Component-centric reduced order modeling for the prediction of the nonlinear geometric response of a part of a stiffened structure

Yuting Wang, X. Q. Wang, Marc Mignolet

Research output: Contribution to journalArticle

Abstract

Component-centric reduced order models (ROMs) have recently been developed in the context of linear structural dynamics. They lead to an accurate prediction of the response of a part of structure (referred to as the b component) while not requiring a similar accuracy in the rest of the structure (referred to as the a component). The advantage of these ROMs over standard modal models is a significantly reduced number of generalized coordinates for structures with groups of close natural frequencies. This reduction is a very desirable feature for nonlinear geometric ROMs, and thus, the focus of the present investigation is on the formulation and validation of component-centric ROMs in the nonlinear geometric setting. The reduction in the number of generalized coordinates is achieved by rotating close frequency modes to achieve unobservable modes in the b component. In the linear case, these modes then completely disappear from the formulation owing to their orthogonality with the rest of the basis. In the nonlinear case, however, the generalized coordinates of these modes are still present in the nonlinear stiffness terms of the observable modes. A closure-type algorithm is then proposed to finally eliminate the unobserved generalized coordinates. This approach, its accuracy and computational savings, is demonstrated first on a simple beam model and then more completely on the 9-bay panel model considered in the linear investigation.

Original languageEnglish (US)
Article number121006
JournalJournal of Computational and Nonlinear Dynamics
Volume13
Issue number12
DOIs
StatePublished - Dec 1 2018

Fingerprint

Reduced-order Modeling
Reduced Order Model
Prediction
Formulation
Structural Dynamics
Natural Frequency
Orthogonality
Stiffness
Rotating
Closure
Eliminate
Structural dynamics
Model
Natural frequencies
Term

Keywords

  • Component-centric modeling
  • Nonlinear geometric response
  • Reduced order modeling
  • Structural dynamics

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Mechanical Engineering
  • Applied Mathematics

Cite this

@article{7c18500afc634fe9bcdc8c18984a2713,
title = "Component-centric reduced order modeling for the prediction of the nonlinear geometric response of a part of a stiffened structure",
abstract = "Component-centric reduced order models (ROMs) have recently been developed in the context of linear structural dynamics. They lead to an accurate prediction of the response of a part of structure (referred to as the b component) while not requiring a similar accuracy in the rest of the structure (referred to as the a component). The advantage of these ROMs over standard modal models is a significantly reduced number of generalized coordinates for structures with groups of close natural frequencies. This reduction is a very desirable feature for nonlinear geometric ROMs, and thus, the focus of the present investigation is on the formulation and validation of component-centric ROMs in the nonlinear geometric setting. The reduction in the number of generalized coordinates is achieved by rotating close frequency modes to achieve unobservable modes in the b component. In the linear case, these modes then completely disappear from the formulation owing to their orthogonality with the rest of the basis. In the nonlinear case, however, the generalized coordinates of these modes are still present in the nonlinear stiffness terms of the observable modes. A closure-type algorithm is then proposed to finally eliminate the unobserved generalized coordinates. This approach, its accuracy and computational savings, is demonstrated first on a simple beam model and then more completely on the 9-bay panel model considered in the linear investigation.",
keywords = "Component-centric modeling, Nonlinear geometric response, Reduced order modeling, Structural dynamics",
author = "Yuting Wang and Wang, {X. Q.} and Marc Mignolet",
year = "2018",
month = "12",
day = "1",
doi = "10.1115/1.4041472",
language = "English (US)",
volume = "13",
journal = "Journal of Computational and Nonlinear Dynamics",
issn = "1555-1415",
publisher = "American Society of Mechanical Engineers(ASME)",
number = "12",

}

TY - JOUR

T1 - Component-centric reduced order modeling for the prediction of the nonlinear geometric response of a part of a stiffened structure

AU - Wang, Yuting

AU - Wang, X. Q.

AU - Mignolet, Marc

PY - 2018/12/1

Y1 - 2018/12/1

N2 - Component-centric reduced order models (ROMs) have recently been developed in the context of linear structural dynamics. They lead to an accurate prediction of the response of a part of structure (referred to as the b component) while not requiring a similar accuracy in the rest of the structure (referred to as the a component). The advantage of these ROMs over standard modal models is a significantly reduced number of generalized coordinates for structures with groups of close natural frequencies. This reduction is a very desirable feature for nonlinear geometric ROMs, and thus, the focus of the present investigation is on the formulation and validation of component-centric ROMs in the nonlinear geometric setting. The reduction in the number of generalized coordinates is achieved by rotating close frequency modes to achieve unobservable modes in the b component. In the linear case, these modes then completely disappear from the formulation owing to their orthogonality with the rest of the basis. In the nonlinear case, however, the generalized coordinates of these modes are still present in the nonlinear stiffness terms of the observable modes. A closure-type algorithm is then proposed to finally eliminate the unobserved generalized coordinates. This approach, its accuracy and computational savings, is demonstrated first on a simple beam model and then more completely on the 9-bay panel model considered in the linear investigation.

AB - Component-centric reduced order models (ROMs) have recently been developed in the context of linear structural dynamics. They lead to an accurate prediction of the response of a part of structure (referred to as the b component) while not requiring a similar accuracy in the rest of the structure (referred to as the a component). The advantage of these ROMs over standard modal models is a significantly reduced number of generalized coordinates for structures with groups of close natural frequencies. This reduction is a very desirable feature for nonlinear geometric ROMs, and thus, the focus of the present investigation is on the formulation and validation of component-centric ROMs in the nonlinear geometric setting. The reduction in the number of generalized coordinates is achieved by rotating close frequency modes to achieve unobservable modes in the b component. In the linear case, these modes then completely disappear from the formulation owing to their orthogonality with the rest of the basis. In the nonlinear case, however, the generalized coordinates of these modes are still present in the nonlinear stiffness terms of the observable modes. A closure-type algorithm is then proposed to finally eliminate the unobserved generalized coordinates. This approach, its accuracy and computational savings, is demonstrated first on a simple beam model and then more completely on the 9-bay panel model considered in the linear investigation.

KW - Component-centric modeling

KW - Nonlinear geometric response

KW - Reduced order modeling

KW - Structural dynamics

UR - http://www.scopus.com/inward/record.url?scp=85056650348&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85056650348&partnerID=8YFLogxK

U2 - 10.1115/1.4041472

DO - 10.1115/1.4041472

M3 - Article

AN - SCOPUS:85056650348

VL - 13

JO - Journal of Computational and Nonlinear Dynamics

JF - Journal of Computational and Nonlinear Dynamics

SN - 1555-1415

IS - 12

M1 - 121006

ER -