Stability analysis of uncertain spring vibration equations

Abstract

As a type of uncertain differential equation, the uncertain vibration equation investigates the vibration of a spring–mass system whose external force is affected by an uncertain interference. The solution and inverse uncertainty distribution of the solution for a special type of uncertain spring vibration equation are derived, and an existence and uniqueness theorem of the solution is proved. Based on these results, the ‘stability in measure’ and ‘stability in mean’ are discussed for a general uncertain spring vibration equation.

Keywords:

• Spring vibration equation
• stability
• uncertain differential equation
• uncertain process

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Lifen Jia  http://orcid.org/0000-0003-3537-6254

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (No. 71720107002), the Great Wall Scholar Training Program of Beijing Municipality (CIT&TCD 20190338), and the Humanities and Social Science Fund of the Ministry of Education of China (No. 19YJAZH005).