Leif Kari

Bio: Leif Kari is an academic researcher from Royal Institute of Technology. The author has contributed to research in topic(s): Natural rubber & Audio frequency. The author has an hindex of 21, co-authored 105 publication(s) receiving 1371 citation(s).

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.

Nonlinear Isolator Dynamics at Finite Deformations: An Effective Hyperelastic, Fractional Derivative, Generalized Friction Model

Abstract: In presenting a nonlinear dynamic model of a rubber vibration isolator, the quasistatic and dynamic motion influences on the force response are investigated within the time and frequency domain. It is found that the dynamic stiffness at the frequency of a harmonic displacement excitation, superimposed upon the long term isolator response, is strongly dependent on static precompression, dynamic amplitude and frequency. The problems of simultaneously modelling the elastic, viscoelastic and friction forces are removed by additively splitting them, modelling the elastic force response by a nonlinear, shape factor based approach, displaying results that agree with those of a neo-Hookean hyperelastic isolator at a long term precompression. The viscoelastic force is modeled by a fractional derivative element, while the friction force governs from a generalized friction element displaying a smoothed Coulomb force. A harmonic displacement excitation is shown to result in a force response containing the excitation frequency and its every other higher-order harmonic, while using a linearized elastic force response model, whereas all higher-order harmonics are present for the fully nonlinear case. It is furthermore found that the dynamic stiffness magnitude increases with static precompression and frequency, while decreasing with dynamic excitation amplitude-eventually increasing at the highest amplitudes due to nonlinear elastic effects-with its loss angle displaying a maximum at an intermediate amplitude. Finally, the dynamic stiffness at a static precompression, using a linearized elastic force response model, is shown to agree with the fully nonlinear model except at the highest dynamic amplitudes.

A simplified methodology to predict the dynamic stiffness of carbon-black filled rubber isolators using a finite element code

Abstract: A new and different approach to the inclusion of the amplitude-dependent effect, known as the Fletcher-Gent effect or Payne effect, in a linear viscoelastic rubber material model is presented to predict the dynamic stiffness of filled rubber isolators using a finite element (FE) code. The technique is based on providing a linear viscoelastic model with the adequate material data set, once the dynamic strain amplitude, to which the rubber mount is subjected, is estimated. A generalized Zener model is adopted to describe the frequency-dependent behaviour of the material through the use of hereditary integrals. The dynamic strain amplitude dependence is not modelled through any friction model or plasticity theory, as usually is in literature. It is introduced by considering the frequency-dependent properties of the compound at an adequate strain value, which enforces the estimation of an equivalent strain value. As a first approximation, a quasi-static value is used as the reference value at which material properties should be provided to the linear viscoelastic model. The technique works directly in frequency domain, the dynamic stiffness of the bushing being directly obtained. The methodology is applied to evaluate the dynamic stiffness of a real bushing in working conditions with very satisfactory results. Despite the assumptions made, especially regarding the estimation of the equivalent strain amplitude value, errors of the predictions fall within the limits usually accepted by rubber manufacturers.

Amplitude and frequency dependence of magneto-sensitive rubber in a wide frequency range

Abstract: Two new aspects of the dynamic behaviour in the audible frequency range of magneto-sensitive (MS) rubber are highlighted: the existence of an amplitude dependence of the shear modulus—referred to as the Fletcher–Gent effect—for even small displacements, and the appearance of large MS effects. In order to illustrate these two features, results are presented of measurements performed in the audible frequency range on two different kinds of rubber: silicone and natural rubber with a respective iron particle volume concentration of 33%. The particles used are of irregular shape and randomly distributed within the rubber. An external magnetic field of 0–0.8 T is applied. Both kinds of rubber are found to be strongly amplitude dependent and, furthermore, displaying large responses to externally applied magnetic fields—a maximum of 115%. Also included are graphs of measurements on silicone and natural rubber devoid of iron particles. Those results support the conclusion that introducing iron particles in the rubber gives rise to a strong, non-negligible, amplitude dependence in the entire frequency range.

General shell model for a rotating pretwisted blade

Abstract: A novel dynamic model for a pretwisted rotating compressor blade mounted at an arbitrary stagger angle using general shell theory and including the rotational velocity is developed to study the eigenfrequencies and damping properties of the pretwisted rotating blade. The strain-displacement relation and constitutive model based on the general (thick) shell theory are applied to bring out the strain energy of the rotating blade. Using the Hamilton’s principle, the variational form of the total energy is derived in order to obtain the corresponding weak form for the numerical simulation. The model is validated by comparing to literature results and Ansys results, showing good agreement. Parametric analyses are carried out to study the influence of the rotation velocity, the stagger angle and the radius of the disk on the eigenfrequencies of the pretwisted blade. Proportional damping is included into the proposed model to investigate the influence of rotational velocity on the damping characteristics of the pretwisted rotating blade system. It is shown that, due to inertial and Coriolis e ects, damping decreases as the rotation velocity increases for the lower part of the velocity range considered and either decreases or increases depending on the mode order for higher velocities. Furthermore, frequency loci veering as a result of the rotation velocity is observed. The proposed model is an e cient and accurate tool for predicting the dynamic behavior of compressor blades of arbitrary thickness, stagger angle and pretwist, potentially during the early designing stage of turbomachinery.

