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 β component) while not requiring a similar accuracy in the rest of the structure (referred to as the α 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 β 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.

References

References
1.
Patil
,
M. J.
,
Hodges
,
D. H.
, and
Cesnik
,
C. E. S.
,
2001
, “
Nonlinear Aeroelasticity and Flight Dynamics of High-Altitude Long-Endurance Aircraft
,”
J. Aircr.
,
38
(
1
), pp.
88
94
.
2.
Levy
,
R.
, and
Spillers
,
W. R.
,
2013
,
Analysis of Geometrically Nonlinear Structures
,
Springer
, The Netherlands.
3.
Falkiewicz
,
N. J.
,
Cesnik
,
C. E. S.
,
Crowell
,
A. R.
, and
McNamara
,
J. J.
,
2011
, “
Reduced Order Aerothermoelastic Framework for Hypersonic Vehicle Control Simulation
,”
AIAA J.
,
49
(
8
), pp.
1625
1646
.
4.
Culler
,
A. J.
, and
McNamara
,
J. J.
,
2011
, “
Impact of Fluid-Thermal-Structural Coupling on Response Prediction of Hypersonic Skin Panels
,”
AIAA J.
,
49
(
11
), pp.
2393
2406
.
5.
Matney
,
A.
,
Perez
,
R.
, and
Mignolet
,
M. P.
, 2011, “
Nonlinear Unsteady Thermoelastodynamic Response of a Panel Subjected to an Oscillating Flux by Reduced Order Models
,”
AIAA
Paper No. AIAA 2011-2016.https://arc.aiaa.org/doi/abs/10.2514/6.2011-2016
6.
Matney
,
A. K.
,
Spottswood
,
S. M.
,
Mignolet
,
M. P.
,
Culler
,
A. J.
, and
McNamara
,
J. J.
,
2013
, “
Coupled Reduced Order Model-Based Structural-Thermal Prediction of Hypersonic Panel Response
,”
11th International Conference on Recent Advances in Structural Dynamics
, Pisa, Italy, July 1–3, Paper No. 890.
7.
Matney
,
A.
,
Mignolet
,
M. P.
,
Culler
,
A. J.
,
McNamara
,
J. J.
, and
Spottswood
,
S. M.
, 2015, “
Panel Response Prediction Through Reduced Order Models With Application to Hypersonic Aircraft
,”
AIAA
Paper No. AIAA 2015-1630.https://arc.aiaa.org/doi/abs/10.2514/6.2015-1630
8.
Gogulapati
,
A.
,
Deshmukh
,
R.
,
Crowell
,
A. R.
,
McNamara
,
J. J.
,
Vyas
,
V.
,
Wang
,
X. Q.
,
Mignolet
,
M.
,
Beberniss
,
T.
,
Spottswood
,
S. M.
, and
Eason
,
T. G.
, 2014, “
Response of a Panel to Shock Impingement: Modeling and Comparison With Experiments
,”
AIAA
Paper No. AIAA 2014-0148.https://arc.aiaa.org/doi/10.2514/6.2015-0685
9.
Gogulapati
,
A.
,
Deshmukh
,
R.
,
McNamara
,
J. J.
,
Vyas
,
V.
,
Wang
,
X. Q.
,
Mignolet
,
M. P.
,
Beberniss
,
T.
,
Spottswood
,
S. M.
, and
Eason
,
T. G.
,
2015
, “
Response of a Panel to Shock Impingement: Modeling and Comparison With Experiments—Part 2
,”
AIAA
Paper No. AIAA 2015-0685.https://arc.aiaa.org/doi/pdf/10.2514/6.2015-0685
10.
Gogulapati
,
A.
,
Brouwer
,
K.
,
Wang
,
X. Q.
,
Murthy
,
R.
,
McNamara
,
J. J.
, and
Mignolet
,
M. P.
,
2017
, “
Full and Reduced Order Aerothermoelastic Modeling of Built-Up Aerospace Panels in High-Speed Flows
,”
AIAA
Paper No. AIAA 2017-0180.https://arc.aiaa.org/doi/pdf/10.2514/6.2017-0180
11.
Perez
,
R. A.
,
Smarslok
,
B. P.
,
McNamara
,
J. J.
, and
Brouwer
,
K.
,
2015
, “
Investigating Model Uncertainty in the Nonlinear Aeroelastic Response of Thin Panels
,”
AIAA
Paper No. AIAA 2015-1600.https://arc.aiaa.org/doi/pdf/10.2514/6.2015-1600
12.
Perez
,
R. A.
,
Spottswood
,
S. M.
,
Beberniss
,
T. J.
,
Bartram
,
G. W.
, and
Eason
,
T. G.
,
2016
, “
Nonlinear Dynamic Response Prediction of a Thin Panel in a Multi-Discipline Environment—Part II: Numerical Predictions
,”
34th International Modal Analysis Conference (IMAC-34)
, Orlando, FL, Jan. 25–28.
13.
Mignolet
,
M. P.
,
Przekop
,
A.
,
Rizzi
,
S. A.
, and
Spottswood
,
S. M.
,
2013
, “
A Review of Indirect/Non-Intrusive Reduced Order Modeling of Nonlinear Geometric Structures
,”
J. Sound Vib.
,
332
(
10
), pp.
2437
2460
.
14.
