The effect of fractional thermoelasticity on a two-dimensional problem of a mode I crack in a rotating fiber-reinforced thermoelastic medium

This article is concerned with the effect of rotation on the general model of the equations of the generalized thermoe- lasticity for a homogeneous isotropic elastic half-space solid, whose surface is subjected to a Mode-I crack problem. The fractional order theory of thermoelasticity is used to obtain the analytical solutions for displacement components, force stresses, and temperature. The boundary of the crack is subjected to a prescribed stress distribution and temperature. The normal mode analysis technique is used to solve the resulting non-dimensional coupled governing equations of the problem. The variations of the considered variables with the horizontal distance are illustrated graphically. Some particular cases are also discussed in the context of the problem. Effects of the fractional parameter, reinforcement, and rotation on the varia- tions of different field quantities inside the elastic medium are analyzed graphically. Comparisons are made between the results in the presence and those in the absence of fiber-reinforcing, rotating and fractional parameters.

Using the Fractional Order Method to Generalize Strengthening Buffer Operator and Weakening Buffer Operator

To reveal the relationship between a weakening buffer operator and strengthening buffer operator, the traditional integer order buffer operator is extended to one that is fractional order. Fractional order buffer operator not only can generalize the weakening buffer operator and the strengthening buffer operator, but also results in small adjustments of the buffer effect.The effectiveness of the grey model(GM(1,1)) with the fractional order buffer operator is validated by six cases.

Dynamic response of bilayered saturated porous media based on fractional thermoelastic theory

Considering the thermal contact resistance and elastic wave impedance at the interface,in this paper we theoretically investigate the thermo-hydro-mechanical(THM)coupling dynamic response of bilayered saturated porous media.Fractional thermoelastic theory is applied to porous media with imperfect thermal and mechanical contact.The analytical solutions of the dynamic response of the bilayered saturated porous media are obtained in frequency domain.Furthermore,the effects of fractional derivative parameters and thermal contact resistance on the dynamic response of such media are systematically discussed.Results show that the effects of fractional derivative parameters on the dynamic response of bilayered saturated porous media are related to the thermal contact resistance at the interface.With increasing thermal contact resistance,the displacement,pore water pressure,and stress decrease gradually.

EFFECT OF FRACTIONAL ORDER PARAMETER ON THERMOELASTIC BEHAVIORS IN INFINITE ELASTIC MEDIUM WITH A CYLINDRICAL CAVITY

The thermal shock problems involved with fractional order generalized theory is studied by an analytical method. The asymptotic solutions for thermal responses induced by transient thermal shock are derived by means of the limit theorem of Laplace transform. An infinite solid with a cylindrical cavity subjected to a thermal shock at its inner boundary is studied. The propagation of thermal wave and thermal elastic wave, as well as the distributions of displacement, temperature and stresses are obtained from these asymptotic solutions. The investigation on the effect of fractional order parameter on the propagation of two waves is also conducted.

SOLVABILITY FOR FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATION BOUNDARY VALUE PROBLEMS AT RESONANCE

The paper deals a fractional functional boundary value problems with integral boundary conditions. Besed on the coincidence degree theory, some existence criteria of solutions at resonance are established.