A set of wave equations with fractional loss operators in time and space are analyzed. The fractional Szabo equation, the power law wave equation and the causal fractional Laplacian wave equation are all found to be low-frequency approximations of the fractional Kelvin-Voigt wave equation and the more general fractional Zener wave equation. The latter two equations are based on fractional const...

....................................................................................................................... ii DEDICATION................................................................................................................... iv ACKNOWLEDGEMENTS................................................................................................ v VITA.............................

high weissenberg boundary layer flow of viscoelastic fluids on a stretching surface has been studied. the flow is considered to be steady and two dimensional. flows of viscoelastic liquids at high weissenberg number exhibit stress boundary layers near walls. these boundary layers are caused by the memory of the fluid. upon proper scaling and by means of an exact similarity transformation, the n...

The forced vibration behaviors are examined for nonlocal strain gradient nanobeams with surface effects subjected to a moving harmonic load travelling with a constant velocity in terms of three beam models namely, the Euler-Bernoulli, Timoshenko and modified Timoshenko beam models. The modification for nonlocal strain gradient Timoshenko nanobeams is exerted to the constitutive equations by exc...

The present investigation analysis a problem of r­­­eflection and transmission at an interface of two micropolar orthotropic piezothermoelastic media. The basic equations and constitutive relations for micropolar orthotropic piezothermoelastic media for G-L theory are derived. The expressions for amplitude ratios corresponding to reflected and transmitted waves are derived analytically. The eff...

The capability of sand constitutive models is remarkably improved by taking into account the effect of soil state in their formulations. In this study, it has been shown that considering the effect of soil state leads to better simulation of soil instability of shear banding type. To this aim, constitutive equations of a state dependent sand model are explained first. Consequently, the general ...

In this paper, an analytical study is made for the dynamic behavior of human brain tissue under transient loading. In this analytical model the Mooney-Rivlin constitutive law is coupled with visco-elastic constitutive equations to take into account both the nonlinear and time-dependent mechanical behavior of brain tissue. Five ordinary differential equations representing the relationships of fi...

in this paper, free vibration of functionally graded rectangular simply supported thick plates based on two variable refined plate theory is presented. according to a power-law distribution, the mass density and elasticity modulus of the plate are considered to vary while poisson’s ratio is constant. in order to extract the five constitutive equations of motion, hamilton principle is employed. ...

I calculate the hydrodynamic limit of the BGK approximation of the Boltzmann equation for the case of a long stress relaxation time and find that the stress obeys a viscoelastic constitutive equation. The constitutive equation is different from standard constitutive equations used for polymeric liquids in that it is not “objective” because inertial effects are important. I calculate the exact s...