Dynamic condensation for structural redesign

AbstractThis design study applied parameterisation to rotor blade for improved performance. In the design, parametric equations were used to represent blade planform changes over the existing rotor blade model. Design variables included blade twist, sweep, dihedral, and radial control point. Updates to the blade structural properties with changes in the design variables allowed accurate evaluation of performance objectives and realistic structural constraints – blade stability, steady moments (flap bending, chord bending, and torsion), and the high g manoeuvring pitch link loads. Performance improvement was demonstrated with multiple parametric designs. Using a parametric design with advanced aerofoils, the predicted power reduction was 1·0% in hover, 10·0% at μ = 0·30, and 17·0% at μ = 0·40 relative to the baseline UH-60A rotor, but these were obtained with a 35% increase in the steady chord bending moment at μ = 0·30 and a 20% increase in the half peak-to-peak pitch link load during the UH-60A UTTAS manoeuvre Low vibration was maintained for this design. More rigorous design efforts, such as chord tapering and/or structural redesign of the blade cross section, would enlarge the feasible design space and likely provide significant performance improvement.

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Implementing model reduction to the JuliaFEM platform

Rakenteiden Mekaniikka ◽

10.23998/rm.69026 ◽

2018 ◽

Vol 51 (1) ◽

pp. 36-54 ◽

Cited By ~ 1

Author(s):

Marja Liisa Rapo ◽

Jukka Aho ◽

Hannu Koivurova ◽

Tero Frondelius

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Model Reduction ◽

Open Source ◽

Degrees Of Freedom ◽

Mass Matrices ◽

Dynamic Condensation ◽

Dynamic Analyses ◽

Reduction Methods ◽

Large Model

JuliaFEM is an open source finite element method solver written in the Julia language. This paper presents an implementation of two common model reduction methods: the Guyan reduction and the Craig-Bampton method. The goal was to implement these algorithms to the JuliaFEM platform and demonstrate that the code works correctly. This paper first describes the JuliaFEM concept briefly after which it presents the theory of model reduction, and finally, it demonstrates the implemented functions in an example model. This paper includes instructions for using the implemented algorithms, and reference the code itself in GitHub. The reduced stiness and mass matrices give the same results in both static and dynamic analyses as the original matrices, which proves that the code works correctly. The code runs smoothly on relatively large model of 12.6 million degrees of freedom. In future, damping could be included in the dynamic condensation now that it has been shown to work.

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A dynamic condensation method with free interface substructuring

Mechanical Systems and Signal Processing ◽

10.1016/j.ymssp.2019.04.021 ◽

2019 ◽

Vol 129 ◽

pp. 218-234 ◽

Cited By ~ 1

Author(s):

Jeong-Ho Kim ◽

Seung-Hwan Boo ◽

Phill-Seung Lee

Keyword(s):

Free Interface ◽

Condensation Method ◽

Dynamic Condensation

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Dynamic Condensation of Structural Systems

IABSE Symposium Report ◽

10.2749/222137810796064011 ◽

2010 ◽

Vol 97 (4) ◽

pp. 69-76

Author(s):

Odine Manfroni ◽

Davide Rocchi ◽

Gianluca Tiraferri

Keyword(s):

Structural Systems ◽

Dynamic Condensation

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Iterative method for dynamic condensation combined with substructuring scheme

Journal of Sound and Vibration ◽

10.1016/j.jsv.2008.02.046 ◽

2008 ◽

Vol 317 (1-2) ◽

pp. 199-218 ◽

Cited By ~ 35

Author(s):

Dongsoo Choi ◽

Hyungi Kim ◽

Maenghyo Cho

Keyword(s):

Iterative Method ◽

Dynamic Condensation

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Consideration of structural constraints in passive rotor blade design for improved performance

The Aeronautical Journal ◽

10.1017/aer.2016.77 ◽

2016 ◽

Vol 120 (1232) ◽

pp. 1604-1631 ◽

Cited By ~ 2

Author(s):

J.W. Lim

Keyword(s):

Performance Improvement ◽

Rotor Blade ◽

Parametric Design ◽

Control Point ◽

Bending Moment ◽

Structural Constraints ◽

Design Variables ◽

Significant Performance ◽

Structural Redesign ◽

Improved Performance

ABSTRACTThis design study applied parameterisation to rotor blade for improved performance. In the design, parametric equations were used to represent blade planform changes over the existing rotor blade model. Design variables included blade twist, sweep, dihedral and the radial control point. Updates to the blade structural properties with changes in the design variables allowed accurate evaluation of performance objectives and realistic structural constraints – blade stability, steady moments (flap bending, chord bending and torsion) and the high-g manoeuvre pitch link loads. Performance improvement was demonstrated with multiple parametric designs. Using a parametric design with advanced aerofoils, the predicted power reduction was 1.0% in hover, 10.0% at μ = 0.30 and 17.0% at μ = 0.40, relative to the baseline UH-60A rotor, but these were obtained with a 35% increase in the steady chord bending moment at μ = 0.30 and a 20% increase in the half peak-to-peak pitch link load during the UH-60A UTTAS manoeuvre. Low vibration was maintained for this design. More rigorous design efforts, such as chord tapering and/or structural redesign of the blade cross section, would enlarge the feasible design space and likely provide significant performance improvement.

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Dynamic Condensation of Nonclassically Damped Models

Model Order Reduction Techniques ◽

10.1007/978-1-4471-3827-3_8 ◽

2004 ◽

pp. 163-216

Author(s):

Zu-Qing Qu

Keyword(s):

Dynamic Condensation

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Reduction of Hybrid FE-SEA Model for the Mid-Frequency Vibration of Vibro-Acoustic Systems Using Dynamic Condensation Approach

Journal of Vibration and Acoustics ◽

10.1115/1.4042930 ◽

2019 ◽

Vol 141 (4) ◽

Author(s):

Ruxin Gao ◽

Yahui Zhang ◽

David Kennedy

Keyword(s):

Present Method ◽

Degrees Of Freedom ◽

Dynamic Stiffness ◽

Fe Model ◽

Dynamic Matrix ◽

Acoustic Cavity ◽

Hybrid Finite Element ◽

Flexibility Matrix ◽

Point Of Interest ◽

Dynamic Condensation

In this paper, an improved hybrid finite element (FE)-statistical energy analysis (SEA) method is proposed for the mid-frequency vibration of vibro-acoustic systems. Within the framework of the hybrid FE-SEA method, the present method reduces the size of the total dynamic matrix of a vibro-acoustic system by employing dynamic condensation to reduce the order of the dynamic matrix of the acoustic cavity. A fast algorithm is introduced to obtain the dynamic flexibility matrix of the slave degrees-of-freedom (DOFs) of the acoustic cavity FE model, thereby avoiding the direct inverse computation of a large dynamic stiffness matrix at each frequency point of interest. The first numerical example illustrates the validity and efficiency of the present method, while the convergence and accuracy analysis of the proposed method is investigated numerically by the second example.

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