Open AccessFrequency formula for a class of fractal vibration system
Author(s) -
Yi Tian,
AUTHOR_ID
Publication year - 2022
Publication title -
reports in mechanical engineering
Language(s) - English
Resource type - Journals
ISSN - 2683-5894
DOI - 10.31181/rme200103055y
Subject(s) - fractal , fractal derivative , duffing equation , mathematics , mathematical analysis , multifractal system , simple (philosophy) , nonlinear system , fractal landscape , fractal dimension on networks , inverse , fractal dimension , fractal analysis , physics , geometry , quantum mechanics , philosophy , epistemology
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.