He’s frequency formula to fractal undamped Duffing equation

The current paper investigates the dynamical property of a pendulum attached to a rotating rigid frame with a constant angular velocity about the vertical axis passing to the pivot point of the pendulum. He’s homotopy perturbation method is used to obtain the analytic solution of the governing nonlinear differential equation of motion. The fourth-order Runge-Kutta method (RKM) and He’s frequency formulation are used to verify the high accuracy of the obtained solution. The stability condition of the motion is examined and discussed. Some plots of the time histories of the gained solutions are portrayed graphically to reveal the impact of the distinct parameters on the dynamical motion.

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“…This is exactly same as that given in Equation (40). Applications of He's frequency formulation are referred to refs [40][41][42][43][44][45].…”

Section: He's Frequency Formulationmentioning

confidence: 91%

Periodic Property and Instability of a Rotating Pendulum System

Amer

Elnaggar

et al. 2021

Axioms

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“…With the help of equations ( 33), (44), and (45), the equation of pressure gradient can be expressed as…”

Section: Methods Of Solutionmentioning

confidence: 99%

“…e governing equations of motion are simplified by employing longer wavelength and low Reynolds number assumptions. ese equations are analytically solved with regard to the adequate boundary conditions by utilizing various analytical methods [38][39][40][41][42][43][44]. e distributions of an axial velocity, temperature, and concentration are achieved.…”

Section: Introductionmentioning

confidence: 99%

Insight into the Significance of Hall Current and Joule Heating on the Dynamics of Darcy–Forchheimer Peristaltic Flow of Rabinowitsch Fluid

Mostapha

2021

Journal of Mathematics

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This paper aims to present the significance of the Hall current and Joule heating impacts on a peristaltic flow of a Rabinowitsch fluid through tapered tube. The Darcy–Forchheimer scheme is used for a porous medium; a mild stenosis is considered to study the impacts of radiative heat transfer and chemical reactions. Convective conditions are postulated for heat and mass transfer. In the meantime, the slip conditions are presumed for the velocity distribution. Soret and Dufour features bring the coupled differential systems. The hypotheses of a long wavelength and low Reynolds number are employed to approximate the governing equations of motion, and finally the homotopy perturbation method is adopted for numerical study. Pumping characteristics are revealed and the trapping procedure correlated with peristaltic transport is elucidated. The present study is very important in many medical applications, such as the gastric juice motion in the small intestine and the flow of blood in arteries. The mechanism of peristaltic transport with mild stenosis has been exploited for industrial applications like sanitary fluid transport and blood pumps in heart-lung machine. The influences of various physical parameters of the problem are debated and graphically drawn across a set of figures. It is noted that the axial velocity is reduced with the increase of the Hartmann number. However, enhancing both the Rabinowitsch parameter and the Forchheimer parameter gives rise to the fluid velocity. As well, it is debated that Rabinowitsch fluid produces a cubic term of pressure gradient. Therefore, the relation between mean flow rate and the pressure rise does not stay linear. It is recognized that the temperature rises with the enhancement of both Dufour number and Soret number. Furthermore, it is illustrated that the concentration impedes with the increase of the mass transfer Biot number. Also, it is revealed that the trapped bolus contracts in size by enlarging the maximum height of stenosis.

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“…Pandey et al [51] investigated the initiation of convection in a horizontal layer of Walter' B visco-elastic nanofluid. Equation (57) can also be solved by other analytical methods [52][53][54][55][56], especially He's frequency formulation [55,56]. Due to the practical implications of the porous media, the media are presumed to be fully saturated in porous structure.…”

Section: Discussionmentioning

confidence: 99%

Nonlinear EHD Instability of Two-Superposed Walters’ B Fluids Moving through Porous Media

Moatimid

Sayed

2021

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The current work examines the application of the viscous potential flow to the Kelvin-Helmholtz instability (KHI) of a planar interface between two visco-elastic Walters’ B fluids. The fluids are fully saturated in porous media in the presence of heat and mass transfer across the interface. Additionally, the structure is pervaded via a uniform, normal electrical field in the absence of superficial charges. The nonlinear scheme basically depends on analyzing the linear principal equation of motion, and then applying the appropriate nonlinear boundary-conditions. The current organization creates a nonlinear characteristic equation describing the amplitude performance of the surface waves. The classical Routh–Hrutwitz theory is employed to judge the linear stability criteria. Once more, the implication of the multiple time scale with the aid of Taylor theory yields a Ginzburg–Landau equation, which controls the nonlinear stability criteria. Furthermore, the Poincaré–Lindstedt technique is implemented to achieve an analytic estimated bounded solution for the surface deflection. Many special cases draw upon appropriate data selections. Finally, all theoretical findings are numerically confirmed in such a way that ensures the effectiveness of various physical parameters.

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He’s frequency formula to fractal undamped Duffing equation

Cited by 70 publications

References 41 publications

Periodic Property and Instability of a Rotating Pendulum System

Periodic Property and Instability of a Rotating Pendulum System

Insight into the Significance of Hall Current and Joule Heating on the Dynamics of Darcy–Forchheimer Peristaltic Flow of Rabinowitsch Fluid

Nonlinear EHD Instability of Two-Superposed Walters’ B Fluids Moving through Porous Media

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