Uncertain vibration analysis based on the conceptions of differential and integral of interval process

Recently, the authors proposed a new mathematical model called as the “interval process model” for quantifying uncertainty of time–varying parameters by making extension of the interval method into the time domain. In the interval process model, the imprecision of a time-varying parameter at arbitrary time point is described using an interval rather than the precise probability distribution, which makes the interval process model having some advantages over the traditional stochastic process in uncertainty quantification. Further, the authors proposed the important conceptions of limit, continuity, differential and integral of interval process, enriching the theory of interval process model. This paper applies the newly developed conceptions of differential and integral of interval process into the vibration analysis of mechanical structures or systems subjected to uncertain external excitations. By means of this application, the formulations of dynamic bounds of the velocity and acceleration responses are derived for the linear/multiple single degree of freedom (SDOF/MDOF) vibration systems subjected to dynamic uncertain excitations, which can provide some important reference information for reliability analysis and safety design of many practical mechanical structures or systems. The effectiveness of the proposed method are validated by investigating a spring-mass-damper system and a vehicle vibration problem.