Approximate frequency–amplitude relationship for a singular oscillator

This paper focuses on a fractal Phi-4 equation with time-space fractal derivatives, though its solitary solutions have been deeply studied, its periodic solution was rarely revealed due to its strong nonlinearity. Now the condition is completely changed, He?s frequency formulation provides with a universal tool to having a deep insight into the periodic property of the fractal Phi-4 equation. The two-scale transform is used to convert approximately the fractal Phi-4 equation to a differential model, and a criterion is suggested for the existence of a periodic solution of the equation, the effect of fractal orders on the periodic property is also elucidated.

Section: Periodic Solutionmentioning

confidence: 99%

Periodic solution of fractal Phi-4 equation

Liu

2021

“…When the high-speed jet moves along an equipotential line, the acceleration is zero, and the jet splits freely, forming splitting jets. At this time, any small disturbance will cause the instability of the vibration of the moving jet [27,28], non-linear oscillation models can be solved by Taylor series method [29], the variational method [30][31][32][33], and He's frequency formulation [34,35] to reveal the frequency-amplitude relation as discussed in [36][37][38][39][40][41][42][43][44][45][46]. In this paper, the region of jet bifurcation is called as the zero accelerated region.…”

Section: Electrospinning and Analysismentioning

confidence: 99%

Fractal-like multiple jets in electrospinning process

Liu

2020

The electrospinning process is greatly affected by the instability of Taylor cone, an instable point can eject a jet, and multiple instable points can produce multiple jets. A fractal-like multi-jet phenomenon was found in electrospinning process with auxiliary electrodes, and main factors affecting the spinning process were studied experimentally, which included solution viscosity, surface tension, and conductivity. The fractal-like multi-jet is feasible to control the fiber morphology and its output.

“…Equation ( 1) can be effectively solved by some analytical methods, for examples, the variational iteration method [13][14][15][16], the variational approach [17][18][19], the homotopy perturbation method [20-28], He's frequency formulation [2][3][4][5][6][7][8][9][10][11][12], and Taylor series method Though the analytical methods can reveal the basic property of the vibration, it is impossible to present the packing system from vibration.…”

Section: Packing Dynamical Systemmentioning

confidence: 99%

“…The vibration can be described by the well-known hyperbolic tangent oscillator [1], and it is easy to predict accurately the frequency-amplitude relationship [2][3][4][5][6][7][8][9][10][11][12], which is the main factor affecting the safe loading. Though we have many technologies to absorb the kinetic energy of the loading goods, a safe loading is almost impossible unless the loading kinetic energy is zero when loaded.…”

Section: Introductionmentioning

confidence: 99%

A thermodynamic model for a packing dynamical system

Song

2020

So far shock and vibration are the inherent properties of all packing systems, and various mitigation measures have been considered using packing materials, which result in a large packing size. Now the thing changes, this paper gives an effective thermodynamic technology that can completely avoid shock and vibration. An aerial delivery system is used as an example to elucidate the novel packing system, which requires zero loading velocity when loaded. A thermodynamic model is established to reveal the main factors affecting the packing system.