Fractional Derivative Viscoelastic Model for the Analysis of Two Colliding Spherical Shells

2012 ◽  
Author(s):  
Yury A. Rossikhin ◽  
Marina V. Shitikova
Keyword(s):  
Fractional Derivative ◽  
Equations Of Motion ◽  
Viscoelastic Model ◽  
Wave Fronts ◽  
Spherical Shells ◽  
Reflected Waves ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
The Moment ◽  
Contact Domain

The collision of two isotropic spherical shells is investigated for the case when the viscoelastic features of the shells represent themselves only in the place of contact and are governed by the standard linear solid model with fractional derivatives. Thus, the problem concerns the shock interaction of two shells, wherein the generalized fractional-derivative standard linear law instead of the Hertz contact law is employed as a low of interaction. The pans of the shells beyond the contact domain are assumed to be elastic, and their behavior is described by the equations of motion which take rotary inertia and shear deformations into account. The model developed here suggests that after the moment of impact quasi-longitudinal and quasi-transverse shock waves are generated, which then propagate along the spherical shells. Due to the short duration of contact interaction, the reflected waves are not taken into account. The solution behind the wave fronts is constructed with the help of the theory of discontinuities. To determine the desired values behind the wave fronts, one-term ray expansions are used, as well as the equations of motion of the contact domains for the both spherical shells.

scholarly journals Analysis of Two Colliding Thin Spherical Shells

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Shock Waves ◽  
Wave Theory ◽  
Contact Theory ◽  
Hertz Contact ◽  
Wave Fronts ◽  
Spherical Shells ◽  
Elastic Shells ◽  
Hertz Contact Theory ◽  
The Moment ◽  
Contact Domain

In the present paper, the collision of two elastic spherical shells is investigated using the wave theory of impact. The model developed here suggests that after the moment of impact quasi-longitudinal and quasi-transverse shock waves are generated, which then propagate along the spherical shells. The solution behind the wave fronts is constructed with the help of the theory of discontinuities. Since the local bearing of the materials of the colliding elastic shells is taken into account, then the solution in the contact domain is found via the Hertz contact theory.

Discrete Spectral Modelling of Continuous Structures With Fractional Derivative Viscoelastic Behaviour

2007 ◽  
Author(s):  
Giuseppe Catania ◽  
Silvio Sorrentino
Keyword(s):  
Fractional Derivative ◽  
State Space ◽  
Linear Models ◽  
Equations Of Motion ◽  
Ritz Method ◽  
Computational Effort ◽  
Viscoelastic Behaviour ◽  
Rheological Models ◽  
Standard Linear Solid ◽  
Standard Linear

Fractional derivative rheological models were recognised to be very effective in describing the viscoelastic behaviour of materials, especially of polymers, and when applied to dynamic problems the resulting equations of motion, after a fractional state-space expansion, can still be studied in terms of modal analysis. But the growth in matrix dimensions brought about by this expansion is in general so fast as to make the calculations too cumbersome. In this paper a discretization method for continuous structures is presented, based on the Rayleigh-Ritz method, aimed at reducing the computational effort. The solution of the equation of motion is approximated by a linear combination of shape-functions selected among the analytical eigenfunctions of standard known structures. The resulting condensed eigen-problem is then expanded in a low dimension fractional state-space. The Fractional Standard Linear Solid is the adopted rheological model, but the same methodology could be applied to problems involving different fractional derivative linear models. Examples regarding two different continuous structures are proposed and discussed in detail.

scholarly journals Application of a Viscoelastic Model to Creep Settlement of High-Fill Embankments

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Liang Jia ◽  
Guangli Huang
Keyword(s):  
Viscoelastic Model ◽  
In Situ Monitoring ◽  
One Dimensional ◽  
Time Calculation ◽  
Load Increase ◽  
Hereditary Integral ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Precise Prediction

In order to predict the creep settlement of high-fill embankments, the time-dependent viscoelastic model of Poynting–Thomson (the standard linear solid) has been chosen to represent the creep behavior of soils. In the present study, the hereditary integral was applied to calculate the strain while the load increase is varied with time. Calculation expressions of the creep settlement of an embankment during and after construction were obtained under one-dimensional compression conditions. Using this approach, the three parameters of every layer can be determined and adjusted to accommodate in situ monitoring data. The calculated results agreed well with those from the field, which imply that the method proposed in this paper can give a precise prediction of creep settlement of high-fill embankments.

