scholarly journals Stabilized Solution to Spurious Mode Problem and Ill-Conditioning in Interface Force Based Substructure Coupling Method

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Hui-hua Feng ◽  
Xiao-long Mou ◽  
Khaled Teffah
Keyword(s):  
Degrees Of Freedom ◽  
Component Mode Synthesis ◽  
Coupling Method ◽  
Synthesis Methods ◽  
Assembly Method ◽  
Spurious Mode ◽  
Ill Conditioning ◽  
Fixed Interface ◽  
Matrix Problems ◽  
Value Decomposition

There are two major types of substructure mode synthesis methods, i.e., the fixed-interface component mode synthesis and free-interface component mode synthesis. There are two coupling methods, the interface degrees of freedom based coupling method and the interface force based coupling method, the former one is referred to as the primary assembly method, and the latter is referred to as the dual assembly method. However, the dual assembly method is theoretically shown to be unstable in this research, such reduced stiffness matrix is indefinite, this fatal weakness can be conquered by further interface reduction, and the interface compatibility is therefore rigorously enforced. Unfortunately, Craig’s method leads to another numerical instability when inverting a submatrix of residual flexibility on the interface degrees of freedom, this problem is neglectable in small dimensional matrix problems, but it is prominent in large models when the number of interface degrees of freedom is large, this ill-conditioning problem may be circumvented by truncated singular value decomposition technique; here, a more efficient strategy is proposed, the substructure reduction is modified, this modification proves to be numerically stable, and it can be even more accurate than the prevailing Craig-Bampton method; the numerical examples validate the suggestion.

scholarly journals On Hurty/Craig-Bampton Substructuring With Interface Reduction on Contacting Surfaces

2017 ◽  
Author(s):  
Robert J. Kuether ◽  
Peter B. Coffin ◽  
Adam R. Brink
Keyword(s):  
Degrees Of Freedom ◽  
Local Level ◽  
Cost Savings ◽  
Synthesis Methods ◽  
Finite Element Models ◽  
Interface Reduction ◽  
Restoring Forces ◽  
Fixed Interface ◽  
The Cost ◽  
Dynamics Models

Structural dynamics models with localized nonlinearities can be reduced using Hurty/Craig-Bampton component mode synthesis methods. The interior degrees-of-freedom of the linear subcomponents are reduced with a set of dynamic fixed-interface modes while the static constraint modes preserve the physical coordinates at which the nonlinear restoring forces are applied. For finite element models with a highly refined mesh at the boundary, a secondary modal analysis can be performed to reduce the interface down to a truncated set of local-level characteristic constraint modes. In this research, the cost savings and accuracy of the interface reduction technique are evaluated on a simple example problem involving two elastic blocks coming into contact.

scholarly journals Component Mode Synthesis Using Undeformed Interface Coupling Modes to Connect Soft and Stiff Substructures

2013 ◽  
Vol 20 (1) ◽  
pp. 157-170 ◽  
Author(s):  
Eskil Lindberg ◽  
Nils-Erik Hörlin ◽  
Peter Göransson
Keyword(s):  
Degrees Of Freedom ◽  
Component Mode Synthesis ◽  
Vehicle Suspension ◽  
Synthesis Methods ◽  
Test Case ◽  
Rotation Axes ◽  
Acoustic Modelling ◽  
Stiffness Properties ◽  
Rubber Bushing ◽  
Vehicle Suspension System

Classical component mode synthesis methods for reduction are usually limited by the size and compatibility of the coupling interfaces. A component mode synthesis approach with constrained coupling interfaces is presented for vibro-acoustic modelling. The coupling interfaces are constrained to six displacement degrees of freedom. These degrees of freedom represent rigid interface translations and rotations respectively, retaining an undeformed interface shape. This formulation is proposed for structures with coupling between softer and stiffer substructures in which the displacement is chiefly governed by the stiffer substructure. Such may be the case for the rubber-bushing/linking arm assembly in a vehicle suspension system. The presented approach has the potential to significantly reduce the modelling size of such structures, compared with classical component mode synthesis which would be limited by the modelling size of the interfaces. The approach also eliminates problems of nonconforming meshes in the interfaces since only translation directions, rotation axes and the rotation point need to be common for the coupled substructures. Simulation results show that the approach can be used for modelling of systems that resemble a vehicle suspension. It is shown for a test case that adequate engineering accuracy can be achieved when the stiffness properties of the connecting parts are within the expected range of rubber connected to steel.

scholarly journals Evaluation of Component Mode Synthesis Methods for the Detection of Modal Interaction Through Rotor Stator Contacts

