A MODIFIED FREQUENCY–AMPLITUDE FORMULATION FOR FRACTAL VIBRATION SYSTEMS

Chun-Hui He and Chao Liu
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Chun-Hui He: School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an, Shaanxi, P. R. China
Chao Liu: School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an, Shaanxi, P. R. China†School of Science, Xi’an University of Architecture and Technology, Xi’an, Shaanxi, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 03, 1-8

Abstract: 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.

Keywords: Fractal Vibration; Duffing Equation; Periodic Solution; Frequency–Amplitude Formulation; Two-Scale Fractal Derivative; Fractional Calculus (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22500463

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