplitude, frequency and the magnetic dependency for Magneto-sensitive rubber. Journal of Sound and Vibration, 438, 344-352
Open this publication in new window or tab >>A nonlinear constitutive model by spring, fractional derivative and modified bounding surface model to represent the amplitude, frequency and the magnetic dependency for Magneto-sensitive rubber
2019 (English)In: Journal of Sound and Vibration, ISSN 0022-460X, E-ISSN 1095-8568, Vol. 438, p. 344-352Article in journal (Refereed) Published
Abstract [en]

Magneto-sensitive (MS) rubber is a kind of smart material mainly consisting of magnetizable particles and rubber. Inspired by experimental observation that the shear modulus for MS rubber is strongly dependent on amplitude, frequency and magnetic field; while the impact for the magnetic field and strain to the loss factor is relatively small, a new nonlinear constitutive model for MS rubber is presented. It consists of a fractional viscoelastic model, an elastic model and a bounding surface model with parameters sensitive to the magnetic field. To our knowledge, it is the first time that the bounding surface model is incorporated with the magnetic sensitivity and used to predict the mechanical properties for MS rubber. After comparison with the measurement results, it is found that the shear modulus and the loss factor derived from the simulation fit well with the experimental data. This new constitutive model with only eight parameters can be utilized to describe the amplitude, frequency and the magnetic field dependence for MS rubber. It provides a possible new way to understand the mechanical behavior for MS rubber. More importantly, the constitutive model with an accurate prediction property for the dynamic performance of MS rubber is of interest for MS rubber applications in noise and vibration reduction area.

Place, publisher, year, edition, pages
Academic Press, 2019
Keywords
Amplitude dependency nonlinear, Bounding surface model, Frequency dependency, Magneto-sensitive rubber, Constitutive models, Elastic moduli, Magnetic fields, Mechanical properties, Rubber, Shear strain, Viscoelasticity, Amplitude dependency, Fractional derivatives, Frequency dependencies, Magnetic field dependences, Noise and vibration reductions, Nonlinear constitutive model, Rubber applications
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-236332 (URN)10.1016/j.jsv.2018.09.028 (DOI)000447906200020 ()2-s2.0-85053892193 (Scopus ID)
Note

QC 20181112

Available from: 2018-11-12 Created: 2018-11-12 Last updated: 2018-11-12Bibliographically approved
Blanco, B., Alonso, A., Kari, L., Gil-Negrete, N. & Gimenez, J. G. (2019). Implementation of Timoshenko element local deflection for vertical track modelling. Vehicle System Dynamics, 57(10), 1421-1444
Open this publication in new window or tab >>Implementation of Timoshenko element local deflection for vertical track modelling
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2019 (English)In: Vehicle System Dynamics, ISSN 0042-3114, E-ISSN 1744-5159, Vol. 57, no 10, p. 1421-1444Article in journal (Refereed) Published
Abstract [en]

A vertical track model suitable for the study of the dynamic response and the interaction between wheel and rail in the time domain is developed by using Timoshenko beam elements, and its performance is optimised by accounting for the local deflection of these type of elements. Implementation of the local system enables one to obtain an accurate description of the contact force in a more computationally efficient way than other numerical methods, and it leads to an almost total elimination of the discontinuities caused by the local displacement underestimation and the shear incompatibilities introduced by the conventional formulation with Timoshenko beam elements. The work presented here describes both static and dynamic approaches of the local system directly obtained through the resolution of the beam governing equations. The dynamic approach guarantees the shear rotation continuity and describes accurately the track frequency content. The method is tested for parametric excitation, in which it ensures the smoothness of the response. Secondly, it is tested for short-pitch corrugated rails, where overestimation of the contact force is avoided with a reduced model size when compared with conventional Timoshenko element formulation. The results are validated by comparison with those from previous studies.

Place, publisher, year, edition, pages
TAYLOR & FRANCIS LTD, 2019
Keywords
Timoshenko element, rail modelling, local deformation, dynamic local system, discontinuity in slope deflection, corrugation
National Category
Vehicle Engineering
Identifiers
urn:nbn:se:kth:diva-256233 (URN)10.1080/00423114.2018.1513538 (DOI)000478606800002 ()2-s2.0-85053032740 (Scopus ID)
Note

