Highly accurate analytical solution for free vibrations of strongly nonlinear Duffing oscillator

Based on the suggested parameter, a new analytical perturbation technique is presented to obtain highly ordered accurate analytical solutions for nonlinear Duffing oscillator with nonlinearity of high order. Comparing the obtained results with the numerical and other previously published results reveals the usefulness and correctness of the present technique. It is shown that the results are valid for small and large amplitudes. Indeed, it is found that our proposed technique produces more accurate and computationally results than the rival known methods. The obtained results show the efficiency and capability of the present perturbation technique to be applied to various strongly nonlinear differential equations.

Hunting for QCD strings in e+e−-annihilation

We develop a new mathematical method of extraction of nonperturbative corrections in QCD. The main attention is directed to the study of dimension 2 operator and its properties. The ordinary perturbation theory (PT) and analytical perturbation theory (APT) are used. The D-function is explored in dependence on both Q2 and Borel parameter M2. It is shown that the C2 coeffcient of the dimension 2 operator is negative and its compatibility to zero depends on choice of PT or APT and can vary in chosen ranges of M2. The strong (anti)correlation between C2 and gluon condensate found previously is confirmed.

An analytical approach for vibration analysis of laminated orthotropic beam based on nonlocal theory

On the basis of the first-order shear deformation beam theory, free vibrations and dynamic response of orthotropic laminated beam subjected to transient and harmonic loading have been studied based on Eringen’s nonlocal elasticity theory. Three coupled nonlinear governing partial differential equations of motion are derived using Hamilton’s principle. The purely analytical perturbation method as well as the method of multiple scales are used for the solution. A parametric study is carried out to realize the effect of small-scale and axial static load on the natural frequencies, transient, and harmonic responses. In addition, the obtained results have been compared with numerical solutions and literature.

BUOYANCY AND CHEMICAL REACTION EFFECTS ON MHD FREE CONVECTIVE SLIP FLOW OF NEWTONIAN AND POLAR FLUID THROUGH POROUSMEDIUM IN THE PRESENCE OF THERMAL RADIATION AND OHMIC HEATING WITH DUFOUR EFFECT

The present paper investigates the effects of thermal radiation, joule heating on an unsteady hydro magnetic free convective flow of a viscous electrically conductive Newtonian and polar fluid past a semi-infinite vertical plate embedded in a porous media in the presence of heat absorption, chemical reaction, slip flow and Dufour effect. Analytical perturbation solutions are obtained for the velocity, temperature and concentration fields as well as for the skin friction coefficient, Nusselt number and Sharewood number. The results are presented in graphical forms to study the effects of various parameters.

Magnetohydrodynamic radiative nanofluid flow over a rotating surface with Soret effect

Purpose The purpose of this paper is to theoretically investigate the boundary layer nature of magnetohydrodynamic nanofluid flow past a vertical expanding surface in a rotating geometry with viscous dissipation, thermal radiation, Soret effect and chemical reaction. Design/methodology/approach The self-similarity variables are deliberated to transmute the elementary governing equations. The analytical perturbation technique is used to elaborate the united nonlinear ODEs. Findings To check the disparity on the boundary layer nature, the authors measured two nanofluids, namely, Cu-water and Cu-Kerosene based nanofluids. It is found that the Cu-water is effectively enhancing the thermal conductivity of the flow when compared with the Cu-kerosene. Originality/value Till now no analytical studies are reported on heat transfer enhancement of the rotating nanofluid flow by considering two different base fluids.

Antisymmetric Post-Buckling Localization of an Infinite Column on a Nonlinear Foundation with Softening

Field observations reveal that very long members such as railway tracks and pipelines which are subjected to axial compression, induced usually by temperature and/or pressure increases, experience localized buckling. This paper presents a solution for the antisymmetric post-buckling of such members when restrained by a nonlinear foundation that includes softening effects. The principle of minimum total potential is invoked in order to develop the governing differential equations of buckling, as well as the non-linear equations of equilibrium in the post-buckled range of structural response. In order to solve these equations, a semi-analytical solution is proposed based on a perturbation technique, as well as a numerical technique based on a single shooting procedure for the solution of boundary value problems. The results of the analysis show that the post-buckling configuration of the column changes from a lengthwise periodic mode at the initial stages of loading to an isolated sinusoidal mode at the later stages of post-buckling, which represents a localization in the post-buckling range. This response is typical of that observed often in practice. Comparisons between the results of the perturbation technique and those of the numerical approach indicate that the semi-analytical perturbation solution predicts the initial post-buckling response of a column on a nonlinear foundation quite accurately.