Modeling and Semi-Analytic Stability Analysis for Dynamics of AC Machines

In this article, the mathematical modeling and dynamic analysis for a motion of a rigid body mounted on a vibrating base affected by a strongly nonlinear damping and an attractive Newtonian field are investigated. The governing equations are derived, and specific conditions for asymptotic stability of the motion are stated. Results of analytical analysis are used to identify some distinct types of motion, including the cases that are apparently regular or chaotic. A reduction technique via averaging is used to obtain the amplitude equation and the response diagrams to identify regions where the jump phenomenon may occur. Moreover, a simple analytical relationship between the parameters of the system, describing whether the jump phenomenon will be possible, is obtained. Homoclinic bifurcation diagrams are used to argue apparently that the chaotic behavior is slowly approaching a strange attractor at specific values of system parameters. Results of numerical solutions using the fourth-order Runge-Kutta method are closely coincided with the analytical ones to verify all types of motion.

show abstract

“…From Floquet theory, it is clear that this equation admits solutions of period π or 2π, cf. [33,34].…”

Section: Linear Analysismentioning

confidence: 99%

Modeling and Dynamic Analysis for a Motion of Mounted-Based Axisymmetric Rigid Body under Self-Excited Vibrations in an Attractive Newtonian Field

El-Borhamy

El-Sheikh

ali

2022

Mathematical Problems in Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…Rashad, I. Sobhy and M.K. El-Sayed [14] proposes an innovative semi-analytical procedure for the prediction of stable periodic responses of AC electrical machines capturing the correct selections of machine variables highlighting that, compared to the experimental results, the derived analytical results are relatively well suited to the practical cases studied.…”

mentioning

confidence: 99%

Preface to the Special Issue “Mathematical Modeling in Industrial Engineering and Electrical Engineering”—Special Issue Book

Versaci

2022

Mathematics

View full text Add to dashboard Cite

show abstract

An application of stability charts to prediction of buckling instability in tapered columns via Galerkin’s method

El-Borhamy,

Dabaon

2024

Discov Appl Sci

View full text Add to dashboard Cite

This work tackles the mathematical modeling of buckling problem to obtain their critical loads in tapered columns subjected to concentrated and axial distributed loads. The governing model is a general eigenvalue problem that has no exact solution due to some new terms included. A semi-analytical technique satisfying the boundary conditions is proposed for the solution procedure. The minimum residual Galerkin’s method is suggested due to its effectiveness as a semi-analytical tool for the buckling problem to obtain the buckling shape modes by using admissible periodic functions. The study investigates the buckling instability and the responses of tapered columns with different periodic trial shape functions as approximations to the exact solutions. Based on the eigenvalue problem, Galerkin’s method is employed to obtain the transition curves to represent the critical loads. The stability charts (Ince–Strutt diagrams) among the parameters of the problem are proposed to explain the elastic stability of different tapered columns subjected to different shapes of cross sections and distributed weights. Consequently, the influences of the included parameters on the critical buckling loads are discussed. Among the different tapered columns presented, some parameters in the proposed distributions have a big influence on the critical buckling load and the creation of the instability regions in the chart for the clamped-clamped boundary conditions. The results are verified using the analytical solutions for some specific known problems.

show abstract

Modeling and Semi-Analytic Stability Analysis for Dynamics of AC Machines

Cited by 4 publications

References 47 publications

Modeling and Dynamic Analysis for a Motion of Mounted-Based Axisymmetric Rigid Body under Self-Excited Vibrations in an Attractive Newtonian Field

Modeling and Dynamic Analysis for a Motion of Mounted-Based Axisymmetric Rigid Body under Self-Excited Vibrations in an Attractive Newtonian Field

Preface to the Special Issue “Mathematical Modeling in Industrial Engineering and Electrical Engineering”—Special Issue Book

An application of stability charts to prediction of buckling instability in tapered columns via Galerkin’s method

Contact Info

Product

Resources

About