Dual Craig-Bampton component mode synthesis method for model order reduction of nonclassically damped linear systems

Abstract A new method of model-order reduction for the flexible multibody system which undergoes large deformation and rotation is proposed. At first, the flexible multibody system is modeled by absolute nodal coordinate formulation (ANCF), and then, the whole motion process of the system is divided into a series of quasi-static equilibrium configurations according to a given criterion. Afterward, motion equation is locally linearized based on the Taylor expansion. Therefore, the constant tangent stiffness matrix is obtained and does not need to be updated until the next configuration. Based on the locally linearized motion equation, the free-interface component mode synthesis (CMS) method is adopted to reduce the degrees-of-freedom (DOF) of the flexible multibody system molded by ANCF. The generalized-α integrator is used to solve the reduced motion equation. To verify the accuracy and efficiency of the proposed method, three examples including a free-falling pendulum, a flexible spinning beam and a deployable sail arrays are presented. Results show that the proposed method is able to reduce the computing time and maintain high accuracy.

Download Full-text

Model order reduction for discrete-time linear systems with the discrete-time polynomials

Japan Journal of Industrial and Applied Mathematics ◽

10.1007/s13160-019-00384-0 ◽

2019 ◽

Vol 36 (3) ◽

pp. 1005-1020 ◽

Cited By ~ 1

Author(s):

Yao-Lin Jiang ◽

Jun-Man Yang ◽

Kang-Li Xu

Keyword(s):

Linear Systems ◽

Discrete Time ◽

Model Order Reduction ◽

Order Reduction ◽

Model Order ◽

Time Linear

Download Full-text

Parameterized frequency-dependent balanced truncation for model order reduction of linear systems

2017 29th Chinese Control And Decision Conference (CCDC) ◽

10.1109/ccdc.2017.7978648 ◽

2017 ◽

Cited By ~ 1

Author(s):

Xin Du ◽

Peter Benner

Keyword(s):

Linear Systems ◽

Model Order Reduction ◽

Order Reduction ◽

Balanced Truncation ◽

Model Order ◽

Frequency Dependent

Download Full-text

Model order-reduction for discrete-time switched linear systems

International Journal of Systems Science ◽

10.1080/00207721.2011.554911 ◽

2012 ◽

Vol 43 (9) ◽

pp. 1753-1763 ◽

Cited By ~ 17

Author(s):

Abderazik Birouche ◽

Benjamin Mourllion ◽

Michel Basset

Keyword(s):

Linear Systems ◽

Discrete Time ◽

Model Order Reduction ◽

Order Reduction ◽

Model Order ◽

Switched Linear Systems

Download Full-text

Singular perturbation approximation for linear systems with Lévy noise

Stochastics and Dynamics ◽

10.1142/s0219493718500338 ◽

2018 ◽

Vol 18 (04) ◽

pp. 1850033 ◽

Cited By ~ 3

Author(s):

Martin Redmann ◽

Peter Benner

Keyword(s):

Singular Perturbation ◽

Linear Systems ◽

Model Order Reduction ◽

Order Reduction ◽

Reduction Technique ◽

Lévy Noise ◽

Model Order ◽

Linear Evolution Equation ◽

Levy Noise ◽

Perturbation Approximation

To solve a stochastic linear evolution equation numerically, finite dimensional approximations are commonly used. For a good approximation, one might end up with a sequence of ordinary stochastic linear equations of high order. To reduce the high dimension for practical computations, we consider the singular perturbation approximation as a model order reduction technique in this paper. This approach is well-known from deterministic control theory and here we generalize it for controlled linear systems with Lévy noise. Additionally, we discuss properties of the reduced order model, provide an error bound, and give some examples to demonstrate the quality of this model order reduction technique.

Download Full-text

Application of the mode-shape expansion based on model order reduction methods to a composite structure

Open Engineering ◽

10.1515/eng-2017-0026 ◽

2017 ◽

Vol 7 (1) ◽

pp. 199-212 ◽

Cited By ~ 1

Author(s):

Humberto Peredo Fuentes

Keyword(s):

Mode Shape ◽

Model Order Reduction ◽

Strong Influence ◽

Order Reduction ◽

Component Mode Synthesis ◽

Experimental Measurements ◽

Fe Model ◽

Model Order ◽

Mass Matrices ◽

Reduction Methods

AbstractThe application of different mode-shape expansion (MSE) methods to a CFRP based on model order reduction (MOR) and component mode synthesis (CMS) methods is evaluated combining the updated stiffness parameters of the full FE model obtained with a mix-numerical experimental technique (MNET) in a previous work. The eigenvectors and eigenfrequencies of the different MSE methods obtained are compared with respect to the experimental measurements and with a full FE model solutions using the modal assurance criteria (MAC). Furthermore, the stiffness and mass weighted coefficients (K-MAC and M-MAC respectively) are calculated and compared to observe the influence of the different subspace based expansion methods applying the MAC criteria. The K-MAC and M-MAC are basically the MAC coefficients weighted by a partition of the global stiffness and mass matrices respectively. The best K-MAC and M-MAC results per paired mode-sensor are observed in the subspace based expansion MODAL/SEREP and MDRE-WE methods using the updated stiffness parameters. A strong influence of the subspace based on MOR using MSE methods is observed in the K-MAC and M-MAC criteria implemented in SDTools evaluating the stiffness parameters in a contrieved example.

Download Full-text