2009 ◽  
Author(s):  
Alain Batailly ◽  
Mathias Legrand ◽  
Patrice Cartraud ◽  
Christophe Pierre ◽  
Jean-Pierre Lombard
Keyword(s):  
Finite Element ◽  
Equations Of Motion ◽  
Time Integration ◽  
Component Mode Synthesis ◽  
Integration Scheme ◽  
Synthesis Methods ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Free Interface ◽  
Fixed Interface

The study of interactions through direct contact between bladetips and outer casings in modern turbomachines may be very time-consuming when the classical finite element method is used. The construction of reduced-order models using component mode synthesis (CMS) methods generally allows for dramatic increase in computational efficiency and may be used in order to improve the knowledge over these interaction phenomena. Among the available approaches, both a fixed-interface method and a free-interface method are considered here in an original manner to reduce the size of a realistic two-dimensional model. The equations of motion are solved using an explicit time integration scheme with the Lagrange multiplier method where friction is accounted for. This method offers energy momentum conserving which is a critical point to ensure the convergence of the algorithm. Moreover, it is shown that even in a non-linear framework the reduced-order models converge to the finite element solution as the number of modes included in the models increases. Considering the fixed-interface method of Craig-Bampton (CB) and the free-interface method of Craig-Chang-Martinez (CCM), it is shown that a method with fast displacement convergence may be less efficient in terms of motion convergence.

Substructuring: Definition of the Analytical Dynamic Model of a Complex System During its Design Stage

1995 ◽  
Author(s):  
Fabrice Llorca ◽  
Alain Gerard ◽  
Denis Hennequin ◽  
Dominique Brenot
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Dynamic Properties ◽  
Least Square Method ◽  
Close Correlation ◽  
Least Square ◽  
Component Mode Synthesis ◽  
Design Stage ◽  
Synthesis Methods ◽  
Rectangular Plates

Abstract A structure is often an assembly of several components coupled by various joints such as bolted or riveted joints. Component mode synthesis methods are very practical tools to define a dynamic model. But, several points have to be examined and improved in order to give a complet representation of the modal behaviour of the whole structure. For example, rotational degrees of freedom on connecting points between adjacent substructures should be estimated to give a better representation of the multidirectional connecting forces. These informations may be evaluated through a method based on both interpolation and spatial derivation of the experimental translational displacements of the components. Unlike many other structural elements, the dynamic properties of a connection are very difficult to evaluate. So, we propose a method of determining joint stiffness characteristics. We consider only the conservative problem so the damping properties of the different components of the considered assembly are not taken into account. The joint characteristics are extracted comparing experimental modal data base and component mode synthesis simulation. The updating procedure is based on a nonlinear iterative least-square method. Results are presented concerning a particular assemblie of rectangular plates. Structural modification is applied for one component. We show that the joint properties stay the same if the connecting interface is not modified. The close correlation between predicted and experimental results demonstrate that this method is well adaptated to the study of structural modifications.

A Substructure Based Reduced Order Model for Mistuned Bladed Disks

2009 ◽  
Author(s):  
Andreas Hohl ◽  
Christian Siewert ◽  
Lars Panning ◽  
Jo¨rg Wallaschek
Keyword(s):  
Degrees Of Freedom ◽  
Normal Modes ◽  
Forced Response ◽  
Component Mode Synthesis ◽  
Order Model ◽  
Bladed Disks ◽  
Reduced Order ◽  
Symmetry Approach ◽  
Full Structure ◽  
Value Decomposition

A efficient method for the calculation of the forced response of mistuned bladed disks is introduced. Based on the Component Mode Synthesis techniques the structure is divided into substructures, namely the disk and the blades. The Component Mode Synthesis of the disk is calculated with a fast and accurate cyclic symmetry approach. A recently developed method called Wave Based Substructuring is used to describe the (numerous) coupling degrees of freedom between the disk and the blades. The orthogonal waves are derived with a Singular Value Decomposition or a QR decomposition from the coupling nodes’ normal modes calculated by a modal analysis of the full structure.

scholarly journals Study of Component Mode Synthesis Methods in a Rotor-Stator Interaction Case

2007 ◽  
Author(s):  
Alain Batailly ◽  
Mathias Legrand ◽  
Patrice Cartraud ◽  
Christophe Pierre ◽  
Jean-Pierre Lombard
Keyword(s):  
Equations Of Motion ◽  
Time Integration ◽  
Component Mode Synthesis ◽  
Integration Scheme ◽  
Synthesis Methods ◽  
Specific Contact ◽  
Time Integration Scheme ◽  
Rotor Stator Interaction ◽  
Fixed Interface

