The stochastic theory of nonlinear vibration for 1-D and 3-D beams and its application to anomalous core barrel motion in nuclear reactors

We propose a stochastic theory of nonlinear vibration for beam elements under the influence of fluid flow. First, a stochastic theory of linear and nonlinear vibrations for 1-D beams is presented. Secondly, a stochastic theory of 3-D beam is developed; it is shown that the governing equations of the 3-D beam can be reduced to a non-linear stochastic model with two-degrees of freedom. Thirdly, the derived stochastic model is successfully applied to the anomalous core barrel motion observed in the WWER-440 type reactors: (i) the feasibility of statistical analysis with the use of the stochastic nonlinear single-mass model is demonstrated; (ii) the origins of anomalous core barrel motion are clarified from the physical and mathematical points of view. (author)