A comparison study between the Craig - Bampton model reduction method and traditional finite element method for analyzing the dynamic behavior of vibrating structures

In this method, the internal DOFs are separated from the boundary DOFs, and decomposed onto a basis of static modes, and a basis of fixed interface modes [Craig et Bampton, 1968]. The use of a reduced basis for the fixed interface modes makes it possible to reduce the size of the system to be solved, and therefore to save the computational time compared to a classical finite element computation involving the complete system.
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A comparison study between the Craig - Bampton model reduction method and traditional finite element method for analyzing the dynamic behavior of vibrating structures HỘI NGHỊ KHOA HỌC TOÀN QUỐC VỀ CƠ KHÍ – ĐIỆN – TỰ ĐỘNG HÓA (MEAE2021) A comparison study between the Craig - Bampton model reduction method and traditional finite element method for analyzing the dynamic behavior of vibrating structures. Kieu Duc Thinh 1,*, Trinh Minh Hoang 2, Nguyen The Hoang 1 1 Hanoi University of Mining and Geology, , hanhchinhtonghop@humg.edu.vn 2 Hanoi University of Science and Technology, hcth@hust.edu.vnARTICLE INFO ABSTRACTArticle history: Many studies have shown that the method of dynamic substructuring ofReceived 15th Jun 2021 Craig-Bampton (CB) which showed the effectiveness, will be used to studyAccepted 16th Aug 2021 the dynamic response of the structure with respect to the excitationAvailable online 19th Dec 2021 frequency [Dennis Klerk et al, 2008; Duc Thinh Kieu et al, 2019; J. Wijker,Keywords: 2008; Mapa et al 2021]. Its capacity to effectively reduce the number ofCraig-Bampton, dynamic degrees of freedom (DOFs) and also the computational costs will besubstructuring, model evaluated in comparison with computations carried out with a complete finite element (FE) model. The CB method is one of the most popularreduction method, vibrating substructuring methods and is based on a formalization which will bestructure, finite element presented in this paper. In this method, the internal DOFs are separatedmodel from the boundary DOFs, and decomposed onto a basis of static modes, and a basis of fixed interface modes [Craig et Bampton, 1968]. The use of a reduced basis for the fixed interface modes makes it possible to reduce the size of the system to be solved, and therefore to save the computational time compared to a classical finite element computation involving the complete system. We will apply the Craig-Bampton method to an academic structure composed of three plates connected by springs and we will be interested in the frequency response functions of the deformation energies of the different plates. To evaluate the influence of the number of modes selected on the results, we will consider two bases of fixed interface modes of different sizes. Copyright © 2021 Hanoi University of Mining and Geology. All rights reserved.1. Introduction necessary to reduce the size of the models to solve. One of the efficient model reduction The FE method is a traditional method used to strategies is the well-established Craig-Bamptonperform the dynamic analysis of complex method that is a substructuring technique. Thisindustrial structures. However, it usually involves method reduces the number of DOF ofmodels characterized by large numbers of DOFs substructures by approximations, using a limitedand leads to large computational costs. It may be 160 HỘI NGHỊ KHOA HỌC TOÀN QUỐC VỀ CƠ KHÍ – ĐIỆN – TỰ ĐỘNG HÓA (MEAE2021)number of fixed interface modes. It is useful for In the classical FE method, the unknownstudy the dynamic response of the structure with DOFs are obtained by inverting the aboverespect to the excitation frequency with many system, if the number of DOFs involved isDOFs [Craig et Bampton, 1968; J. Wijker, 2008; important the computational time can beDennis Klerk et al, 2008]. cumbersome. The Craig-Bampton The aim of this paper is to apply the Craig - transformation consists of expressing theBampton method in order to reduce the physical amplitudes {?? ?? }? from generalizedcomputat ...