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

Recent advances in nonlinear passive vibration isolators

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

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

Interfacial damping characteristics of carbon nanotube-based composites

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Formulas For Natural Frequency And Mode Shape

A nonlinear rubber material model is presented, where influences of frequency and dynamic amplitude are taken into account through fractional order viscoelasticity and plasticity, respectively The problem of simultaneously modeling elastic, viscoelastic, and friction contributions is removed by additively splitting them Due to the fractional order representation mainly, the number of parameters of the model remains low, rendering an easy fitting of the values from tests on material samples The proposed model is implemented in a general-purpose finite element (FE) code Since commercial FE codes do not contain any suitable constitutive model that represents the full dynamic behavior of rubber compounds (including frequency and amplitude dependent effects), a simple approach is used based on the idea of adding stress contributions from simple constitutive models: a mesh overlay technique, whose basic idea is to create a different FE model for each material definition (fractional derivative viscoelastic and elastoplastic), all with identical meshes but with different material definition, and sharing the same nodes Fractional-derivative viscoelasticity is implemented through user routines and the algorithm for that purpose is described, while available von Mises' elastoplastic models are adopted to take rate-independent effects into account Satisfactory results are obtained when comparing the model results with tests carried out in two rubber bushings at a frequency range up to 500 Hz, showing the ability of the material model to accurately describe the complex dynamic behavior of carbon-black filled rubber compounds

A Nonlinear Rubber Material Model Combining Fractional Order Viscoelasticity and Amplitude Dependent Effects

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

The nonlinear, preload-dependent dynamic stiffness of a cylindrical vibration isolator is examined via measurements and modeling within an audible frequency range covering 50 to 1000 Hz at various preloads. The stiffness is found to depend strongly on frequency-resulting in peaks and troughs, and on preload-particularly above 500 Hz. The problems of simultaneously modeling the rubber prestrain dependence and its audible short-term response are removed by adopting a nearly incompressible material model, being elastic in dilatation while displaying viscoelasticity in deviation. The latter exhibits a time strain separable relaxation tensor with a single function embodying its time dependence. This function is based on a continuous fractional order derivative model, the main advantage being the minimum number of parameters required to successfully model the rubber properties over a broad structure-borne sound frequency domain, while embodying a continuous distribution of relaxation time. The weak formulations corresponding to the stiffness problem are solved by an updated Lagrangian nonlinear finite-element procedure. The model and measurement results agree strikingly well with static and dynamic measurements throughout the whole frequency domain for the examined preloads.

Leif Kari

Papers

A Nonlinear Rubber Material Model Combining Fractional Order Viscoelasticity and Amplitude Dependent Effects

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

On the dynamic stiffness of preloaded vibration isolators in the audible frequency range: Modeling and experiments

Frequency and amplitude dependence of the axial and radial stiffness of carbon-black filled rubber bushings

Testing of nonlinear interaction effects of sinusoidal and noise excitation on rubber isolator stiffness