标题： 重力、摩擦和热膨胀作用下竖直杆横向振动的动力学研究 显示英文标题

标题： Investigation of the dynamics of transverse oscillations of a vertical rod under gravity, friction, and thermal expansion

摘要： 本文研究了重力、摩擦和脉冲外力作用下竖直杆横向振动的数学模型，这种脉冲外力会导致杆的热膨胀。 所研究系统的动力学特性对应于脉冲反应堆中燃料组件（FE）的行为，并与其中发生的动态稳定性相关。 燃料组件的动力学由四阶非齐次线性微分方程描述，其系数不是常数。 初始边界条件是非光滑的，因为它们对应于燃料组件表面暴露于中子脉冲辐射的部分瞬间加热。 将来，所得的精确解将作为输入数据，用于模拟由超过50个燃料组件组成的自洽系统动力学。 显示英文摘要

摘要： The paper considers the mathematical formulation of the problem of transverse oscillations of a vertical rod under gravity, friction and external pulse effect, leading to thermal expansion of the rod. The dynamics of the system under consideration corresponds to the behavior of a fuel element (FE) in a pulsed reactor and is related to the dynamic stability of the processes occurring in it. The FE dynamics is described by inhomogeneous linear differential equation of the fourth order with non-constant coefficients. Initial boundary conditions are not smooth since they correspond to the instant heating of the part of the FE surface exposed to neutron pulse radiation. In the future the obtained exact solutions will be used as input data to simulate self-consistent system dynamics of more than 50 FE.