Energy-rate method and stability chart of parametric vibrating systems

Jazar, Reza N.; Mahinfalah, M.; Mahmoudian, Nina; Rastgaar, Mo

doi:10.1590/s1678-58782008000300002

Cited by 14 publications

(3 citation statements)

References 7 publications

(7 reference statements)

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“…Based on the constructed semi-analytical solutions, it is readily to apply the energy-rate method to obtain three dimensional illustration of stability surface showing a sense of relative stability of parameter plane, cf. [48][49][50]. Based on the shown figure, Figure 3, the stability regions lie on the domain |h| < 1.…”

Section: Construction Of Stability Domainsmentioning

confidence: 82%

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 Stability Domainsmentioning

confidence: 82%

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

et al. 2021

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“…(34) undergoes no change. To proceed, we first make use of the energy-rate method [4] to plot an energy transfer diagram of the dimensionless system of equations as shown in…”

Section: Parametrically Enhanced Dynamicsmentioning

confidence: 99%

“…Qualitative predictions of perturbation analysis are exhaustively checked by numerical simulation. The frequency and intensity requirements for efficient energy transfer between electric and magnetic degrees of freedom driven by light are examined using the energy-rate method [4]. Finally, the equations of motion are shown to reduce to a complex Mathieu equation.…”

Section: Introductionmentioning

confidence: 99%

Light-induced dynamics in the Lorentz oscillator model with magnetic forces

Fisher

Rand

2010

Phys. Rev. A

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The classical Lorentz oscillator model of bound electron motion ordinarily excludes magnetic forces at nonrelativistic intensities for the simple reason that their magnitude is small. However, perturbative and numerical results show that when the v × B term is retained, dynamically enhanced terms give rise to large amplitude, magnetically induced charge displacements at zero frequency and at twice the driving frequency in the Cartesian laboratory frame. Numerical simulations of electron motion are in accord with the predictions of perturbative theory for steady-state motion in the classical picture. Direct integration shows that magnetic response which is comparable to electric dipole response can arise in transparent dielectrics at optical frequencies. Parametric instability in the equations of motion is implicated as the source of rapid energy transfer from electric to magnetic motions by reduction of the equations to a complex Mathieu equation.

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