Stability Analysis for Haptic Rendering of Virtual Kelvin Viscoelastic Objects

2010 ◽  
Author(s):  
Tama´s Kerekes ◽  
Ali Bonakdar ◽  
Jo´zsef Ko¨vecses
Keyword(s):  
Pid Control ◽  
Viscoelastic Model ◽  
Solid Model ◽  
Haptic Display ◽  
Single Degree Of Freedom ◽  
Kelvin Model ◽  
Standard Linear Solid Model ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
The Stability

In this paper we investigate the stability properties of a single degree of freedom (DoF) haptic display while a virtual viscoelastic object is touched where the viscoelastic object is modeled using the standard linear solid model (also called the Kelvin model). We will demonstrate that this model leads to a discrete-time PID control-like representation of the virtual environment. A detailed dynamic analysis and simulations are presented in this paper with a particular attention to determine stability charts in the space of the parameters given by the virtual viscoelastic model.

A Nonlinear Viscoelastic Model for Polyester Mooring Line Analysis

2011 ◽  
Author(s):  
J. W. Kim ◽  
J. H. Kyoung ◽  
A. Sablok ◽  
K. Lambrakos
Keyword(s):  
Dynamic Stiffness ◽  
Relaxation Times ◽  
Viscoelastic Model ◽  
Line Tension ◽  
Mooring Line ◽  
Prony Series ◽  
Nonlinear Viscoelastic ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Nonlinear Viscoelastic Model

A viscoelastic model considering multiple relaxation times and nonlinearity in dynamic stiffness has been developed. The model is based on the Maxwell-Wiechert model, which is an extension of an earlier model based on the standard linear solid (SLS) model. The time-dependent elastic modulus of polyester rope is represented by a 4-term Prony series (MW4 model). Relaxation times and coefficients of the Prony series have been determined from test data of dynamic stiffness at different loading periods. Nonlinearity in dynamic stiffness is considered by iteratively adjusting the dynamic stiffness of polyester rope based on the calculated mean load on the rope. The developed model has been applied in the global performance analysis of a Spar platform moored in deep water. Platform offset and mooring-line tension comparisons between the SLS and the MW4 models are given for intact and broken mooring-line cases.

Hysteresis and Viscoelastic Modeling of a Piezo-Optic Voltage Sensor

2008 ◽  
Author(s):  
Charles E. Seeley ◽  
Glen Koste ◽  
Craig Stringer
Keyword(s):  
Viscoelastic Model ◽  
Voltage Sensor ◽  
Sensor Technology ◽  
Optical Wave ◽  
Viscoelastic Effects ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Optical Wave Guide ◽  
Electro Magnetic ◽  
Viscoelastic Modeling

There is growing interest in sensor technology that is immune to electro-magnetic interference. By nature, development of this technology covers multiple physical domains including electronics, optics, mechanics and materials. This paper discusses development of a mathematical model to compensate for the hysteresis and viscoelastic effects of a piezo-optic voltage sensor. The sensor utilizes piezoelectric fibers with interdigitated electrodes coupled to an optical wave guide via a dielectric matrix. The unknown voltage energizes the piezoelectric fibers to deform fiber Bragg gratings (FBGs) on the waveguide. Therefore, a measurable change in wavelength is related to the unknown voltage. The hysteresis model is based on Rayleigh’s Law of magnetization that is adapted for the coupled piezoelectric and optic response, and the viscoelastic model is based on the standard linear solid model using springs and dashpots in combination. Model results compare favorably with experimental results.

Viscoelastic Behavior of a Centrally Loaded Circular Film Being Clamped at the Circumference

2007 ◽  
Vol 1049 ◽  
Author(s):  
Michelle L Oyen ◽  
Kuo-kang Liu ◽  
Kai-tak Wan
Keyword(s):  
Theoretical Model ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Viscoelastic Response ◽  
Circular Membrane ◽  
Hydrogel Membrane ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Preliminary Stress ◽  
Relaxation Experiments

AbstractA new theoretical model is constructed for the viscoelastic response of a clamped circular membrane deformed by a spherical indenter, using the classical Maxwell and Standard Linear Solid (SLS) constitutive equations. Preliminary stress-relaxation experiments are performed for a hydrogel membrane and the corresponding data fitted to the SLS-based viscoelastic model.

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