An enhanced Craig-Bampton method

Abstract

SUMMARYIn this paper, we propose a new component mode synthesis method by enhancing the Craig-Bampton (CB) method. To develop the enhanced CB method, the transformation matrix of the CB method is enhanced considering the effect of residual substructural modes and the unknown eigenvalue in the enhanced transformation matrix is approximated by using O'Callahan's approach in Guyan reduction. Using the newly defined transformation matrix, original finite element models can be more accurately approximated by reduced models. For this reason, the accuracy of the reduced models is significantly improved with a low additional computational cost. We here present the formulation details of the enhanced CB method and demonstrate its performance through several numerical examples.

Evaluating Mode Selection Methods for Component Mode Synthesis

“…where F s is a full flexibility [13] of substructures, and it can then be decomposed by dominant and residual parts as (19) in which r j is labeled as the jth moment vector of u b , and we can get the following relationship:…”

“…In the last five decades, significant progress has been achieved [3][4][5][6][7][8][9][10][11], but various issues remain, including searching for new methodologies [12][13][14], interface reduction [15][16][17][18], error estimation [19][20][21][22][23], and so on. Recently, the CMS method has been employed not only for transient analysis, including nonlinear dynamics [24], but also for biomolecular assembly modeling [25,26].…”

“…Since substructural modal effects are transferred to adjacent fields at the interface degrees of freedom (DOF), well-defined interface handling techniques are important. Depending on the interface handling techniques, the CMS methods are generally categorized into two main groups: fixed interface methods [3][4][5][6]12,13] or free interface methods [7][8][9]. In particular, the enhanced Craig-Bampton (CB) and automated multilevel substructuring (AMLS) methods [12,13] that were recently developed have opened up new possibilities to ensure an extreme accuracy in the reduced model.…”

Dynamic Stiffness Effect of Mechanical Components on Gear Mesh Misalignment

“…In addition, simplifying the dynamic model of the FE housing, which has a tremendous number of DOFs, requires the use of reduced-order modeling (ROM) techniques [22][23][24][25][26][27][28][29][30][31][32][33]. Component mode synthesis (CMS) is currently the most popular ROM technique for dynamic systems [26][27][28][29][30][31]. The typical CMS method uses a small number of important and constraint modes to construct a reduced model that mathematically projects the displacement fields of the gearbox components onto modal coordinates.…”

A Mode Selection Algorithm for the Flexibility-Based Component Mode Synthesis

“…After introducing the first approach of the CMS method in 1960s, various methods have been proposed [1][2][3][4][5][6][7][8][9][10][11][12]. In particular, the flexibility based CMS (F-CMS) method was developed using localized Lagrange multipliers [13], and its extended works have been performed [14,15].…”