Component mode synthesis with subspace iterations for controlled accuracy of frequency and mode shape solutions

Keywords: Frequencies and mode shapes Component mode synthesis Craig–Bampton scheme Bathe subspace iteration method Control of errors a b s t r a c t The objective in this paper is to present an approach to improve component mode synthesis solutions using subspace iterations to obtain frequency and mode shape predictions of controlled accuracy. In traditional component mode synthesis analyses, the calculated frequencies and mode shapes are approximations of the exact frequencies and mode shapes of the finite element model, the error is unknown, may be large, and is usually not assessed. In the approach given here, the error is assessed and can be reduced to the desired level. The Craig–Bampton component mode synthesis is used, but the solution approach is also directly applicable to any other component mode synthesis scheme. Some example solutions are given to illustrate the use and the effectiveness of the solution approach. Component mode synthesis solution techniques [1,2] are widely used in finite element analyses. The solution approach was proposed long ago by Hurty [3], but when seen as a domain decomposition technique can in fact be traced back to much earlier work, see Ref. [4]. These methods can be effective for the solution of frequencies and mode shapes when complex structures are analyzed, as, for example, in the airplane industries. The representation of the complete structure is based on using large substruc-tures. These individual structures, or components, are typically first analyzed in detail for their frequencies and mode shapes, and dynamic response, by different analysis groups. Then the complete structure is considered as an assemblage of the components, which can lead to a very large finite element system. However, usually only the lowest p frequencies and corresponding mode shapes of the complete finite element system with n degrees of freedom are needed, where p (n. The basic approach of a component mode synthesis analysis is to use the mode shape solutions of the individual components, i.e. substructures, to obtain approximations to the exact p frequencies and mode shapes of the complete model [2]. An important such procedure used is the Craig–Bampton method [5]. Since the component mode synthesis procedures only give approximate solutions to the exact eigenvalues and vectors (frequencies and mode shapes) of the complete structural model, it can be important to have some error measure, see Refs. [4,6] and the many references therein, to ensure the reliability of a response prediction. The …