QC 20191022

Available from: 2019-10-22 Created: 2019-10-22 Last updated: 2019-10-22Bibliographically approved
Wang, B. & Kari, L. (2019). Modeling and vibration control of a smart vibration isolation system based on magneto-sensitive rubber. Smart materials and structures (Print), 28(6), Article ID 065026.
Open this publication in new window or tab >>Modeling and vibration control of a smart vibration isolation system based on magneto-sensitive rubber
2019 (English)In: Smart materials and structures (Print), ISSN 0964-1726, E-ISSN 1361-665X, Vol. 28, no 6, article id 065026Article in journal (Refereed) Published
Abstract [en]

Magneto-sensitive (MS) rubber is a kind of smart material, the shear modulus of it can be changed rapidly and reversibly by a magnetic field applied. A smart MS rubber-based isolation system and a nonlinear model based on this MS rubber-based vibration isolation system are developed in this paper. The influence of the amplitude, frequency and magnetic dependency for MS rubber, the mechanical inertance of infinite extended foundation, the mass of solid block and the dimension of MS rubber isolators are all considered in this model. The feasibility of two control strategies aimed at reducing the energy transmitted to the foundation and protecting machine against foundation motion, respectively, is investigated based on this smart vibration isolation system. It is found that compared to the traditional passive rubber isolators, an enhanced vibration isolation effect can be achieved by using MS rubber isolators after control strategies applied. Furthermore, the influence of the amplitude dependency and the response time of MS rubber to the isolation effect is studied. The nonlinear model established for MS rubber isolation system, the control strategies developed and the investigation for the amplitude dependency and the response time of MS rubber to the isolation effect in this paper provide fundamentals for the application of MS rubber in the field of vibration reduction.

Place, publisher, year, edition, pages
IOP PUBLISHING LTD, 2019
Keywords
magneto-sensitive rubber, vibration isolation, amplitude dependency, frequency dependency, magnetic dependency, control strategies
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-252595 (URN)10.1088/1361-665X/ab1ab4 (DOI)000467706900008 ()2-s2.0-85068441497 (Scopus ID)
Note

QC 20190611

Available from: 2019-06-11 Created: 2019-06-11 Last updated: 2019-10-04Bibliographically approved
Wang, B. & Kari, L. (2018). Modeling the the amplitude and magnetic dependency to the vibration isolation effect for magneto-sensitive rubber isolation system by assessing the energy flow. In: Proceedings of ISMA 2018 - International Conference on Noise and Vibration Engineering and USD 2018 - International Conference on Uncertainty in Structural Dynamics: . Paper presented at 28th International Conference on Noise and Vibration Engineering, ISMA 2018 and 7th International Conference on Uncertainty in Structural Dynamics, USD 2018, 17 September 2018 through 19 September 2018 (pp. 4211-4222). KU Leuven - Departement Werktuigkunde
Open this publication in new window or tab >>Modeling the the amplitude and magnetic dependency to the vibration isolation effect for magneto-sensitive rubber isolation system by assessing the energy flow
2018 (English)In: Proceedings of ISMA 2018 - International Conference on Noise and Vibration Engineering and USD 2018 - International Conference on Uncertainty in Structural Dynamics, KU Leuven - Departement Werktuigkunde , 2018, p. 4211-4222Conference paper, Published paper (Refereed)
Abstract [en]

A highly nonlinear model which consider the impact of the frequency, amplitude and magnetic field dependency for MS rubber and mobility for the foundation is developed for a MS rubber isolation system. Harmonic loadings ranging from 60 to 160 Hz with different levels of force magnitude are applied for the system. Vibration isolation effect is evaluated by assessing the energy flow into the foundation. It is found that the energy flow into the system and the vibration isolation effect for MS isolator are highly related to the amplitude and magnetic field dependency for MS rubber. Furthermore, by comparing the energy flow to the foundation under zero and saturation magnetic field, a control strategy to reduce the energy flow to the foundation by changing the magnetic field is obtained. After applying the control strategy it is found that the energy flow into the foundation can be reduced by about 20% by changing the magnetic field compared to traditional passive rubber isolators.

Place, publisher, year, edition, pages
KU Leuven - Departement Werktuigkunde, 2018
National Category
Energy Systems
Identifiers
urn:nbn:se:kth:diva-246507 (URN)2-s2.0-85060402294 (Scopus ID)9789073802995 (ISBN)
Conference
28th International Conference on Noise and Vibration Engineering, ISMA 2018 and 7th International Conference on Uncertainty in Structural Dynamics, USD 2018, 17 September 2018 through 19 September 2018
Note

