He’s frequency formula to fractal undamped Duffing equation
Guang-Qing Feng
Abstract
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 establishes a fractal undamped Duffing equation through the two-scale fractal derivative in a fractal space. Its variational principle is established, and the two-scale transform method and the fractal frequency formula are adopted to find the approximate frequency of the fractal oscillator. The numerical result shows that He’s frequency formula is a unique tool for the fractal equations.
Topics & Concepts
FractalFractal derivativeDuffing equationMathematical analysisMathematicsSimple (philosophy)Nonlinear systemOscillation (cell signaling)Fractal dimensionScale (ratio)Fractal analysisPhysicsQuantum mechanicsPhilosophyGeneticsBiologyEpistemologyFractional Differential Equations SolutionsChaos control and synchronizationStatistical Mechanics and Entropy