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

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Xiaowen Wang ◽  
Yixian Zhou

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.

2010 ◽  
Vol 2010 (0) ◽  
pp. _224-1_-_224-6_
Author(s):  
Shinichi MARUYAMA ◽  
Ken-ichi NAGAI ◽  
Ryusuke KOBAYASHI ◽  
Takao YAMAGUCHI

2010 ◽  
Vol 2010 (0) ◽  
pp. _140-1_-_140-6_
Author(s):  
Ken-ichi NAGAI ◽  
Shinichi MARUYAMA ◽  
Katsuya ISHIGAMI ◽  
Takao YAMAGUCHI

Author(s):  
Zhibiao Rao ◽  
Shixiao Fu ◽  
Jianmin Yang ◽  
Runpei Li

The main objective of this paper is to study the effect of non-sinusoidal mode shape on the identification of modal weights. The simplified analytical solution of the transverse vibration equation of uniform tensioned long flexible riser was presented, and the corresponding non-sinusoidal but orthogonal mode shape function is deduced. Then the data from the VIV model tests of long flexible riser conducted by ExxonMobil at MARINTEK are analyzed by the mode superposition method. Modal weights calculated by two different mode shape functions, sinusoidal and non-sinusoidal function, with two methods, namely direct method and indirect method are compared. The comparison shows the good performance of the non-sinusoidal mode shape in the identification of modal weights.


2014 ◽  
Vol 919-921 ◽  
pp. 1330-1333 ◽  
Author(s):  
Yong Li Li ◽  
Zhi Gang Zhao ◽  
Hua Yang

The method of convolution-type point collocation to calculate the beam with arbitrary boundary conditions was presented by using series function in time domain and the mode shape function of the beam in space domain. And this method is applied to solve dynamic problems of beam with arbitray boundary condition. The calculation example showed this method was very simple, highly accurate and effective.


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