QC 20190402

Available from: 2019-04-02 Created: 2019-04-02 Last updated: 2019-04-02Bibliographically approved
Blanco, B., Kari, L., Gil-Negrete, N. & Alonso, A. (2018). Modelling of the track supports with elements over elastic foundation together with dynamic internal degrees of freedom. In: W. Desmet, B. Pluymers, D. Moens, W. Rottiers (Ed.), Proceedings of ISMA 2018 - International Conference on Noise and Vibration Engineering and USD 2018 - International Conference on Uncertainty in Structural Dynamics2018, Pages 3255-326828th International Conference on Noise and Vibration Engineering, ISMA 2018 and 7th International Conference on Uncertainty in Structural Dynamics, USD 2018; Leuven; Belgium; 17 September 2018 through 19 September 2018: . Paper presented at Leuven; Belgium; 17 September 2018 through 19 September 2018 (pp. 3255-3268). KU Leuven - Departement Werktuigkunde
Open this publication in new window or tab >>Modelling of the track supports with elements over elastic foundation together with dynamic internal degrees of freedom
2018 (English)In: Proceedings of ISMA 2018 - International Conference on Noise and Vibration Engineering and USD 2018 - International Conference on Uncertainty in Structural Dynamics2018, Pages 3255-326828th International Conference on Noise and Vibration Engineering, ISMA 2018 and 7th International Conference on Uncertainty in Structural Dynamics, USD 2018; Leuven; Belgium; 17 September 2018 through 19 September 2018 / [ed] W. Desmet, B. Pluymers, D. Moens, W. Rottiers, KU Leuven - Departement Werktuigkunde , 2018, p. 3255-3268Conference paper, Published paper (Refereed)
Abstract [en]

Formulation of the Timoshenko elements is improved with the use of internal degrees of freedom (iDOF) representing the local displacements, leading to a new finite element approach specially devoted to the numeric analysis of the track dynamics. The dynamic formulation of the local displacement is proved to correct the frequency content of the track model. Regarding time domain studies, this approach avoids the displacement underestimation and shear discontinuity between elements, which are sources of inaccuracies and irregular behaviour.  Those rail sections located above the supports are modelled with Timoshenko element over elastic foundation (TEEF), and the rest with conventional Timoshenko elements (TIM4). By using TEEF prompt disruption of the contact force at support surpassing is avoided, and the frequency response of the track around the `pinned-pinned' frequency is corrected. Moreover the TEEF formulation is extended in order to account for the sleeper pitch rotation, and evaluation of its influence over the track dynamics is performed. 

Place, publisher, year, edition, pages
KU Leuven - Departement Werktuigkunde, 2018
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-244300 (URN)2-s2.0-85060393553 (Scopus ID)9789073802995 (ISBN)
Conference
Leuven; Belgium; 17 September 2018 through 19 September 2018
Note

QC 20190220

Available from: 2019-02-18 Created: 2019-02-18 Last updated: 2019-02-20Bibliographically approved
Lundberg, O., Kari, L. & Lopez Arteaga, I. (2017). A compact internal drum test rig for measurements of rolling contact forces between a single tread block and a substrate. Measurement, 103, 370-378
Open this publication in new window or tab >>A compact internal drum test rig for measurements of rolling contact forces between a single tread block and a substrate
2017 (English)In: Measurement, ISSN 0263-2241, E-ISSN 1873-412X, Vol. 103, p. 370-378Article in journal (Refereed) Published
Abstract [en]

A novel test rig design is presented which enables detailed studies of the three force components generated in the impact and release phase of rolling contact between a tyre tread block and a substrate. The design of the compact internal drum test rig provides realistic impact and release angles for the tread block-substrate contact and enables force measurements at high rolling speeds with a high signal-to-noise ratio. Measurements of the rolling contact forces are presented for different values of rolling velocity, static pre-load and acceleration. It is demonstrated that this test rig provides results which contribute to the understanding of tyre road interaction and can be used as input to modelling-based development of both tyres and roads aiming for improved handling, safety, energy efficiency and comfort.

