Showing papers by "Leif Kari published in 2002"

Non-Linear Behavior of a Rubber Isolator System Using Fractional Derivatives

Abstract: A non-linear rubber isolator included in a dynamic system is examined where influences of dynamic amplitude and frequency are investigated through measurements and modeling. The frequency dependence of the isolator is modeled by a fractional calculus element while a frictional component accounts for its amplitude dependence. The model works in the time-domain and simulations of harmonic and non-harmonic motion are compared to measurements. Good agreement is obtained in a wide frequency and amplitude range for a freely oscillating one degree of freedom system, with the isolator acting as a coupling between exciting foundation and mass, and for a single isolator showing the typical amplitude dependence known as the Payne effect. The model is found to be superior to the commonly applied Kelvin-Voigt element in modeling the dynamic isolator properties.

Dynamic stiffness matrix of a long rubber bush mounting

Abstract: The complete blocked dynamic stiffness matrix of along 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

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.

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.

An analytical temperature-dependent collocation model for preloaded rubber cylinders

Abstract: The non-linear temperature-dependent stiffness of an axially preloaded rubber cylinder is examined by an analytical collocation model, where influences of temperature, cylinder diameter and length, material parameters and prestrain are investigated. The rubber is assumed to be incompressible with the deviatoric response determined by an extended neo-Hookean free energy function, embodying a temperature shift function, being directly proportional to the temperature and to the temperature-dependent rubber density. The model is based on a semi-inverse method where the motion is split into two deformations: the first, a homogeneous temperature expansion, while the second, a preload deformation where material planes parallel to the bonded metal plate in the rubber cylinder are assumed to remain parallel, with the boundary conditions on the free rubber surface satisfied by collocation. The stiffness depends strongly on the preload—particularly for larger diameter-length ratios—and on the temperature covering —6...