Periodic solution of fractal Phi-4 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: 89%

Periodic Property and Instability of a Rotating Pendulum System

Amer

Elnaggar

et al. 2021

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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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“…Equation ( 9) and its modifications were widely used in the literature to find a periodic solution of a nonlinear oscillator. 34,35 For equation ( 1), we have…”

Section: He's Frequency Formulationmentioning

confidence: 99%