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

2017 ◽  
Vol 140 (5) ◽  
Author(s):  
Luigi Carassale ◽  
Mirko Maurici
Keyword(s):  
Degrees Of Freedom ◽  
Axial Compressor ◽  
Component Mode Synthesis ◽  
Order Model ◽  
Reduced Order ◽  
Interface Reduction ◽  
Interface Displacement ◽  
Polynomial Series ◽  
Efficient Representation

The component mode synthesis (CMS) based on the Craig–Bampton (CB) method has two strong limitations that appear when the number of the interface degrees-of-freedom (DOFs) is large. First, the reduced-order model (ROM) obtained is overweighed by many unnecessary DOF. Second, the reduction step may become extremely time consuming. Several interface reduction (IR) techniques addressed successfully the former problem, while the latter remains open. In this paper, we tackle this latter problem through a simple IR 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 IR methods on a case study regarding a rotor blade of an axial compressor.

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.

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 Fully Parameterized Reduced Order Models Using Hyper-Dual Numbers and Component Mode Synthesis

2015 ◽  
Author(s):  
Matthew S. Bonney ◽  
Daniel C. Kammer ◽  
Matthew R. W. Brake
Keyword(s):  
Truncation Error ◽  
Sampling Methods ◽  
Latin Hypercube Sampling ◽  
Component Mode Synthesis ◽  
Reduced Order Models ◽  
Dual Numbers ◽  
Order Model ◽  
Full System ◽  
Reduced Order ◽  
Computational Burden

The uncertainty of a system is usually quantified with the use of sampling methods such as Monte-Carlo or Latin hypercube sampling. These sampling methods require many computations of the model and may include re-meshing. The re-solving and re-meshing of the model is a very large computational burden. One way to greatly reduce this computational burden is to use a parameterized reduced order model. This is a model that contains the sensitivities of the desired results with respect to changing parameters such as Young’s modulus. The typical method of computing these sensitivities is the use of finite difference technique that gives an approximation that is subject to truncation error and subtractive cancellation due to the precision of the computer. One way of eliminating this error is to use hyperdual numbers, which are able to generate exact sensitivities that are not subject to the precision of the computer. This paper uses the concept of hyper-dual numbers to parameterize a system that is composed of two substructures in the form of Craig-Bampton substructure representations, and combine them using component mode synthesis. The synthesis transformations using other techniques require the use of a nominal transformation while this approach allows for exact transformations when a perturbation is applied. This paper presents this technique for a planar motion frame and compares the use and accuracy of the approach against the true full system. This work lays the groundwork for performing component mode synthesis using hyper-dual numbers.

scholarly journals A Reduced Order Model of Mistuning Using a Subset of Nominal System Modes

1999 ◽  
Author(s):  
M.-T. Yang ◽  
J. H. Griffin
Keyword(s):  
Degrees Of Freedom ◽  
Reduced Order Model ◽  
Reduced Order Models ◽  
Order Model ◽  
Disk System ◽  
Element Analysis ◽  
Reduced Order ◽  
Nominal System ◽  
Harmonic Response ◽  
Bladed Disk

Reduced order models have been reported in the literature that can be used to predict the harmonic response of mistuned bladed disks. It has been shown that in many cases they exhibit structural fidelity comparable to a finite element analysis of the full bladed disk system while offering a significant improvement in computational efficiency. In these models the blades and disk are treated as distinct substructures. This paper presents a new, simpler approach for developing reduced order models in which the modes of the mistuned system are represented in terms of a sub-set of nominal system modes. It has the following attributes: the input requirements are relatively easy to generate; it accurately predicts mistuning effects in regions where frequency veering occurs; as the number of degrees of freedom increases it converges to the exact solution; it accurately predicts stresses as well as displacements; and it accurately models the deformation and stresses at the blades’ bases.

Identification of Structural Systems With Limited Number of Sensors and Actuators

2004 ◽  
Author(s):  
Jun Yu ◽  
Maura Imbimbo ◽  
Raimondo Betti
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Models ◽  
Solution Space ◽  
Order Model ◽  
Sensors And Actuators ◽  
Common Assumption ◽  
Reduced Order ◽  
Different Types ◽  
The Common ◽  
Inverse Vibration

The common assumption in the so-called linear inverse vibration problem, which provides the mass/stiffness/damping matrices of second order dynamic models, is the availability of a full set of sensors and actuators. In “reduced-order” problems (with limited number of instrumentation), only the components of the eigenvector matrix regarding the measured degrees of freedom can be successfully identified while nothing can be said about the components connected to the unmeasured degrees of freedom. This paper presents a recently developed “reduced-order” model and expands such a model to a “full-order” one that is quite useful in damage detection. The five representative categories of “reduced-order” problems, defined by considering different types of geometrical conditions, are analyzed and a discussion on their solution space has been performed. The effectiveness and robustness of this approach is shown by means of a numerical example.

