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

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.

The Calculation of the Dynamic Problem for the Beam with Arbitrary Boundary Condition by Method of Convolution-Type Point Collocation

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.

Design of Shaped PVDF Radiation Mode Sensor and its Application in Active Structural Acoustic Control System

This paper presents a new strategy for the design of radiation mode sensors by using shaped PVDF films for one-dimension structures. Based on a modal approach, the shape of a PVDF sensor is analytically determined in such a way that the output signal of the sensor is directly proportional to amplitude of a particular radiation mode. Other modes are filtered out. A general expression of the PVDF sensor shape is obtained. It is found that the modal sensor shape can be expressed as a function of the second spatial derivative of the structural mode shape function. Finally, with an example of a vibrating beam, the proposed PVDF radiation mode sensor is used in an active structural acoustic control system for reduction of the structural-borne noise.

The Application of Non-Sinusoidal Mode Shape Function in the Identification of Modal Weight

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.