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.

最近，作者提出了一种新的数学模型，称为“间隔过程模型”，通过将间隔方法扩展到时域来量化时变参数的不确定性。在区间过程模型中，使用间隔而不是精确的概率分布来描述时变参数在任意时间点的不精确性，这使得区间过程模型在不确定性量化方面具有优于传统随机过程的优势。此外，作者提出了区间过程的极限，连续性，微分和积分的重要概念，丰富了区间过程模型的理论。本文将新开发的微分和积分过程的概念应用于受不确定外部激励的机械结构或系统的振动分析中。通过此应用，得出了受到动态不确定激励的线性/多个单自由度（SDOF / MDOF）振动系统的速度和加速度响应的动态范围公式，这可以为可靠性提供一些重要的参考信息。许多实际机械结构或系统的分析和安全设计。通过研究弹簧质量阻尼器系统和车辆振动问题，验证了所提出方法的有效性。推导了动态不确定激励作用下线性/多个单自由度（SDOF / MDOF）振动系统的速度和加速度响应的动态边界公式，为许多机构的可靠性分析和安全设计提供了重要的参考信息。实际的机械结构或系统。通过研究弹簧质量阻尼器系统和车辆振动问题，验证了所提出方法的有效性。推导了动态不确定激励作用下线性/多个单自由度（SDOF / MDOF）振动系统的速度和加速度响应的动态边界公式，为许多机构的可靠性分析和安全设计提供了重要的参考信息。实际的机械结构或系统。通过研究弹簧质量阻尼器系统和车辆振动问题，验证了所提出方法的有效性。