Spectral ACMS: A Robust Localized Approximated Component Mode Synthesis Method

The component mode synthesis (CMS) methods are often utilized for modal analysis to investigate the vibration characteristics of the complex structures which are commonly divided into several substructures. However, non-matching finite element meshes may occur at the interfaces between components and virtual gaps are easily produced along the curved interfaces, which limit the application of CMS and lead to larger numerical errors for vibration analysis. To overcome the problem, a novel gap element method (GEM) is employed into a free-interface CMS method in this paper, where both displacements and forces of the nodes on the incompatible interfaces are introduced by two independent Lagrange multipliers to enforce the compatibility conditions. Two-dimensional numerical examples are given to validate the effectiveness of the proposed method. The results of natural frequencies and modal shapes obtained using the proposed method agree very well with the ones obtained using full finite elements model, no matter the gaps along the interface exist or not. The influence of the number of nodes on the non-matching interfaces on the accuracy of frequencies is also discussed.

Element-by-element model updating of large-scale structures based on component mode synthesis method

This paper is concerned with solving large-scale eigenvalue problems by algebraic substructuring. Algebraic substructuring refers to the process of applying matrix reordering and partitioning algorithms to divide a large sparse matrix into smaller submatrices from which a subset of spectral components are extracted and combined to form approximate solutions to the original problem. Through an algebraic analysis, we identify critical conditions under which a simple version of algebraic substructuring works well. This particular version of substructuring is identical to the component mode synthesis (CMS) method (see [R. R. Craig and M. C. C. Bampton, {\em Coupling of substructures for dynamic analysis}, AIAA J., 6 (1968), pp. 1313--1319] and [W. C. Hurty, {\em Vibrations of structure systems by component-mode synthesis}, J. Engrg. Mech., 86 (1960), pp. 51--69]) when the matrix reordering is based on a geometric partitioning of the computational domain. We observe an interesting connection between the accuracy of an approximate eigenpair obtained through substructuring and the distribution of the components of eigenvectors of a canonical matrix pencil congruent to the original problem. A priori error bounds for the smallest eigenpair approximation are developed. This development leads to a simple heuristic for choosing spectral components (modes) from each substructure. The effectiveness of such a heuristic is demonstrated with numerical examples. We show that algebraic substructuring can be effectively used to solve a generalized eigenvalue problem arising from the finite element analysis of an accelerator structure.

One of the most popular methods for reducing the complexity of assemblies of finite element models in the field of structural dynamics is component mode synthesis. A main challenge of component mode synthesis is balancing model complexity and model accuracy, because it is difficult to predict how component reduction influences assembly model accuracy. This work introduces an approach that allows for the translation of assembly model accuracy requirements in the frequency domain to the automatic selection of the cut-off frequencies for the model-order reduction (MOR) of components. The approach is based on a mathematical approach for MOR for coupled linear systems in the field of systems and control. We show how this approach is also applicable to structural dynamics models. We demonstrate the use of this approach in the scope of component mode synthesis (CMS) methods with the aim to reduce the complexity of component models while guaranteeing accuracy requirements of the assembly model. The proposed approach is illustrated on a mechanical, three-component structural dynamics system for which reduced-order models are computed that are reduced further compared to reduction using standard methods. This results in lower simulation cost, while maintaining the required accuracy.

A system-level interface sampling and reduction method for component mode synthesis with varying parameters

The wave-based substructuring approach for the efficient description of interface dynamics in substructuring

An efficient methodology for predicting the nonlinear forced vibration response of a turbine engine rotor with a cracked blade is presented and used to investigate the effects of the damage on the forced response. The effects of small, random blade-to-blade differences (mistuning) and rotation on the forced response are also considered. Starting with a finite element model, a hybrid-interface method of Component Mode Synthesis (CMS) is employed to generate a reduced-order model (ROM). The crack surfaces are retained as physical degrees of freedom in the ROM so that the forces due to contact interaction in three-dimensional space can be properly calculated. The resulting nonlinear equations of steady-state motion are solved by applying an alternating frequency/time-domain method, which is much more computationally efficient than traditional time integration. Using this reduced-order modeling and analysis framework, the effects of the cracked blade on the system response are investigated for various mistuning levels and rotation speeds. First, the advantages of the selected hybrid-interface CMS method are discussed and demonstrated. Then, the resonant frequency shift associated with the stiffness loss due to the crack, as well as vibration localization about the cracked blade are thoroughly investigated. In addition, the results of the nonlinear ROMs are compared to those obtained with linear ROMs as well as blade-alone ROMs. It is shown that several key system vibration characteristics are not captured by the simpler models, but that some insight into the system response can be gained from the blade-alone response predictions. Furthermore, it is demonstrated that while the effects of the crack often appear similar those of mistuning, differences between the effects of mistuning and damage can be discerned by observing and comparing the response across different families of system modes.

Application of Wilson-Ritz vectors in dynamic substructuring

Dynamic characteristics investigation of a dual rotor-casing system considering the comprehensive stiffness of the intermediate bearing

Model reduction schemes for the wave and finite element method using the free modes of a unit cell

The aim of this study is the prediction of the dynamic response of damaged laminated composite structures in the context of component mode synthesis. Hence, a method of damage localization of complex structures is proposed. The dynamic behavior of transversely isotropic layers is expressed through elasticity coupled with damage based on an existing macro model for cracked structures. The damage is located only in some regions of the whole structure, which is decomposed on substructures. The incremental linear dynamic governing equations are obtained by using the classical linear Kirchhoff-Love theory of plates. Then, considering the damage-induced nonlinearity, the obtained nonlinear dynamic equations are solved in time domain. However, a detailed finite element modelling of such structure on the scale of localized damage would generate very high computational costs. To reduce this cost, Component Mode Synthesis method (CMS) is used for modelling a nonlinear fine-scale substructure damaged, connected to linear dynamic models of the remaining substructures, which can be condensed and not updated at each iteration. Numerical results show that the mechanical properties of the structure highly change when damage is taken into account. Under an impact load, damage increases and reaches its highest value with the maximum of the applied load and then remains unchanged. Besides, the eigenfrequencies of the damaged structure decrease comparing with those of an undamaged one. This methodology can be used for monitoring strategies and lifetime estimations of hybrid complex structures due to the damage state is known in space and time.

On the use of multiple quasi-static mode compensation sets for component mode synthesis of complex structures

Component mode synthesis and polynomial chaos expansions for stochastic frequency functions of large linear FE models

A Study on the Design Improvement of Lathes Based on a Chatter Analysis and a Component Mode Synthesis

A component mode synthesis method capable of estimating acoustic responses efficiently in a coupled structure–acoustic fluid interaction problem is presented. In order to analyze the response in a high-frequency range, a high- and low-order truncatable mode superposition method, namely, the most general mode superposition method by Ma-Hagiwara, is incorporated in the reduction process included in both the formulation of component mode synthesis and solving the superimposed global equation of motion. By truncating lower modes, it becomes possible to analyze a system with fewer degrees of freedom than the existing modal reduction methods. Frequency response analyses of several test problems of damped structures are performed and compared with the multipurpose versatile code, MSC/NASTRAN, to demonstrate the efficiency and versatility of the proposed method.