Solution of the Static Deflection Mode Shape Function of the Cantilever Beam under Transverse Flow Based on the Boundary Shooting Method

Abstract

According to the characteristics of the reactor internal structure of nuclear power plants, the vibration of the secondary core support pillar in water can be modeled as the vibration of the cantilever beam structure under the action of transverse flow, and its first beam mode is highly likely to be activated. It is thus necessary to dedicate a separate study on the first-order beam mode. In this work, we study the secondary core support pillar in nuclear reactor AP1000 under the action of transverse flow and focus on the derivation of its static cantilever deflection mode shape function in order to lay a foundation for the calculation of hydrodynamic added mass and frequency for the nuclear reactor internal components and their structural integrity evaluation. First, we proposed a set of nonlinear differential equations for the analysis of the single cantilever beam. Second, to solve the nonlinear differential equations, we used a boundary shooting framework in combination with the Runge–Kutta method. The results of the numerical simulation agree with the analytical solution to a very high degree, which demonstrates the effectiveness of the simulation method. Finally, we solved the static deflection mode shape function of the secondary core support pillar under the normal operating conditions. The nonlinear differential model and simulation method proposed in this paper can be used to solve the static cantilever deflection mode shape function of the equipment support tube.