Frequency formula for a class of fractal vibration system
Yi Tian
Abstract
Four fractal nonlinear oscillators (The fractal Duffing oscillator, fractal attachment oscillator, fractal Toda oscillator, and a fractal nonlinear oscillator) are successfully established by He’s fractal derivative in a fractal space, and their variational principles are obtained by semi-inverse transform method. The approximate frequency of the four fractal oscillators are found by a simple frequency formula. The results show the frequency formula is a powerful and simple tool to a class of fractal oscillators.
Topics & Concepts
FractalFractal derivativeDuffing equationMathematicsMathematical analysisMultifractal systemSimple (philosophy)Nonlinear systemFractal landscapeInverseFractal dimension on networksFractal dimensionFractal analysisStatistical physicsPhysicsGeometryQuantum mechanicsPhilosophyEpistemologyFractional Differential Equations SolutionsAcoustic Wave Phenomena ResearchChaos control and synchronization