Nonlinear Dynamic Analysis of Cantilever Beam Using POD Based Reduced Order Model

2015 ◽  
Vol 786 ◽  
pp. 398-403 ◽  
Author(s):  
Kulkarni Atul Shankar ◽  
Manoj Pandey
Keyword(s):  
Dynamic Analysis ◽  
Large Deformation ◽  
Cantilever Beam ◽  
Nonlinear Dynamic ◽  
Degrees Of Freedom ◽  
Numerical Technique ◽  
Nonlinear Dynamic Analysis ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order

In this paper, a reduced order model is obtained for nonlinear dynamic analysis of a cantilever beam. Nonlinearity in the system is basically due to large deformation. A reduced order model is an efficient method to formulate low order dynamical model which can be obtained from data obtained from numerical technique such as finite element method (FEM). Nonlinear dynamical models are complex with large number of degrees of freedom and hence, are computationally intensive. With formulation of reduced order models (i.e. Macromodels) number of degrees of freedom are reduced to fewer degrees of freedom by using projection based method like Galerkin’s projection, so as to make system computationally faster and cost effective. These macromodels are obtained by extracting global basis functions from fully meshed model runs. Macromodels are generated using technique called proper orthogonal decomposition (POD) which gives good linear fit for the nonlinear systems. Using POD based macromodel, response of system can be computed using fewer modes instead of considering all modes of system. Macromodel is generated to obtain the response of cantilever beam with large deformation and hence, simulation time is reduced by factor of 90 approximately with error of order of 10-4. Further, method of POD based reduced order model is aplied to beam with different loading conditions to check the robustness of the macromodel. POD based macromodel response gives good agreement with FEA model response for a cantilever beam.

Dynamic Condensation and Synthesis of Unsymmetric Structural Systems

2002 ◽  
Vol 69 (5) ◽  
pp. 610-616 ◽  
Author(s):  
G. Visweswara Rao
Keyword(s):  
Model Reduction ◽  
Degrees Of Freedom ◽  
Structural Systems ◽  
Structural System ◽  
Lanczos Algorithm ◽  
Order Model ◽  
Reduction Procedure ◽  
Reduced Order ◽  
Large Size ◽  
Dynamic Condensation

In this paper model reduction of an unsymmetric and damped structural system is presented using a two-sided dynamic condensation technique. The method is an iterative one and essentially utilizes orthonormalized complex eigenvectors of the unsymmetric system. The eigensolution of the reduced order model with specified master degrees-of-freedom is obtained by Lanczos algorithm. The model reduction procedure is further utilized in substructure synthesis and eigenvalue analysis of large size unsymmetric systems. Application of the condensation technique is illustrated via two example problems of rotor bearing systems.

Reduced Order Model for the Geometric Nonlinear Response of Complex Structures

2012 ◽  
Author(s):  
Ricardo Perez ◽  
X. Q. Wang ◽  
Andrew Matney ◽  
Marc P. Mignolet
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Behavior ◽  
Reduced Order Model ◽  
Model Parameters ◽  
Complex Structures ◽  
Order Model ◽  
Plate Structures ◽  
Reduced Order ◽  
Nonlinear Static ◽  
Selection Of

This paper focuses on the development of nonlinear reduced order modeling techniques for the prediction of the response of complex structures exhibiting “large” deformations, i.e. a geometrically nonlinear behavior, and modeled within a commercial finite element code. The present investigation builds on a general methodology successfully validated in recent years on simpler beam and plate structures by: (i) developing a novel identification strategy of the reduced order model parameters that enables the consideration of the large number of modes (> 50 say) that would be needed for complex structures, and (ii) extending an automatic strategy for the selection of the basis functions used to represent accurately the displacement field. The above novel developments are successfully validated on the nonlinear static response of a 9-bay panel structure modeled with 96,000 degrees of freedom within Nastran.

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