Uncertain spring vibration equation

Lifen Jia; Wei Dai

doi:10.3934/jimo.2021073

Article Contents

2022, Volume 18, Issue 4: 2401-2414. Doi: 10.3934/jimo.2021073

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Uncertain spring vibration equation

Lifen Jia^1, and
Wei Dai^2, ,

1.
School of Management and Engineering, Capital University of Economics and Business, Beijing, China
2.
Department of Financial Engineering, Central University of Finance and Economics, Beijing 100081, China

^* Corresponding author: Wei Dai
^* Corresponding author: Wei Dai

Received: June 30, 2020

Revised: December 31, 2020

Published: July 2022

The first author is supported by the Beijing Municipal Education Commission Foundation of China (No. KM202110038001), the Young Academic Innovation Team of Capital University of Economics and Business (No. QNTD202002), and the special fund of basic scientific research business fees of Beijing Municipal University of Capital University of Economics and Business (No. XRZ2020016)

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Abstract

The spring vibration equation is to model the behavior of a spring which has a time varying force acting on it. The stochastic spring vibration equation was proposed for modeling spring vibration phenomena with noise described by Wiener process. However, there exists a paradox in some cases. Thus, as a counterpart, this paper proposes uncertain spring vibration equation driven by Liu process to describe the noise. Moreover, the analytic solution of uncertain spring vibration equation is derived and the inverse uncertainty distribution of solution is proved. At last, this paper presents a paradox of stochastic spring vibration equation.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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