Weak solvability of fractional Voigt model of viscoelasticity

A short overview of recent results on the effects of pressure (collisions) regarding the shape of isolated infrared lines of water vapour is presented. The first part of this study considers the basic collisional quantities, which are the pressure-broadening and -shifting coefficients, central parameters of the Lorentzian (and Voigt) profile and thus of any sophisticated line-shape model. Through comparisons of measured values with semi-classical calculations, the influences of the molecular states (both rotational and vibrational) involved and of the temperature are analysed. This shows the relatively unusual behaviour of H 2 O broadening, with evidence of a significant vibrational dependence and the fact that the broadening coefficient (in cm −1 atm −1 ) of some lines increases with temperature. In the second part of this study, line shapes beyond the Voigt model are considered, thus now taking ‘velocity effects’ into account. These include both the influence of collisionally induced velocity changes that lead to the so-called Dicke narrowing and the influence of the dependence of collisional parameters on the speed of the radiating molecule. Experimental evidence of deviations from the Voigt shape is presented and analysed. The interest of classical molecular dynamics simulations, to model velocity changes, together with semi-classical calculations of the speed-dependent collisional parameters for line-shape predictions from ‘first principles’, are discussed.

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Non-Newtonian pulsating blood flow-induced dynamic instability of visco-carotid artery within soft surrounding visco-tissue using differential cubature method

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406214566038 ◽

2015 ◽

Vol 229 (16) ◽

pp. 3002-3012 ◽

Cited By ~ 3

Author(s):

A Tabatabaie Arani ◽

Ali Ghorbanpour Arani ◽

Reza Kolahchi

Keyword(s):

Blood Flow ◽

Carotid Arteries ◽

Shell Theory ◽

Dynamic Instability ◽

Current Model ◽

Biomechanical Model ◽

Realistic Model ◽

Instability Region ◽

Tissue Stiffness ◽

Voigt Model

The high blood rate that often occurs in carotid arteries may play a role in artery failure and tortuosity which leads to blackouts, transitory ischemic attacks, and other diseases. However, dynamic analysis of carotid arteries conveying blood is lacking. The objective of this study was to present a biomechanical model for dynamic instability analysis of the embedded carotid arteries conveying pulsating blood flow. In order to present a realistic model, the carotid arteries and tissues are assumed viscoelastic using Kelvin–Voigt model. Carotid arteries are modeled as elastic cylindrical vessels based on Mindlin cylindrical shell theory (MCST). One of the main advantages of this study is considering the pulsating non-Newtonian nature of the blood flow using Carreau, Casson, and power law models. Applying energy method, Hamilton’s principle and differential cubature method (DCM), the dynamic instability region (DIR) of the visco-carotid arteries is obtained. The detailed parametric study is conducted, focusing on the combined effects of the elastic medium and non-Newtonian models on the dynamic instability of the visco-carotid arteries. It can be seen that with increasing the tissue stiffness, the natural frequency of visco-carotid arteries decreases. The current model provides a powerful tool for further experimental investigation about arterial tortuosity.

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Nonlinear Vibrations of Viscoelastic Plane Truss Under Harmonic Excitation

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455414500096 ◽

2014 ◽

Vol 14 (04) ◽

pp. 1450009 ◽

Cited By ~ 7

Author(s):

Andrew Yee Tak Leung ◽

Hong Xiang Yang ◽

Ping Zhu

Keyword(s):

Steady State ◽

Fractional Derivatives ◽

Harmonic Excitation ◽

Homotopy Continuation ◽

Response Curves ◽

System A ◽

Structural Responses ◽

Voigt Model ◽

Two Degree Of Freedom ◽

Steady State Solutions

This paper is concerned with the steady state bifurcations of a harmonically excited two-member plane truss system. A two-degree-of-freedom Duffing system having nonlinear fractional derivatives is derived to govern the dynamic behaviors of the truss system. Viscoelastic properties are described by the fractional Kelvin–Voigt model based on the Caputo definition. The combined method of harmonic balance and polynomial homotopy continuation is adopted to obtain steady state solutions analytically. A parametric study is conducted with the help of amplitude-response curves. Despite its seeming simplicity, the mechanical system exhibits a wide variety of structural responses. The primary and sub-harmonic resonances and chaos are found in specific regions of system parameters. The dynamic snap-through phenomena are observed when the forcing amplitude exceeds some critical values. Moreover, it has been shown that, suppression of undesirable responses can be achieved via changing of viscosity of the system.

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CONTACT PROBLEMS FOR NONLINEARLY ELASTIC MATERIALS: WEAK SOLVABILITY INVOLVING DUAL LAGRANGE MULTIPLIERS

The ANZIAM Journal ◽

10.1017/s1446181111000629 ◽

2010 ◽

Vol 52 (2) ◽

pp. 160-178 ◽

Cited By ~ 15

Author(s):

A. MATEI ◽

R. CIURCEA

Keyword(s):

Lagrange Multipliers ◽

Variational Equation ◽

Small Deformation ◽

Contact Problems ◽

Point Theory ◽

The Body ◽

Elastic Materials ◽

Weak Formulation ◽

Nonlinearly Elastic ◽

Weak Solvability

AbstractA class of problems modelling the contact between nonlinearly elastic materials and rigid foundations is analysed for static processes under the small deformation hypothesis. In the present paper, the contact between the body and the foundation can be frictional bilateral or frictionless unilateral. For every mechanical problem in the class considered, we derive a weak formulation consisting of a nonlinear variational equation and a variational inequality involving dual Lagrange multipliers. The weak solvability of the models is established by using saddle-point theory and a fixed-point technique. This approach is useful for the development of efficient algorithms for approximating weak solutions.

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