FRACTAL OSCILLATION AND ITS FREQUENCY-AMPLITUDE PROPERTY
Ji‐Huan He, SHUAI-JIA KOU, Chun‐Hui He, Zuowei Zhang, Khaled A. Gepreel
Abstract
When an oscillator vibrates in a porous medium or along an unsmooth surface, a fractal model can be adopted using the two-scale fractal derivative. This paper elucidates a simple but effective method for fast and exclusive insight into the asymptotically periodic property at the initial stage and the extremely low frequency property when time tends to infinity. Some examples are illustrated to show the one-step solution process and the accurate results.
Topics & Concepts
FractalProperty (philosophy)Oscillation (cell signaling)Mathematical analysisMathematicsSimple (philosophy)InfinityAmplitudeFractal derivativeScale (ratio)Process (computing)Fractal dimensionFractal analysisPhysicsComputer scienceOpticsPhilosophyEpistemologyQuantum mechanicsGeneticsOperating systemBiologyFractional Differential Equations SolutionsAcoustic Wave Phenomena ResearchExperimental and Theoretical Physics Studies