4,415 research outputs found
Creep, Relaxation and Viscosity Properties for Basic Fractional Models in Rheology
The purpose of this paper is twofold: from one side we provide a general
survey to the viscoelastic models constructed via fractional calculus and from
the other side we intend to analyze the basic fractional models as far as their
creep, relaxation and viscosity properties are considered. The basic models are
those that generalize via derivatives of fractional order the classical
mechanical models characterized by two, three and four parameters, that we
refer to as Kelvin-Voigt, Maxwell, Zener, anti-Zener and Burgers. For each
fractional model we provide plots of the creep compliance, relaxation modulus
and effective viscosity in non dimensional form in terms of a suitable time
scale for different values of the order of fractional derivative. We also
discuss the role of the order of fractional derivative in modifying the
properties of the classical models.Comment: 41 pages, 8 figure
Structural identifiability of viscoelastic mechanical systems
We solve the local and global structural identifiability problems for
viscoelastic mechanical models represented by networks of springs and dashpots.
We propose a very simple characterization of both local and global structural
identifiability based on identifiability tables, with the purpose of providing
a guideline for constructing arbitrarily complex, identifiable spring-dashpot
networks. We illustrate how to use our results in a number of examples and
point to some applications in cardiovascular modeling.Comment: 3 figure
The effects of localized damping on structural response
The effect of localized structural damping on the excitability of higher order normal modes of the large space telescope was investigated. A preprocessor computer program was developed to incorporate Voigt structural joint damping models in a NASTRAN finite-element dynamic model. A postprocessor computer program was developed to select critical modes for low-frequency attitude control problems and for higher frequency fine-stabilization problems. The mode selection is accomplished by ranking the flexible modes based on coefficients for rate gyro, position gyro, and optical sensors, and on image-plane motions due to sinusoidal or random power spectral density force and torque inputs
Phase synchronization of coupled bursting neurons and the generalized Kuramoto model
Bursting neurons fire rapid sequences of action potential spikes followed by
a quiescent period. The basic dynamical mechanism of bursting is the slow
currents that modulate a fast spiking activity caused by rapid ionic currents.
Minimal models of bursting neurons must include both effects. We considered one
of these models and its relation with a generalized Kuramoto model, thanks to
the definition of a geometrical phase for bursting and a corresponding
frequency. We considered neuronal networks with different connection topologies
and investigated the transition from a non-synchronized to a partially
phase-synchronized state as the coupling strength is varied. The numerically
determined critical coupling strength value for this transition to occur is
compared with theoretical results valid for the generalized Kuramoto model.Comment: 31 pages, 5 figure
Rheological Model for Wood
Wood as the most important natural and renewable building material plays an
important role in the construction sector. Nevertheless, its hygroscopic
character basically affects all related mechanical properties leading to
degradation of material stiffness and strength over the service life.
Accordingly, to attain reliable design of the timber structures, the influence
of moisture evolution and the role of time- and moisture-dependent behaviors
have to be taken into account. For this purpose, in the current study a 3D
orthotropic elasto-plastic, visco-elastic, mechano-sorptive constitutive model
for wood, with all material constants being defined as a function of moisture
content, is presented. The corresponding numerical integration approach, with
additive decomposition of the total strain is developed and implemented within
the framework of the finite element method (FEM). Moreover to preserve a
quadratic rate of asymptotic convergence the consistent tangent operator for
the whole model is derived.
Functionality and capability of the presented material model are evaluated by
performing several numerical verification simulations of wood components under
different combinations of mechanical loading and moisture variation.
Additionally, the flexibility and universality of the introduced model to
predict the mechanical behavior of different species are demonstrated by the
analysis of a hybrid wood element. Furthermore, the proposed numerical approach
is validated by comparisons of computational evaluations with experimental
results.Comment: 37 pages, 13 figures, 10 table
E. Cartan's attempt at bridge-building between Einstein and the Cosserats -- or how translational curvature became to be known as {\em torsion}
\'Elie Cartan's "g\'en\'eralisation de la notion de courbure" (1922) arose
from a creative evaluation of the geometrical structures underlying both,
Einstein's theory of gravity and the Cosserat brothers generalized theory of
elasticity. In both theories groups operating in the infinitesimal played a
crucial role. To judge from his publications in 1922--24, Cartan developed his
concept of generalized spaces with the dual context of general relativity and
non-standard elasticity in mind. In this context it seemed natural to express
the translational curvature of his new spaces by a rotational quantity (via a
kind of Grassmann dualization). So Cartan called his translational curvature
"torsion" and coupled it to a hypothetical rotational momentum of matter
several years before spin was encountered in quantum mechanics.Comment: 36 p
Suitable weak solutions to the 3D Navier-Stokes equations are constructed with the Voigt Approximation
In this paper we consider the Navier-Stokes equations supplemented with
either the Dirichlet or vorticity-based Navier boundary conditions. We prove
that weak solutions obtained as limits of solutions to the Navier-Stokes-Voigt
model satisfy the local energy inequality. Moreover, in the periodic setting we
prove that if the parameters are chosen in an appropriate way, then we can
construct suitable weak solutions trough a Fourier-Galerkin finite-dimensional
approximation in the space variables
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