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.