Fundamentals, processes and applications of high-permittivity polymer–matrix composites

Abstract: There is an increasing need for high-permittivity (high-k) materials due to rapid development of electrical/electronic industry. It is well-known that single composition materials cannot meet the high-k need. The combination of dissimilar materials is expected to be an effective way to fabricate composites with high-k, especial for high-k polymer–matrix composites (PMC). This review paper focuses on the important role and challenges of high-k PMC in new technologies. The use of different materials in the PMC creates interfaces which have a crucial effect on final dielectric properties. Therefore it is necessary to understand dielectric properties and processing need before the high-k PMC can be made and applied commercially. Theoretical models for increasing dielectric permittivity are summarized and are used to explain the behavior of dielectric properties. The effects of fillers, fabrication processes and the nature of the interfaces between fillers and polymers are discussed. Potential applications of high-k PMC are also discussed.

Recent advances in nonlinear passive vibration isolators

Abstract: The theory of nonlinear vibration isolation has witnessed significant developments due to pressing demands for the protection of structural installations, nuclear reactors, mechanical components, and sensitive instruments from earthquake ground motion, shocks, and impact loads. In view of these demands, engineers and physicists have developed different types of nonlinear vibration isolators. This article presents a comprehensive assessment of recent developments of nonlinear isolators in the absence of active control means. It does not deal with other means of linear or nonlinear vibration absorbers. It begins with the basic concept and features of nonlinear isolators and inherent nonlinear phenomena. Specific types of nonlinear isolators are then discussed, including ultra-low-frequency isolators. For vertical vibration isolation, the treatment of the Euler spring isolator is based on the post-buckling dynamic characteristics of the column elastica and axial stiffness. Exact and approximate analyses of axial stiffness of the post-buckled Euler beam are outlined. Different techniques of reducing the resonant frequency of the isolator are described. Another group is based on the Gospodnetic–Frisch-Fay beam, which is free to slide on two supports. The restoring force of this beam resembles to a great extent the restoring roll moment of biased ships. The base isolation of buildings, bridges, and liquid storage tanks subjected to earthquake ground motion is then described. Base isolation utilizes friction elements, laminated-rubber bearings, and the friction pendulum. Nonlinear viscoelastic and composite material springs, and smart material elements are described in terms of material mechanical characteristics and the dependence of their transmissibility on temperature and excitation amplitude. The article is closed by conclusions, which highlight resolved and unresolved problems and recommendations for future research directions.

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

Interfacial damping characteristics of carbon nanotube-based composites

Abstract: Because of their ultra small, nanometer scale size and low density, the surface area to mass ratio (specific area) of carbon nanotubes (CNTs) is extremely large. Therefore, in a nanotube-based polymeric composite structure, it is anticipated that high damping can be achieved by taking advantage of the interfacial friction between the nanotubes and the polymer resin. In addition, the CNT’s large aspect ratio and high elastic modulus features allow for the design of such composites with large differences in strain between the constituents, which could further enhance the interfacial energy dissipation ability. Despite their wonderful engineering potential, the damping properties of CNT-based composites have not been examined in any detail. The purpose of this paper is to investigate the structural damping characteristics of polymeric composites containing single-walled carbon nanotubes (SWNTs), with a focus on analyzing the interfacial interaction between the CNT and the resin materials. The system is modeled using a four-phase composite, composed of a resin, voids, and bonded and debonded nanotubes. A micromechanical model is proposed to describe interfacial debonding evolution. To characterize the overall behavior, Weibull’s statistical function is employed to describe the varying probability of nanotube debonding under uniaxial loading. To address damping effects, the concept of interfacial “stick-slip” frictional motion between the nanotubes and the resin is proposed. The developed method is extended to analyze composites with randomly oriented nanotubes. The analytical results show that the critical shear stress, nanotube weight ratio and structure deformation are the factors affecting the damping characteristic. Experiments are also performed to verify the trends predicted by the analysis. Through comparing with neat resin specimens, the study shows that one can enhance damping by adding CNT fillers into polymeric resins. It is also observed that SWNT-based composites could achieve higher damping than composites with several other types (different size, surface area, density and stiffness) of fillers. These results confirm the possible advantage of using CNTs for damping enhancement.

Formulas For Natural Frequency And Mode Shape

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