Place, publisher, year, edition, pages
Elsevier, 2017
Keywords
Tread block, Road, Contact forces, Rubber friction, Rolling contact, Test rig
National Category
Vehicle Engineering
Identifiers
urn:nbn:se:kth:diva-207648 (URN)10.1016/j.measurement.2016.12.041 (DOI)000400033300038 ()2-s2.0-84994633128 (Scopus ID)
Note

QC 20170607

Available from: 2017-06-07 Created: 2017-06-07 Last updated: 2017-11-10Bibliographically approved
Kari, L. (2017). Dynamic stiffness of chemically and physically ageing rubber vibration isolators in the audible frequency range. Continuum Mechanics and Thermodynamics, 29(5), 1027-1046
Open this publication in new window or tab >>Dynamic stiffness of chemically and physically ageing rubber vibration isolators in the audible frequency range
2017 (English)In: Continuum Mechanics and Thermodynamics, ISSN 0935-1175, E-ISSN 1432-0959, Vol. 29, no 5, p. 1027-1046Article in journal (Refereed) Published
Abstract [en]

The constitutive equations of chemically and physically ageing rubber in the audible frequency range are modelled as a function of ageing temperature, ageing time, actual temperature, time and frequency. The constitutive equations are derived by assuming nearly incompressible material with elastic spherical response and viscoelastic deviatoric response, using Mittag-Leffler relaxation function of fractional derivative type, the main advantage being the minimum material parameters needed to successfully fit experimental data over a broad frequency range. The material is furthermore assumed essentially entropic and thermo-mechanically simple while using a modified William-Landel-Ferry shift function to take into account temperature dependence and physical ageing, with fractional free volume evolution modelled by a nonlinear, fractional differential equation with relaxation time identical to that of the stress response and related to the fractional free volume by Doolittle equation. Physical ageing is a reversible ageing process, including trapping and freeing of polymer chain ends, polymer chain reorganizations and free volume changes. In contrast, chemical ageing is an irreversible process, mainly attributed to oxygen reaction with polymer network either damaging the network by scission or reformation of new polymer links. The chemical ageing is modelled by inner variables that are determined by inner fractional evolution equations. Finally, the model parameters are fitted to measurements results of natural rubber over a broad audible frequency range, and various parameter studies are performed including comparison with results obtained by ordinary, non-fractional ageing evolution differential equations.

Place, publisher, year, edition, pages
SPRINGER, 2017
Keywords
Chemically and physically ageing, Mittag-Leffler function, William-Landel-Ferry function, Fractional differential equation, Doolittle equation, Fractional free volume
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-214318 (URN)10.1007/s00161-017-0569-7 (DOI)000408062000001 ()2-s2.0-85019059305 (Scopus ID)
Note

QC 20170914

Available from: 2017-09-14 Created: 2017-09-14 Last updated: 2017-10-20Bibliographically approved
Kari, L. (2017). Dynamic stiffness of chemically and physically ageing rubber vibration isolators in the audible frequency range: Part 2-waveguide solution. Continuum Mechanics and Thermodynamics, 29(5), 1047-1059
Open this publication in new window or tab >>Dynamic stiffness of chemically and physically ageing rubber vibration isolators in the audible frequency range: Part 2-waveguide solution
2017 (English)In: Continuum Mechanics and Thermodynamics, ISSN 0935-1175, E-ISSN 1432-0959, Vol. 29, no 5, p. 1047-1059Article in journal (Refereed) Published
Abstract [en]

The dynamic stiffness of a chemically and physically ageing rubber vibration isolator in the audible frequency range is modelled as a function of ageing temperature, ageing time, actual temperature, time, frequency and isolator dimension. In particular, the dynamic stiffness for an axially symmetric, homogeneously aged rubber vibration isolator is derived by waveguides where the eigenmodes given by the dispersion relation for an infinite cylinder satisfying traction free radial surface boundary condition are matched to satisfy the displacement boundary conditions at the lateral surface ends of the finite rubber cylinder. The constitutive equations are derived in a companion paper (Part 1). The dynamic stiffness is calculated over the whole audible frequency range 20-20,000 Hz at several physical ageing times for a temperature history starting at thermodynamic equilibrium at +25 degrees C and exposed by a sudden temperature step down to -60 degrees C and at several chemical ageing times at temperature +25 degrees C with simultaneous molecular network scission and reformation. The dynamic stiffness results are displaying a strong frequency dependence at a short physical ageing time, showing stiffness magnitude peaks and troughs, and a strong physical ageing time dependence, showing a large stiffness magnitude increase with the increased physical ageing time, while the peaks and troughs are smoothed out. Likewise, stiffness magnitude peaks and troughs are frequency-shifted with increased chemical ageing time. The developed model is possible to apply for dynamic stiffness prediction of rubber vibration isolator over a broad audible frequency range under realistic environmental condition of chemical ageing, mainly attributed to oxygen exposure from outside and of physical ageing, primarily perceived at low-temperature steps.

