NONLINEAR VIBRATION WITH DISCONTINUITIES IN A FRACTAL SPACE: ITS VARIATIONAL FORMULATION AND PERIODIC PROPERTY

Yue Shen, Chun-Hui He, Abdulrahman Ali Alsolami and Dan Tian
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Yue Shen: School of Science, Xi’an University of Architecture and Technology, Xi’an, P. R. China
Chun-Hui He: ��School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an, P. R. China‡Department of Mathematics, Faculty of Science, King Abdulaziz University Jeddah, Saudi Arabia
Abdulrahman Ali Alsolami: ��Department of Mathematics, Faculty of Science, King Abdulaziz University Jeddah, Saudi Arabia
Dan Tian: School of Science, Xi’an University of Architecture and Technology, Xi’an, P. R. China

FRACTALS (fractals), 2023, vol. 31, issue 07, 1-9

Abstract: A vibration system with discontinuities has triggered off rocketing interest in various fields including mechanical engineering, physics, and mathematics because it has many striking and amazing properties which cannot be unexplained by traditional vibration theory. This paper studies the problem using the energy conservation frame in a fractal time. A variational formulation is developed, and its periodic property is elucidated by the frequency–amplitude formulation. For discontinuity, this paper aims to propose a new frequency formulation by means of the golden average. Comparison between the approximate and exact frequency values is presented to validate our method.

Keywords: Fractal Oscillator; Fractal Space; Variational Theory; Periodic Property (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23500706

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