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Finite element model updating of jointed structure based on modal and strain frequency response function

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Abstract

To acquire a reasonable model for structural dynamic strength analysis, a bottom-up finite element modeling and updating methodology based on multi responses is proposed. The fundamental principles of structural dynamics analysis and model updating were introduced, and the proposed strategy was applied to the case study of an L-shaped jointed structure. Components of the jointed structure were modeled sequentially, and inaccurate model parameters were updated based on the corresponding experimental modal results in the first stage. In the second stage, components were connected together by bolts. The joint interfaces were represented by thin-layer elements, and local joint parameters were updated based on strain frequency response function (FRF). Finally, the precision of finite element model (FEM) was validated by acceleration frequency response function. The results indicated that the proposed methodology is able to reduce model simulation errors in both components and the overall jointed structure. Not only can the updated model of a jointed structure reproduce the experimental results used in updating, but also predict responses that are not used in the process of model updating.

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Abbreviations

M :

Mass matrix of a system

C :

Damping matrix of a system

K :

Stiffness matrix of a system

X :

Nodal displacement vector

F :

Exciting force vector

s :

Transformation factor

Φ :

Mode shape matrix

Q :

Modal coordinate matrix

M r :

The r-th modal mass

C r :

The r-th modal damping

K r :

The r-th modal stiffness

ϕ r :

The r-th mode shape

ω r :

The r-th modal frequency

ζ r :

The r-th modal damping ratio

H X :

Displacement FRF

\(\varepsilon _i^e\) :

The strain at any point within i-th element

B :

Mapping matrix between displacement and strain

\({\boldsymbol{x}}_i^e\) :

Nodal displacement vector of i-th element in the elemental coordinate

n g :

The number of elements sharing the j-th node

\(\varepsilon _{i,g}^e\) :

Nodal strain value of j-th node in g-th element

x l :

Nodal displacement in elemental coordinate

x :

Nodal displacement in global coordinate

T l :

Mapping matrix between elemental and global coordinate

ε j :

Strain matrix at the j-th node

ε :

Strain matrix of the system

H ε :

Strain FRF

ω A :

Simulative modal frequency

ω E :

Experimental modal frequency

E ω :

Modal frequency error

\(\phi _A^a\) :

The a-th mode shape of simulation

\(\phi _E^b\) :

The b-th mode shape of experimental test

MAC :

Modal assurance criterion

SC :

Shape correlation of FRF

AC :

Amplitude correlation of FRF

\({\boldsymbol{H}}_A^p\) :

The p-th column of simulative FRF matrix

\({\boldsymbol{H}}_E^q\) :

The q-th column of experimental FRF matrix

θ :

Updating parameters

R a :

Simulative results used for updating

R e :

Experimental results used for updating

lb :

Lower boundary of updating parameters

ub :

Upper boundary of updating parameters

W f :

Weighting factor

G :

Error of structural characteristic or response

N r :

The number of frequencies used in FEM updating

N p :

The number of columns used in FRF based updating

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Acknowledgments

This work was supported by the National Science Foundation of China (Grant No. 51505398, U1530122), and the Aeronautical Science Foundation of China (20150968003, 20172852024). The authors also gratefully thank the editors and reviewers of this manuscript.

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Authors and Affiliations

  1. College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Zhan Ming, Guo Qintao & Yue Lin

  2. School of Aerospace Engineering, Xiamen University, Xiamen, 361005, China

    Zhang Baoqiang

Authors
  1. Zhan Ming
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  2. Guo Qintao
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  3. Yue Lin
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  4. Zhang Baoqiang
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Corresponding author

Correspondence to Guo Qintao.

Additional information

Recommended by Associate Editor Kyoung-Su Park

Zhan Ming has a Ph.D. in Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, China. His research interests are in areas of finite element modeling and simulation, model updating and validation and structural dynamic optimization design.

Guo Qintao is an Assistant Professor of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, China. His research interests are in areas of finite element modeling and simulation, model updating and validation and structural dynamic optimization design.

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Ming, Z., Qintao, G., Lin, Y. et al. Finite element model updating of jointed structure based on modal and strain frequency response function. J Mech Sci Technol 33, 4583–4593 (2019). https://doi.org/10.1007/s12206-019-0902-0

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  • DOI: https://doi.org/10.1007/s12206-019-0902-0

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