Sezgin Altay Demirbağ

Approximate solutions for nonlinear oscillation of a mass attached to a stretched elastic wire

In this paper, the approximate solutions of the mathematical model of a mass attached to a stretched elastic wire are presented. At the beginning of the study, the equation of motion is derived in a detailed way. Hes max-min approach, Hes frequency-amplitude method and the parameter-expansion method are implemented to solve the established model. The numerical results are further compared with the approximate analytical solutions for both a small and large amplitude of oscillations, and a very good agreement is observed. The relative errors are computed to illustrate the strength of agreement between the numerical and approximate analytical results.

Approximate solutions for nonlinear transverse vibrations of elastically restrained tapered beams

This paper introduces the approximate solutions of the mathematical model of an elastically restrained tapered beam. At the beginning of the study, the equation of motion is derived in a detailed way. The frequency–amplitude relation is deduced and solved numerically. The nonlinear natural frequencies for the transverse vibrations of an elastically restrained tapered beam are provided using Mathematica software. The max–min approach, the frequency–amplitude method and the parameter-expansion method are applied in order to obtain an approximated solution. The approximate analytical results are further compared with the numerical results for both small and large amplitude oscillations, and very good agreement is observed.

Hyper-Generalized Quasi Einstein Manifolds Satisfying Certain Ricci Conditions

In the present paper, we deal with hyper-generalized quasi Einstein manifold. First, we investigate geometric properties of this manifold with respect to its generators. Then, we study some classes of hypergeneralized quasi Einstein manifold satisfying certain Ricci conditions. Precisely, we obtain some necessary conditions for hyper-generalized quasi Einstein manifold to be a generalized quasi Einstein or a quasi Einstein manifold.

Approximate Solutions for a Nonlinear Transverse Vibration of an Elastically Restrained Tapered Beam

This paper introduces the approximate solutions of the mathematical model of elastically restrained tapered beam. At the beginning of the study, the equation of motion is derived. The frequency‐amplitude relation is deduced and numerically solved. Hamiltonian approach method is implemented to solve the established model. The numerical results for the first, the second and the third order approximations are further compared with the approximate analytical solutions for both small and large amplitude of oscillations, and a very good agreement is observed.