Place, publisher, year, edition, pages
SPRINGER, 2017
Keywords
Dynamic stiffness, Vibration isolator, Chemically and physically ageing, Waveguide, Mode-matching
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-214319 (URN)10.1007/s00161-017-0573-y (DOI)000408062000002 ()2-s2.0-85019180612 (Scopus ID)
Note

QC 20170913

Available from: 2017-09-13 Created: 2017-09-13 Last updated: 2017-09-13Bibliographically approved
Kari, L. (2017). Torsional wave propagation in tough, rubber like, doubly crosslinked hydrogel. In: Constitutive Models for Rubber X - Proceedings of the 10th European Conference on Constitutive Models for Rubber, ECCMR X 2017: . Paper presented at 10th European Conference on Constitutive Models for Rubber, ECCMR X 2017, 28 August 2017 through 31 August 2017 (pp. 423-426). CRC Press/Balkema
Open this publication in new window or tab >>Torsional wave propagation in tough, rubber like, doubly crosslinked hydrogel
2017 (English)In: Constitutive Models for Rubber X - Proceedings of the 10th European Conference on Constitutive Models for Rubber, ECCMR X 2017, CRC Press/Balkema , 2017, p. 423-426Conference paper, Published paper (Refereed)
Abstract [en]

Torsional wave amplitude for tough, rubber like, doubly crosslinked hydrogel decreases rapidly with propagation distance where maximum decrease after one wave length is at frequency with maximum loss factor of shear modulus. Doubly crosslinked hydrogel is containing macromolecular polymer network with both chemical and physical crosslinks where it is possible to adaptively tune the frequency for maximum loss factor of shear modulus. This rubber like material has thus a potential to serve as vibration isolator and damper. Torsional dynamic stiffness of a cylindrical vibration isolator is modelled, displaying resonances and anti-resonances with a strong damping. 

Place, publisher, year, edition, pages
CRC Press/Balkema, 2017
Keywords
Constitutive models, Crosslinking, Elastic moduli, Hydrogels, Shear flow, Shear strain, Vibrations (mechanical), Wave propagation, Cross-linked hydrogels, Cylindrical vibrations, Macromolecular polymers, Propagation distances, Rubberlike materials, Strong damping, Torsional dynamics, Vibration isolators, Rubber
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-246956 (URN)10.1201/9781315223278-76 (DOI)2-s2.0-85054822833 (Scopus ID)9781138030015 (ISBN)
Conference
10th European Conference on Constitutive Models for Rubber, ECCMR X 2017, 28 August 2017 through 31 August 2017
Note

QC 20190619

Available from: 2019-06-19 Created: 2019-06-19 Last updated: 2019-06-19Bibliographically approved
Österlöf, R., Wentzel, H. & Kari, L. (2016). A finite strain viscoplastic constitutive model for rubber with reinforcing fillers. International journal of plasticity, 87, 1-14
Open this publication in new window or tab >>A finite strain viscoplastic constitutive model for rubber with reinforcing fillers
2016 (English)In: International journal of plasticity, ISSN 0749-6419, E-ISSN 1879-2154, Vol. 87, p. 1-14Article in journal (Refereed) Published
Abstract [en]

A three dimensional viscoplastic constitutive model for finite strains in a co-rotational explicit scheme is developed and implemented using finite elements that captures the amplitude dependency, commonly referred to as the Fletcher-Gent effect, and frequency dependency of rubber with reinforcing fillers. The multiplicative split of the deformation gradient is utilized and the plastic flow rule stems from an extension to finite strains of a boundary surface model with a vanishing elastic region. The storage and loss modulus for a 50 phr carbon black filled natural rubber are captured over a large range of strain amplitudes, 0.2-50% shear strain, and frequencies, 0.2-20 Hz. In addition, bimodal excitation is replicated accurately, even though this measurement data is not included when obtaining material parameters. This capability is essential when non-sinusoidal loading conditions are to be replicated. By separating the material and geometrical influence on the properties of a component, the design engineers have the capability to evaluate more concepts early in the design phase. This also reduces the need of complex prototypes for physical testing, thereby saving both time and money.

Place, publisher, year, edition, pages
Elsevier, 2016
Keywords
Finite strain, Viscoplastic material, Polymeric material, Finite elements, Fletcher-Gent effect
National Category
Materials Engineering
Identifiers
urn:nbn:se:kth:diva-198951 (URN)10.1016/j.ijplas.2016.08.008 (DOI)000387529100001 ()2-s2.0-84992179901 (Scopus ID)
Note

QC 20170113

Available from: 2017-01-13 Created: 2016-12-22 Last updated: 2017-11-29Bibliographically approved
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ORCID iD: ORCID iD iconorcid.org/0000-0001-5760-3919

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