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Constitutive models of magneto-sensitive rubber under a continuum mechanics basis and the application in vibration isolation
KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Marcus Wallenberg Laboratory MWL.ORCID iD: 0000-0002-3091-1257
2020 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Due to its durability, stretchability, relatively low stiffness and high damping, rubber is widely used in engineering anti-vibration fields. However, a major deficiency is that once installed, the mechanical properties of traditional rubber-based devices are fixed where its adaptability to various loading conditions is poor. An alternative to traditional rubber materials is magneto-sensitive (MS) rubber. The main componentsof MS rubber are a rubber matrix and ferromagnetic particles. Under a magnetic field, the modulus of MS rubber can be altered rapidly and reversibly. Therefore, compared with conventional rubber-based devices, the stiffness of MS rubber-based devices can be adapted to various loading conditions and an enhanced vibration reduction effect can be achieved. Measurement results revealed that the mechanical behavior of MS rubber is not simple. To be specific, the dynamic modulus of MS rubber has a magnetic, frequency,amplitude and temperature dependency. In order to promote the applications of MS rubber in the anti-vibration area, models to depict the above properties are needed. The main goal of this thesis is to model the magnetic, frequency, amplitude and temperature dependence of MS rubber under a continuum mechanics basis. The research results regarding the constitutive modeling consist of three papers (Paper A, C and D). The simulation results show a good agreement with the measurement data, which proves the accuracy and feasibility of the developed model. In addition to the constitutive models of MS rubber, an investigation of MS rubber application in the vibration isolation system under harmonic and random loading cases is numerically conducted (Paper B). In order to achieve an enhanced vibration isolation effect, two control algorithms corresponding to the harmonic and random loading are developed. Numerical results verify that the vibration isolation effect ofMS rubber vibration isolator is better than the traditional rubber-based isolator. In this thesis, the model developed for MS rubber deepens the understanding of how magnetic, frequency, amplitude and temperature affect the mechanical performance of MS rubber. Moreover, the research of MS rubber application in vibration isolators and the corresponding control strategies are helpful for the design of MS rubber-based anti-vibration devices.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology , 2020. , p. 71
Series
TRITA-SCI-FOU ; 2020:19
Keywords [en]
Magneto-sensitive rubber, magnetic dependency, frequency dependency, amplitude dependency, temperature dependency, vibration isolation
National Category
Engineering and Technology
Research subject
Engineering Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-273565ISBN: 978-91-7873-557-0 (print)OAI: oai:DiVA.org:kth-273565DiVA, id: diva2:1431021
Public defence
2020-06-10, online via Zoom, 10:00 (English)
Opponent
Supervisors
Note

QC 200519

Available from: 2020-05-19 Created: 2020-05-18 Last updated: 2020-05-19Bibliographically approved
List of papers
1. 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
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: 2020-05-18Bibliographically approved
2. Modeling and vibration control of a smart vibration isolation system based on magneto-sensitive rubber
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: 2020-05-18Bibliographically approved
3. A visco-elastic-plastic constitutive model of isotropic magneto-sensitive rubber with amplitude, frequency and magnetic dependency
Open this publication in new window or tab >>A visco-elastic-plastic constitutive model of isotropic magneto-sensitive rubber with amplitude, frequency and magnetic dependency
2020 (English)In: International journal of plasticity, ISSN 0749-6419, E-ISSN 1879-2154Article in journal (Refereed) In press
Abstract [en]

A three-dimensional visco-elastic-plastic constitutive model of isotropic magneto-sensitive (MS) rubber with amplitude, frequency and magnetic dependency under a continuum constitutive framework is developed. MS rubber is akind of smart material mainly composed of a rubber matrix and magnetizable particles. Under a magnetic field, there is an increase of its dynamic modulus due to the interaction between the magnetic field and MS rubber, which is often referred to as the magnetic dependency of MS rubber. Experimental results reveal that besides the magnetic dependency, there is a frequency and amplitude dependency of its dynamic modulus. In specific, the modulus of MS rubber increases with increasing frequency and dereases with increasing strain amplitude. To depict the above properties and to consider the balance of energy in continuum mechanics framework, a new constitutive model consisting of a viscoelastic fractional derivative element, a bounding surface model in series with a neo-Hookean elastic model with magnetic sensitivity and a magnetic stress tensor term for MS rubber is proposed. The contribution of this constitutive model is that by using a free energy based method, with only eight material parameters, the amplitude, frequency and magnetic dependency of MS rubber can be reflected. After parameter identification, the simulationresults show a good agreement with those of measurements. Therefore, by utilizing the model proposed, the ability of approaching the dynamic behavior of MS rubber-based vibration reduction devices in the design phase is possible which contributes to the application of MS rubber in noise and vibration reduction area.

Keywords
Magneto-sensitive rubber, Continuum mechanics framework, Amplitude dependency, Frequency dependency, Magnetic dependency
National Category
Engineering and Technology
Research subject
Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-273563 (URN)
Available from: 2020-05-18 Created: 2020-05-18 Last updated: 2020-05-18
4. Constitutive model of isotropic magneto-sensitive rubber with amplitude, frequency, magnetic and temperature dependence under a continuum mechanics basis
Open this publication in new window or tab >>Constitutive model of isotropic magneto-sensitive rubber with amplitude, frequency, magnetic and temperature dependence under a continuum mechanics basis
2020 (English)In: International Journal of Engineering Science, ISSN 0020-7225, E-ISSN 1879-2197Article in journal (Other academic) Submitted
Abstract [en]

A three-dimensional nonlinear constitutive model of the amplitude, frequency, magnetic and temperature-dependent mechanical properties of isotropic magneto-sensitive (MS) rubber is developed. The main components of MS rubberis an elastomer matrix and magnetizable particles. When a magnetic field is applied, the modulus of MS rubber increases, which is known as the magnetic dependence of MS rubber. In addition to the magnetic dependence, there arefrequency, amplitude and temperature dependencies of MS rubber. Specifically, a higher frequency, a smaller strain amplitude and a lower temperature lead to an increased magnitude of the dynamic modulus. To represent the above properties and to stimulate the possible application of MS rubber in the anti-vibration area, a continuum mechanic framework based constitutive model consisting of a fractional standard linear solid (SLS) element, an elastoplastic element and a magnetic stress term of MS rubber is developed. The frequency and amplitude dependencies are depicted by a fractional SLS element and an elastoplastic element, respectively. A hyperbolic tangent function with a scalar product of magnetic flux density as an independent variable is introduced to consider the magnetic dependence. Furthermore, the temperature dependence is taken into account by including the William-Landel-Ferry function and the Arrhenius function to the fractional SLS element and the elastoplastic element, respectively. The technical innovation of this constitutive model is that the amplitude, frequency, magnetic and temperature dependent mechanical properties of MS rubber are incorporated into a whole constitutive model under the continuum mechanics frame and based on the free energy assumption. Comparison between the simulation and measurement results in a wide frequency range with different levels of magnetic field, strain amplitude and temperature shows that the fitting effect of the developed model is very good. Therefore, the constitutive model proposed in this paper enables the prediction ofthe mechanical properties of MS rubber under various operating conditions with high accuracy, which will drive MS rubber’s application in engineering applications, especially in the area of MS rubber-based anti-vibration devices.

Keywords
Magneto-sensitive rubber, Continuum mechanic frame, Amplitude dependence, Frequency dependence, Magnetic dependence, Temperature dependence
National Category
Engineering and Technology
Research subject
Engineering Mechanics; Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-273568 (URN)
Available from: 2020-05-18 Created: 2020-05-18 Last updated: 2020-05-18

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