A hybrid formulation of a component mode synthesis method (original) (raw)
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On a component mode synthesis method and its application to incompatible substructures
Computers & Structures, 1994
Component Mode Synthesis (CMS) methods are substructuring techniques frequently employed in structural dynamics. A given structure is subdivided into components or substructures which are analyzed independently for natural frequencies and for mode shapes. The substructure mode shapes are then assembled to give frequencies and mode shapes of the original structure. In this paper, we construct a substructure interface impedance operator and present a spectral analysis that demonstrates that the method of Craig and Bampton (CB) is the most 'natural' CMS method. Next, we consider the CB method for assembling heterogeneous substructures and recast it into a hybrid variational formulation. We develop finite element procedures for 'gluing' non-conforming and incompatible finite element substructure models, and discuss their computational aspects. The result is a Hybrid Craig-Bampton (HCB) method that is a finite element refinement of the 'intermediate structure' concept introduced by Hale and Meirovitch, and which can be used as an interface reduction method. It is illustrated with the eigen analysis of heterogeneous and homogeneous finite element models of a High Speed Civil Transport (HSCT) aircraft.
Component-mode synthesis method for coupled continuous and FE discretized substructures
Engineering Structures, 2003
The component-mode synthesis method is adopted in order to reduce the number of degrees-of-freedom of structures composed of two or more substructures, without losing the mean physical characteristics of the structure. In this method the substructures are usually modelled by means of finite element (FE) approach. In this paper one of the two substructures is modelled as a continuous beam and a variant of the traditional component-mode synthesis method is treated. The proposed method evaluates the eigenfunctions of the continuous modelled substructure in such a way that the discontinuities in bending moment and shear force along the distributed parameter substructure, due to the contact with the discretized one, can be captured with great accuracy employing just very few eigenfunctions. Finally, the numerical applications show the superiority of the proposed approach over the traditional ones.
Comparative Study of Component Mode Synthesis Methods Applied to Structure Dynamics
2003
The modal synthesis methods are techniques used in the dynamic analysis of large structures comprising of substructures or components. These techniques are known to reduce model size, time and cost of required calculations without any loss of quality in the results. There are several modal synthesis methods, being each characterized through the way the modal subspace is constructed and boundary conditions are selected for the component modal analysis. These methods have been divided into three methodology fields: free interface methods, fixed interface methods and hybrid methods, which include branch mode methods. Regarding the structure complexity (geometry as well as the presence of damping, non-linearities, random features) the most suitable method must be applied considering numerical efficiency and the most faithfull representation of real interface behavior. Applying a general formulation to the component mode synthesis, this work studies some existing component mode methods w...
The investigation of dynamic behaviour of a structure using wave-based substructuring method
There is an increasing need for accurate, efficient and economical methods for the investigation of the dynamic behaviour of large complex structures within the engineering community. The component mode synthesis (CMS) has been perceived by the community to be an attractive efficient method for the investigation. However, the method has substantial shortcomings, particularly in analysing a structure having a large number of interface degrees of freedom (DOFs) between substructures. This paper puts forward a method, based upon the wavebased substructuring (WBS) for the investigation of the dynamic behaviour of a structure with a large number of interface DOFs. The finite element method is used to construct the full finite element model of the structure and NASTRAN 103 is used for the normal modes analysis. A new finite element model of the structure with reduced interface DOFs is constructed based on the WBS. The measurement of the dynamic behaviour of the structure is carried out using free-free boundary conditions and an impact hammer test. The predicted results of the proposed method are then compared with those from the full finite element model and experimental counterparts. The accuracy and efficiency of the proposed method are discussed and illustrated with two different case studies.
Substructure mode synthesis with overlapping connecting elements
Journal of Sound and Vibration, 1990
An approach is presented to synthesize the modal properties of two substructures to obtain the modal properties of the combined structure. The substructures are assumed to be fixed at the interfacing boundary and have overlapping elements. The eigenproperties of the overlapping elements are also used in the synthesis process. The approach can be used with any finite element discretization scheme. The approach avoids the solution of a second eigenvalue problem by conventional means. Instead, the eigenvalues are obtained as the solution of characteristic equations and eigenvectors are defined in closed form. If the complete set of eigenproperties are used. the approach provides the exact eigenproperties.
