Floquet analysis of linear dynamic RLC circuits

El-Borhamy, Mohamed; Rashad, Essam M.; Sobhy, Ismail

doi:10.1515/phys-2020-0136

Cited by 7 publications

(9 citation statements)

References 34 publications

(38 reference statements)

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“…As it is clearly shown in the comparison, the semi-analytical solution is comparable with the numerical one at different values of the perturbation parameter. All results exhibit mostly that the stability characterization achieved merely in the domain of definition: |h| < 1, which is coinciding with the results in [5,38].…”

Section: Construction Of Semi-analytical Solutions Via Vimsupporting

confidence: 89%

“…Indeed, the solution (y(x)) of Equation 11represents the net positive charge that moved past an instantaneous point in a specified direction in the shown circuit under the specified initial conditions and the absence of the voltage supply (V s ), cf. [5].…”

Section: The Governing Dynamic Modelmentioning

confidence: 99%

“…So that, in the case of zero energy-rate, we look for the transition curves by the relation between α and h at fixed values of Q with the period T = π or T = 2π according to Floquet's theory, cf. [5]. The resulting figure at Γ in the domain |h| < 1 is shown in Figure 4 starting with the value of (0, 1).…”

Section: Construction Of Stability Domainsmentioning

confidence: 99%

“…In contrast, analytical descriptions can be of great help in obtaining a qualitative understanding of the complex dynamical behavior, even simple heuristic analytical results may provide a fast and relatively accurate form for maneuver analysis, cf. [4][5][6][7]. For instance, in most engineering control applications, it appears that the trend for autonomous engineering control schemes dictate the use of compact, simple, and analytical expression responses for evolutionary systems, cf.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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In this article, a semi-analytical technique is proposed to predict stable sustained periodic responses of AC electrical machines. Based on such desired outputs, the proper selections of machine variables are captured, such as the perturbation parameter arisen from the relative movement between the stationary and rotating parts. Compared to the experimental results, the derived analytical results are relatively well-fitted with the studied practical cases.

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Section: Construction Of Semi-analytical Solutions Via Vimsupporting

confidence: 89%

Section: The Governing Dynamic Modelmentioning

confidence: 99%

Section: Construction Of Stability Domainsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

et al. 2021

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“…Necessary conditions for generating periodic solutions, and the stability of periodic solution of equation 4at τ c are given by using the method based on Poincare-Lindstedt method and harmonic balance method, cf. [5,36,37].…”

Section: Construction Of Periodic Solutionmentioning

confidence: 99%

Chaos Prediction in Fractional Delayed Energy‐Based Models of Capital Accumulation

2021

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This paper presents the nonlinear dynamic analysis of energy-based models arisen from the applied systems characterized by the energy transport in the presence of fractional order derivative and time delay. The studied model is the fractional version of Bianca-Ferrara-Dalgaard-Strulik (BFDS) model of economy which is viewed as a transport network for energy in which the law of motion of capital occurs. By considering the time delay as bifurcation parameter, a proof to investigate the existence of Hopf bifurcation and the phase lock solutions using the Poincare-Linstedt and the harmonic balance methods is given. At definite values of time delay, period-doubling bifurcations followed up by the consequences of chaotic states are detected. Simulation results assure that the BFDS model can generate new (hyper) chaotic attractors beyond half order derivatives through the effect of the time delay on that system. In accordance with the literatures related to the problem of chaos, the concluded results confirm the proposed theorem by El-Borhamy in which the time delay possesses the ability to change the dynamic state of nonlinear systems from regular to chaotic within the fractional order derivative domain.

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

El-Borhamy,

Dabaon

2024

Discov Appl Sci

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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.

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Floquet analysis of linear dynamic RLC circuits

Cited by 7 publications

References 34 publications

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

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

Chaos Prediction in Fractional Delayed Energy‐Based Models of Capital Accumulation

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

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