Ren’s frequency–amplitude formulation for nonlinear oscillators

Abstract

A fast insight into the frequency-amplitude relationship of a rehabilitation training device and other nonlinear vibrations as well is of great importance. This paper applies Ren's frequency-amplitude formulation to obtain approximate frequencies of nonlinear oscillators with little calculation while keeping high relative accuracy. The golden mean location is used in the example procedures.

Fractal-like multiple jets in electrospinning process

“…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.…”

A thermodynamic model for a packing dynamical system

“…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.…”

“…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.…”

Verification of He's frequency formulation by Duffing-Harmonic Oscillator

“…He's original frequency formulation was derived from an ancient Chinese mathematical algorithm [10,13], recently there was a hot discussion on He's original frequency formulation [14][15][16][17][18][19][20][21][22]. Here we check Ren-Hu's modification [14].…”