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491.
Leif Kari 《Continuum Mechanics and Thermodynamics》2017,29(5):1027-1046
The constitutive equations of chemically and physically ageing rubber in the audible frequency range are modelled as a function of ageing temperature, ageing time, actual temperature, time and frequency. The constitutive equations are derived by assuming nearly incompressible material with elastic spherical response and viscoelastic deviatoric response, using Mittag-Leffler relaxation function of fractional derivative type, the main advantage being the minimum material parameters needed to successfully fit experimental data over a broad frequency range. The material is furthermore assumed essentially entropic and thermo-mechanically simple while using a modified William–Landel–Ferry shift function to take into account temperature dependence and physical ageing, with fractional free volume evolution modelled by a nonlinear, fractional differential equation with relaxation time identical to that of the stress response and related to the fractional free volume by Doolittle equation. Physical ageing is a reversible ageing process, including trapping and freeing of polymer chain ends, polymer chain reorganizations and free volume changes. In contrast, chemical ageing is an irreversible process, mainly attributed to oxygen reaction with polymer network either damaging the network by scission or reformation of new polymer links. The chemical ageing is modelled by inner variables that are determined by inner fractional evolution equations. Finally, the model parameters are fitted to measurements results of natural rubber over a broad audible frequency range, and various parameter studies are performed including comparison with results obtained by ordinary, non-fractional ageing evolution differential equations. 相似文献
492.
In this paper, new nonlinear dynamic formulations for belt drives based on the three-dimensional absolute nodal coordinate formulation are developed. Two large deformation three-dimensional finite elements are used to develop two different belt-drive models
that have different numbers of degrees of freedom and different modes of deformation. Both three-dimensional finite elements
are based on a nonlinear elasticity theory that accounts for geometric nonlinearities due to large deformation and rotations.
The first element is a thin-plate element that is based on the Kirchhoff plate assumptions and captures both membrane and bending stiffness effects. The other three-dimensional
element used in this investigation is a cable element obtained from a more general three-dimensional beam element by eliminating degrees of freedom which are not significant in
some cable and belt applications. Both finite elements used in this investigation allow for systematic inclusion or exclusion
of the bending stiffness, thereby enabling systematic examination of the effect of bending on the nonlinear dynamics of belt
drives. The finite-element formulations developed in this paper are implemented in a general purpose three-dimensional flexible
multibody algorithm that allows for developing more detailed models of mechanical systems that include belt drives subject
to general loading conditions, nonlinear algebraic constraints, and arbitrary large displacements. The use of the formulations
developed in this investigation is demonstrated using two-roller belt-drive system. The results obtained using the two finite-element
formulations are compared and the convergence of the two finite-element solutions is examined. 相似文献
493.