The investigation of dynamic behaviour of a structure using wave-based substructuring method (original) (raw)
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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.
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.
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...
A hybrid formulation of a component mode synthesis method
33rd Structures, Structural Dynamics and Materials Conference, 1992
Component mode synthesis is a substructuring technique frequently employed in structural dynamics. In this method, a given structure is subdivided into components or substructures, each of which is analyzed independently for natural frequencies and for mode shapes. The substructure mode shapes are then assembled to give displacement shapes or load patterns of the original structure. An analytical justification of the basic concept is presented using spectral decompositions, and a variant substructuring approach where intersubstructure continuity is enforced in a weak form is derived. This leads to a hybrid formulation of the basic method which is particularly suitable for assembling heterogeneous substructures and analyzing nonconforming and incompatible finite element substructure models. For problems where both the basic and hybrid methods are applicable, the hybrid variant can be computationally more advantageous.
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.
MATEC Web of Conferences, 2016
The frequency response function based substructuring method (FRF-BSM) for modelling and investigating dynamic behaviour of engineering structures has received much attention in recent years among modal analysts. However, the accuracy and efficiency of the predicted dynamic behaviour of the structures via the method is often found to be different from the test data. The discrepancy is believed to be the result of the coupling types used in the modelling. This paper aims to investigate the potential candidates of coupling types for FRF based substructuring in predicting the dynamic behaviour of a complex assembled structure which consists of a large flat span and two simplified aircraft pylons. Modal tests are performed to measure the dynamic behaviour of the assembled structure and its components. The finite element method is used for constructing analytical models of the assembled structure. The FRF-BSM is then used for the assembly of the span and pylons, and also to predict the dynamic behaviour of the assembled structure using rigid and elastic coupling. The comparison of results revealed that elastic coupling has demonstrated better capabilities to represent the bolted joints in the test structure, which may due to the coupling calculated is reasonably representing the stiffness of the bolted joints.
A wave-based substructuring approach for concept modeling of vehicle joints
Computers & Structures, 2011
In highly competitive fields, such as the automotive industry, complex products must be innovated in short timeframes and at affordable costs. The need for simulation tools, able to steer and support the early design choices, pushes researchers to develop concept modeling techniques.
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.
On the use of an efficient wave based method for steady- state structural dynamic analysis
The Finite Element Method is the most commonly used prediction technique for dynamic simulations of mechanical structures. Given the increasing model sizes and subsequent increasing computational load for increasing frequency, the use of the Finite Element Method (FEM) is limited to low-frequency applications. The Wave Based Method (WBM) is a novel Trefftz-based deterministic prediction tech- nique that is capable of relaxing the existing frequency limit. This paper gives an overview of the principles of the WBM for the steady-state dynamic analysis of structures. First the flat plate bending and membrane behaviour are described. Subsequently, the theory for these two problems is united to handle non-coplanar flat plate assemblies. Finally, a hybrid FE-WBM is shown, which combines the strengths of the FEM and the WBM. Throughout the paper the performance of the WBM is compared with that of the FEM, which demonstrates the enhanced computational efficiency of the WBM.
Mathematics and Mechanics of Solids, 2017
Flexible structural components can be attached to the rest of the structure using different types of joints. For instance, this is the case of solar panels or array antennas for space applications that are joined to the body of the satellite. To predict the dynamic behaviour of such structures under different boundary conditions, such as additional constraints or appended structures, it is possible to start from the frequency response functions in free-free conditions. In this situation, any structure exhibits rigid body modes at zero frequency. To experimentally simulate free-free boundary conditions, flexible supports such as soft springs are typically used: with such arrangement, rigid body modes occur at low non-zero frequencies. Since a flexible structure exhibits the first flexible modes at very low frequencies, rigid body modes and flexible modes become coupled: therefore, experimental frequency response function measurements provide incorrect information about the low freque...