2016
An interpolatory model order reduction (MOR) strategy is proposed to compute the harmonic forced response of structures built up of substructures with frequency-dependent parameters. In this framework, the Craig-Bampton (CB) method is used for modeling each substructure by means of static modes and a reduced number of fixed-interface modes which are interpolated between several master frequencies. Emphasis is on the analysis of several substructures which can vibrate at different scales and, as such, do not need to be modeled with the same sets of interpolation points, depending on whether their modal density is low or high. For this purpose, an error indicator is developed to determine, through greedy algorithm procedure, the optimal number of interpolation points needed for each substructure. Additional investigations concern the selection of the fixed-interface modes which need to be retained for each substructure. Numerical experiments are carried out to highlight the relevance ...
International Journal of Aeronautical and Space Sciences, 2014
The objective of the paper is to clarify a methodology based on the use of the existing component mode synthesis methods for the case of two damped substructures which are coupled through a linking viscoelastic flexible substructure and for which the structural modes with free geometrical interface are used for each main substructure. The proposed methodology corresponds to a convenient alternative to the direct use either of the Craig-Bampton method applied to the three substructures (using the fixed geometric interface modes) or of the flexibility residual approaches initiated by MacNeal (using the free geometric interface modes). In opposite to a geometrical interface which is a topological interface on which there is a direct linkage between the degrees of freedom of substructures, we consider a physical flexible interface which exists in certain present technologies and for which the general framework linear viscoelasticity is used and yields a frequency-dependent damping and stiffness matrices of the physical flexible interface.
Journal of Sound and Vibration, 2010
In the vehicle design process, design decisions are more and more based on virtual prototypes. Due to competitive and regulatory pressure, vehicle manufacturers are forced to improve product quality, to reduce time-to-market and to launch an increasing number of design variants on the global market. To speed up the design iteration process, substructuring and component mode synthesis (CMS) methods are commonly used, involving the analysis of substructure models and the synthesis of the substructure analysis results. Substructuring and CMS enable efficient decentralized collaboration across departments and allow to benefit from the availability of parallel computing environments. However, traditional CMS methods become prohibitively inefficient when substructures are coupled along large interfaces, i.e. with a large number of degrees of freedom (DOFs) at the interface between substructures. The reason is that the analysis of substructures involves the calculation of a number of enrichment vectors, one for each interface degree of freedom (DOF). Since large interfaces are common in vehicles (e.g. the continuous line connections to connect the body with the windshield, roof or floor), this interface bottleneck poses a clear limitation in the vehicle noise, vibration and harshness (NVH) design process. Therefore there is a need to describe the interface dynamics more efficiently. This paper presents a wave-based substructuring (WBS) approach, which allows reducing the interface representation between substructures in an assembly by expressing the interface DOFs in terms of a limited set of basis functions (''waves''). As the number of basis functions can be much lower than the number of interface DOFs, this greatly facilitates the substructure analysis procedure and results in faster design predictions. The waves are calculated once from a full nominal assembly analysis, but these nominal waves can be re-used for the assembly of modified components. The WBS approach thus enables efficient structural modification predictions of the global modes, so that efficient vibroacoustic design modification, optimization and robust design become possible. The results show that wave-based substructuring offers a clear benefit for vehicle design modifications, by improving both the speed of component reduction processes and the efficiency and accuracy of design iteration predictions, as compared to conventional substructuring approaches.
Modal Analysis of Complex Structures via a Sub-Structuring Approach
ADMT Journal, 2021
In this paper, the problems arising from determining the modal properties of large and complex structures are investigated. For this purpose, the free interface component mode synthesis method has been used. In the following, Singular-Value Decomposition (SVD) is applied as a powerful mathematical tool to determine the appropriate coordinates to participate in the coupling process. Also, the effective error resources including modal shear error and the continuous systems overlapping error and their solution are introduced. Initially, a discrete system has been employed to investigate the free interface component mode synthesis method. Eventually, the studied main samples in this research are beam, plate and cylindrical shell. It is worth noting that the application of this method on the cylindrical shell has not been observed in previous researches.
A Unified Approach to Substructuring and Structural Modification Problems
Shock and Vibration, 2004
Substructures coupling is still an important tool in several applications of modal analysis, especially structural modification and structures assembling. The subject is particularly relevant in virtual prototyping of complex systems and responds to actual industrial needs. This paper analyzes the possibility of assembling together different substructures' models. The important role of rotational DoFs is highlighted, underlying the difficulty of assembling theoretical and experimental models, for which, usually, the rotational DoFs are not available. Expansion techniques can be used to provide this information as well as appropriate modelling of joints. With this information FRF models, modal models and FE models can be appropriately combined together and solutions for several cases of practical interest are presented. The analyzed procedures are tested on purpose-built benchmarks, showing limits and capabilities of each of them.