Leif Kari

Bio: Leif Kari is an academic researcher from Royal Institute of Technology. The author has contributed to research in topics: Natural rubber & Audio frequency. The author has an hindex of 21, co-authored 105 publications receiving 1371 citations.

Structure-borne sound properties of isotropic magneto-rheological rubber

Abstract: Magnetorheological (MR) rubber materials are the solid analogue of magnetorheological fluids; i.e. their rheological properties can be controlled continously, rapidly, and reversibly by an applied magnetic field. They consist of magnetically polarisable particles in an elastomer matrix and they can be made to respond to changes in their environment; hence, they are considered as "smart" materials. Examples of potential applications for these materials are adaptive tuned vibration absorbers, stiffness-tuneable mounts and suspensions, and automotive bushings. The purpose of this work was to increase the knowledge relating to magnetorheological materials for damping applications. The materials should exhibit a large response to an applied magnetic field, and have good mechanical and long-term properties. MR rubber materials were made from nitrile, natural and silicone rubber, with irregularly shaped iron particles several micrometres in size. The particles were not aligned by a magnetic field prior to the vulcanisation; hence, the materials can be considered to be isotropic. These materials show a large MR effect, i.e. an increase in the shear modulus when a magnetic field is applied, although the particles are not aligned within the material. This is explained by the low critical particle volume concentration (CPVC) of such particles. Similar behaviour can be obtained with materials containing carbonyl iron, if the particles are aggregated so that they behave like large irregular particles. The iron particle concentration must be very close to the CPVC in order to obtain a large MR effect without alignment of the particles. The absolute MR effect (MPa) in an isotropic MR rubber material with large irregular iron particles is independent of the matrix material, and the relative MR effect (%) can thus be increased by the addition of plasticisers. However, the obtainable effect is limited by the reinforcement of the particles and by friction between the particles. Therefore, it is very difficult, if not impossible, to achieve an MR effect larger than 60%. Other ways of increasing the MR effect are to increase the strength of the magnetic field, although the materials saturate magnetically at high field strengths, or to use small strain amplitudes. The strong strain amplitude dependence of the MR effect suggests that MR rubber materials are most suitable for low amplitude applications, such as sound and vibration insulation. Measurements at frequencies within the audible frequency range show that this is a promising application for MR rubber materials. The incorporation of large amounts of iron into the rubber matrix decreases the oxidative stability dramatically. This is probably due to iron oxides on the surface of the particles, and to the fact that the oxidation rate is enhanced by iron ions, which are able to diffuse into the matrix. Standard antioxidants do not provide sufficient stabilisation for MR rubbers. Thus, proper stabilisation systems have to be found in order for these materials to be successful in applications.

Dynamic stiffness of chemically and physically ageing rubber vibration isolators in the audible frequency range: Part 2—waveguide solution

Abstract: 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 $$+25\,^{\circ }\hbox {C}$$ and exposed by a sudden temperature step down to $$-60\,^{\circ }\hbox {C}$$ and at several chemical ageing times at temperature $$+25\,^{\circ }\hbox {C}$$ 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

Constitutive Model of Isotropic Magneto-Sensitive Rubber with Amplitude, Frequency, Magnetic and Temperature Dependence under a Continuum Mechanics Basis.

Abstract: A three-dimensional nonlinear constitutive model of the amplitude, frequency, magnetic and temperature dependent mechanical property of isotropic magneto-sensitive (MS) rubber is developed. The main components of MS rubber are 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 are frequency, amplitude and temperature dependencies of the dynamic modulus of MS rubber. A continuum mechanical 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 to depict the mechanical behavior of MS rubber. The novelty is that the amplitude, frequency, magnetic and temperature dependent mechancial properties of MS rubber are integrated into a whole constitutive model under the continuum mechanics frame. Comparison between the simulation and measurement results shows that the fitting effect of the developed model is very good. Therefore, the constitutive model proposed enables the prediction of the mechanical properties of MS rubber under various operating conditions with a high accuracy, which will drive MS rubber’s application in engineering problems, especially in the area of MS rubber-based anti-vibration devices.

The non-linear temperature dependent stiffness of precompressed rubber cylinders: An effective shape factor model

Abstract: A shape factor based non-linear model of a rubber cylinder's temperature and preload dependent static stiffness is presented. The influence of temperature, precompression, material parameters, cylinder length and diameter, are investigated; with the motion split into a homogeneous thermal expansion including a globally equivalent preload deformation. Stiffness depends strongly on preload, particularly in larger shape factors, and on temperature. The model proves superior to traditional work in typical shape factors, with results close to those of finite element models.

Application of Fractional Calculus for Dynamic Problems of Solid Mechanics: Novel Trends and Recent Results

Abstract: The present state-of-the-art article is devoted to the analysis of new trends and recent results carried out during the last 10 years in the field of fractional calculus application to dynamic problems of solid mechanics. This review involves the papers dealing with study of dynamic behavior of linear and nonlinear 1DOF systems, systems with two and more DOFs, as well as linear and nonlinear systems with an infinite number of degrees of freedom: vibrations of rods, beams, plates, shells, suspension combined systems, and multilayered systems. Impact response of viscoelastic rods and plates is considered as well. The results obtained in the field are critically estimated in the light of the present view of the place and role of the fractional calculus in engineering problems and practice. This articles reviews 337 papers and involves 27 figures. DOI: 10.1115/1.4000563

Formulas For Natural Frequency And Mode Shape

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