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[EN] The solution of the time-dependent neutron diffusion equation can be approximated using quasi-static methods that factorise the neutronic flux as the product of a time dependent function times a shape function that depends both on space and time. A generalization of this technique is the updated modal method. This strategy assumes that the neutron flux can be decomposed into a sum of amplitudes multiplied by some shape functions. These functions, known as modes, come from the solution of the eigenvalue problems associated with the static neutron diffusion equation that are being updated along the transient. In previous works, the time step used to update the modes is set to a fixed value and this implies the need of using small time-steps to obtain accurate results and, consequently, a high computational cost. In this work, we propose the use of an adaptive control time-step that reduces automatically the time-step when the algorithm detects large errors and increases this value when it is not necessary to use small steps. Several strategies to compute the modes updating time step are proposed and their performance is tested for different transients in benchmark reactors with rectangular and hexagonal geometry., This work has been partially supported by Spanish Ministerio de Economia y Competitividad under projects ENE2017-89029-P and MTM2017-85669-P and financed with the help of a Primeros Proyectos de Investigacion (PAID-06-18) from Vicerrectorado de Investigacion, Innovacion y Transferencia of the Universitat Politecnica de Valencia.

This chapter describes the advanced methods and recent technology to simulate squeak and rattle using the numerical method FEA. It explains the difficulties of direct CAE simulation due to the nonlinear behavior of squeak and rattle. A hybrid nonlinear rattle simulation and a quasi-linear approach to rattle simulation are introduced. The hybrid nonlinear simulation is elaborated with a detailed example of glove box rattle. The quasi-linear method, Rattle HotSpot Check (RHSC), is based on both modal and forced frequency response analysis. It provides comparison among explicit and implicit nonlinear dynamic methods and the linear modal method. The criterion to identify the relative motion velocity of two contact surfaces is established, which can be used to identify potential rattles in systems/components through global excitation. Many implementation examples are provided to demonstrate the effectiveness of this tool. Rattle HotSpot Check is a US Patent owned by the Ford Motor Company since the year 1999.

The determination of the natural frequencies and mode shapes of structures requires an analytical, semi-analytical or numerical method. This paper presents a new semi-analytical approach to determine natural frequencies and mode shapes of a multi-span, continuous, orthotropic bridge deck. The suggested approach is based on the modal method, which differs from other approaches in its decomposition of the admissible functions defining the mode shapes. Implementation of this technique is simple and enables avoidance of cumbersome mathematical calculations. In this paper, application of the semi-analytic approach to a three-span, orthotropic roadway bridge deck is compared in the first 16 modes of previously published fully analytical results and to a finite element method analysis. The simplified implementation matches within 2 % in all cases, with the additional benefit of including intermodal coupling. The approach can be extended to similar bridges with more than three spans. Not applicable au, ti, ke - kpw1/12/11