The study of rotor-stator interactions between blade-tips and outer casings through direct contact in modern turbomachines is very time-consuming if the classical finite element method is used. In order to improve the knowledge over these interaction phenomena, faster methods have to be applied. The construction of reduced-order models using component mode synthesis methods generally allows for dramatic increase in computational efficiency. Two of these methods, namely a fixed interface method and a free interface methods are considered in an original manner to reduce the size of a realistic two-dimensional model. They are then compared in a very specific contact case-study. The equations of motion are solved using an explicit time integration scheme with the Lagrange multiplier method where friction is accounted for. The primary goal of the present study is to investigate the general behavior of such approaches in the presence of contact nonlinearities. It will be shown that in our contact case, a good accuracy can be obtained from a reduced models with very limited number of modes.

Evaluation of free interface-based reduction techniques for nonlinear forced response analysis of shrouded blades

2019 ◽  
Vol 233 (23-24) ◽  
pp. 7459-7475 ◽  
Author(s):  
Fahimeh Mashayekhi ◽  
Stefano Zucca ◽  
Ali S Nobari
Keyword(s):  
Degrees Of Freedom ◽  
Turbine Blades ◽  
Computational Cost ◽  
Forced Response ◽  
Contact Forces ◽  
Component Mode Synthesis ◽  
Response Analysis ◽  
Synthesis Methods ◽  
Free Interface ◽  
Reduction Techniques

The efficient dynamic stress assessment of turbine blades is of prime importance in turbomachinery design. An accurate prediction of forced response level of shrouded blades requires a very detailed finite element model in addition to a nonlinear solver. In order to perform nonlinear forced response analysis of blades at an affordable computational cost, applying a model order reduction technique is essential. The appeal for component mode synthesis methods in dimension reduction of structures with friction contacts is due to the possibility of retaining a subset of physical degrees of freedom (e.g. the contact degrees of freedom) in the set of generalized coordinates. In this paper, a reduction method recently developed for nonlinear forced response analysis of structures with local nonlinearity is evaluated and compared with two classical component mode synthesis reduction techniques. All three methods have the same projection basis, which includes residual flexibility attachment modes and free interface modes, but different implementation. The response is computed in the frequency domain using multiharmonic balance method and periodic contact forces are modeled with a node-to-node 3D friction contact model. In order to demonstrate the efficiency of the three formulations, a rod and a simplified shrouded turbine blade are considered as case studies.

Selection of Degrees of Freedom for Dynamic Analysis

1987 ◽  
Vol 109 (1) ◽  
pp. 65-69 ◽  
Author(s):  
K. W. Matta
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Degrees Of Freedom ◽  
General Purpose ◽  
Component Mode Synthesis ◽  
Complex Structures ◽  
Large Complex ◽  
Static Condensation ◽  
Basis Vectors ◽  
Selection Of

A technique for the selection of dynamic degrees of freedom (DDOF) of large, complex structures for dynamic analysis is described and the formulation of Ritz basis vectors for static condensation and component mode synthesis is presented. Generally, the selection of DDOF is left to the judgment of engineers. For large, complex structures, however, a danger of poor or improper selection of DDOF exists. An improper selection may result in singularity of the eigenvalue problem, or in missing some of the lower frequencies. This technique can be used to select the DDOF to reduce the size of large eigenproblems and to select the DDOF to eliminate the singularities of the assembled eigenproblem of component mode synthesis. The execution of this technique is discussed in this paper. Examples are given for using this technique in conjunction with a general purpose finite element computer program GENSAM[1].

Interface Reduction in Craig-Bampton Component Mode Synthesis by Orthogonal Polynomial Series

2017 ◽  
Author(s):  
Luigi Carassale ◽  
Mirko Maurici
Keyword(s):  
Degrees Of Freedom ◽  
Axial Compressor ◽  
Component Mode Synthesis ◽  
Reduction Techniques ◽  
Interface Reduction ◽  
Reduction Methods ◽  
Interface Displacement ◽  
Polynomial Series ◽  
Efficient Representation

The component mode synthesis based on the Craig-Bampton method has two strong limitations that appear when the number of the interface degrees of freedom is large. First, the reduced-order model obtained is overweighed by many unnecessary degrees of freedom. Second, the reduction step may become extremely time consuming. Several interface reduction techniques addressed successfully the former problem, while the latter remains open. In this paper we tackle this latter problem through a simple interface-reduction technique based on an a-priory choice of the interface modes. An efficient representation of the interface displacement field is achieved adopting a set of orthogonal basis functions determined by the interface geometry. The proposed method is compared with other existing interface reduction methods on a case study regarding a rotor blade of an axial compressor.

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