McEwan
,
M. I.
,
Wright
,
J. R.
,
Cooper
,
J. E.
, and
Leung
,
A. Y. T.
,
2001
, “
A Combined Modal/Finite Element Analysis Technique for the Dynamic Response of a Nonlinear Beam to Harmonic Excitation
,”
J. Sound Vib.
,
243
(
4
), pp.
601
624
.
15.
Hollkamp
,
J. J.
,
Gordon
,
R. W.
, and
Spottswood
,
S. M.
,
2005
, “
Nonlinear Modal Models for Sonic Fatigue Response Prediction: A Comparison of Methods
,”
J. Sound Vib.
,
284
(
3–5
), pp.
1145
1163
.
16.
Przekop
,
A.
, and
Rizzi
,
S. A.
,
2006
, “
Nonlinear Reduced Order Random Response Analysis of Structures With Shallow Curvature
,”
AIAA J.
,
44
(
8
), pp.
1767
1778
.
17.
Przekop
,
A.
, and
Rizzi
,
S. A.
,
2007
, “
Dynamic Snap-Through of Thin-Walled Structures by a Reduced-Order Method
,”
AIAA J.
,
45
(
10
), pp.
2510
2519
.
18.
Hollkamp
,
J. J.
, and
Gordon
,
R. W.
,
2008
, “
Reduced-Order Models for Nonlinear Response Prediction: Implicit Condensation and Expansion
,”
J. Sound Vib.
,
318
(
4–5
), pp.
1139
1153
.
19.
Spottswood
,
S. M.
,
Hollkamp
,
J. J.
, and
Eason
,
T. G.
,
2008
, “
On the Use of Reduced-Order Models for a Shallow Curved Beam Under Combined Loading
,”
AIAA
Paper No. AIAA-2008-1873.https://arc.aiaa.org/doi/pdf/10.2514/6.2008-2235
20.
Kim
,
K.
,
Radu
,
A. G.
,
Wang
,
X. Q.
, and
Mignolet
,
M. P.
,
2013
, “
Nonlinear Reduced Order Modeling of Isotropic and Functionally Graded Plates
,”
Int. J. Non-Linear Mech.
,
49
, pp.
100
110
.
21.
Perez
,
R. A.
,
Wang
,
X. Q.
, and
Mignolet
,
M. P.
,
2014
, “
Non-Intrusive Structural Dynamic Reduced Order Modeling for Large Deformations: Enhancements for Complex Structures
,”
ASME J. Comput. Nonlinear Dyn.
,
9
(
3
), p.
031008
.
22.
Kuether
,
R. J.
,
Allen
,
M. S.
, and
Hollkamp
,
J. J.
,
2016
, “
Modal Substructuring for Geometrically Nonlinear Finite Element Models
,”
AIAA J.
,
54
(
2
), pp.
691
702
.
23.
Kuether
,
R. J.
,
Deaner
,
B.
,
Allen
,
M. S.
, and
Hollkamp
,
J. J.
,
2015
, “
An Evaluation of Nonlinear Reduced Order Models Used to Compute Nonlinear Normal Modes of Geometrically Nonlinear Structures
,”
AIAA J.
,
53
(
11
), pp.
3273
3285
.
24.
Wang
,
X. Q.
,
Perez
,
R.
,
Mignolet
,
M. P.
,
Capillon
,
R.
, and
Soize
,
C.
, 2013, “
Nonlinear Reduced Order Modeling of Complex Wing Models
,”
AIAA
Paper No. AIAA-2013-1520.https://arc.aiaa.org/doi/pdf/10.2514/6.2013-1520
25.
Perez
,
R. A.
,
Smarslok
,
B. P.
, and
Mignolet
,
M. P.
, 2015, “
Deterministic and Stochastic Partial Linearization Approach for Nonlinear Reduced Order Models of Structures
,”
AIAA
Paper No. AIAA 2015-2052.https://arc.aiaa.org/doi/pdf/10.2514/6.2015-2052
26.
Wang
,
Y.
, and
Mignolet
,
M. P.
,
2017
, “
Component-Centric Reduced Order Modeling of the Dynamic Response of Linear Multibay Structures
,”
ASME J. Vib. Acoust.
,
139
(
4
), p.
041007
.
27.
Muravyov
,
A. A.
, and
Rizzi
,
S. A.
,
2003
, “
Determination of Nonlinear Stiffness With Application to Random Vibration of Geometrically Nonlinear Structures
,”
Comput. Struct.
,
81
(
15
), pp.
1513
1523
.
28.
Wang
,
Y.
,
2017
, “
Reduced Order Modeling With Variable Spatial Fidelity for the Linear and Nonlinear Dynamics of Multi-Bay Structures
,”
Ph.D. Dissertation
, Arizona State University, Tempe, AZ.https://repository.asu.edu/attachments/181237/content/Wang_asu_0010E_16677.pdf
29.
Buehrle
,
R. D.
,
Fleming
,
G. A.
,
Pappa
,
R. S.
, and
Grosveld
,
F. W.
,
2000
, “
Finite Element Model Development for Aircraft Fuselage Structures
,” 18th International Modal Analysis Conference (
IMAC
), San Antonio, TX, Feb. 7–10.https://ntrs.nasa.gov/search.jsp?R=20040086465
You do not currently have access to this content.