A concrete beam is a basic element for many applications in architectural engineering, and its vibration property plays an important role in safety and life-span. Previous vibration models were bas...

Low frequency property of a fractal vibration model for a concrete beam

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.

Periodic Property and Instability of a Rotating Pendulum System

Nonlinear oscillation is an increasingly important and extremely interesting topic in engineering. This article completely reviews a simple method proposed by Ji-Huan He and successfully establishe...

https://journals.sagepub.com/doi/pdf/10.1177/1461348421992608

He’s frequency formula to fractal undamped Duffing equation:

The simplest frequency formulation for nonlinear oscillators is introduced and proved, and a modification is suggested. A fractal vibration in a porous medium is introduced, and its low-frequency property is elucidated by the frequency formulation. It reveals that the inertia force in a fractal space is equivalent to a couple of the inertia force and the damping force for the traditional differential model. 

A modified frequency–amplitude formulation for fractal vibration systems

The gecko effect is famous for its smart adhesion, which is achieved by its fractal-like hierarchy from nano scale spatulas to micro scale seta. This paper designs a gecko-inspired receptor system for a three-dimensional printing technology. A fractal oscillator is established and solved for the fractal-like spring system, the experimental results show that any printed objects can be received smoothly without any morphology change.

A gecko-like fractal receptor of a three-dimensional printing technology: a fractal oscillator

This paper recommends a simple and excusive approach to a strongly nonlinear oscillator. Its frequency property can be immediately obtained by the simplest calculation. The results show that the method leads to an approximate solution with relatively high accuracy. Considering the simplest solution process, this paper provides a highly efficient tool for fast determination of the amplitude-frequency relationship of a nonlinear oscillator. The large amplitude vibration of a string is used as an example to illustrate the solution process.

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Wei-Fan Houa

Papers

The fastest insight into the large amplitude vibration of a string