Reduced-Order Modeling of Bladed Disks Considering Small Mistuning of the Disk Sectors

2018 ◽  
Vol 141 (5) ◽  
Author(s):  
Lukas Schwerdt ◽  
Sebastian Willeke ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
Reduction Method ◽  
Order Reduction ◽  
Bladed Disks ◽  
Small Disk ◽  
Model Order ◽  
Reduced Order ◽  
Mass Matrices ◽  
Dense Matrices ◽  
The Individual ◽  
Order Reduction Method

A model order reduction method based on the component mode synthesis for mistuned bladed disks is introduced, with one component for the disk and one component for each blade. The interface between the components at the blade roots is reduced using the wave-based substructuring (WBS) method, which employs tuned system modes. These system modes are calculated first, and used subsequently during the reduction of the individual components, which eliminates the need to build a partially reduced intermediate model with dense matrices. For the disk, a cyclic Craig–Bampton (CB) reduction is applied. The deviations of the stiffness and mass matrices of individual disk sectors are then projected into the cyclic basis of interior and interface modes of the disk substructure. Thereby, it is possible to model small disk mistuning in addition to large mistuning of the blades.

Reduced-Order Modeling of Bladed Disks Considering Small Mistuning of the Disk Sectors

2018 ◽  
Author(s):  
Lukas Schwerdt ◽  
Sebastian Willeke ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
Reduction Method ◽  
Order Reduction ◽  
Bladed Disks ◽  
Small Disk ◽  
Model Order ◽  
Reduced Order ◽  
Mass Matrices ◽  
Dense Matrices ◽  
The Individual ◽  
Order Reduction Method

A model order reduction method based on the Component Mode Synthesis for mistunend bladed disks is introduced, with one component for the disk and one component for each blade. The interface between the components at the blade roots is reduced using the wave-based substructuring method, which employs tuned system modes. These system modes are calculated first, and used subsequently during the reduction of the individual components, which eliminates the need to build a partially reduced intermediate model with dense matrices. For the disk, a cyclic Craig-Bampton reduction is applied. The deviations of the stiffness and mass matrices of individual disk sectors are then projected into the cyclic basis of interior and interface modes of the disk substructure. Thereby it is possible to model small disk mistuning in addition to large mistuning of the blades.

scholarly journals On the Interpolation of Reduced-Order Models

2018 ◽  
Author(s):  
Yao Yue ◽  
Lihong Feng ◽  
Peter Benner
Keyword(s):  
Model Order Reduction ◽  
Reduction Method ◽  
Order Reduction ◽  
Reduced Order Models ◽  
Matching Method ◽  
Model Order ◽  
Reduced Order ◽  
Parametric Model Order Reduction ◽  
Order Reduction Method ◽  
Parameter Dependency

A parametric model-order reduction method based on interpolation of reduced-order models, namely the pole-matching method, is proposed for linear systems in the frequency domain. It captures the parametric dynamics of the system by interpolating the positions and amplitudes of the poles. The pole-matching method relies completely on the reduced-order models themselves, regardless of how they are built. It is able to deal with many parameters as well as complicated parameter dependency. Numerical results show that the proposed pole-matching method gives accurate results even when it interpolates two reduced-order models of completely different nature, one computed by a projection-based method and the other computed by a data-driven method.

scholarly journals AN ITERATIVE MODEL ORDER REDUCTION METHOD FOR LARGE-SCALE DYNAMICAL SYSTEMS

2017 ◽  
Vol 59 (1) ◽  
pp. 115-133
Author(s):  
K. MOHAMED ◽  
A. MEHDI ◽  
M. ABDELKADER
Keyword(s):  
Dynamical Systems ◽  
Model Order Reduction ◽  
Large Scale ◽  
Reduction Method ◽  
Linear Time ◽  
Order Reduction ◽  
Lyapunov Equation ◽  
Model Order ◽  
Iterative Model ◽  
Order Reduction Method

We present a new iterative model order reduction method for large-scale linear time-invariant dynamical systems, based on a combined singular value decomposition–adaptive-order rational Arnoldi (SVD-AORA) approach. This method is an extension of the SVD-rational Krylov method. It is based on two-sided projections: the SVD side depends on the observability Gramian by the resolution of the Lyapunov equation, and the Krylov side is generated by the adaptive-order rational Arnoldi based on moment matching. The use of the SVD provides stability for the reduced system, and the use of the AORA method provides numerical efficiency and a relative lower computation complexity. The reduced model obtained is asymptotically stable and minimizes the error ($H_{2}$and$H_{\infty }$) between the original and the reduced system. Two examples are given to study the performance of the proposed approach.

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