Abstract
This study aims to improve the accuracy of the parametric estimation of systems with modal interference in the frequency domain. The theory of modal identification states that the frequency response function can be expressed as a rational function form by using the curve fitting technique, and the modal parameters can then be estimated from rational fractional coefficients. The conventional common denominator model only indicates the frequency response function of a single-degree-of-freedom system; thus, it cannot acquire the mode shape information. In this paper, we propose the matrix-fractional coefficient model constructed by the frequency response functions of a multiple-degree-of-freedom system for modal identification. To avoid the phenomenon of omitted modes caused by the distortion from modal interference among the vibration modes of systems during modal estimation, we use a system model with higher-order matrix-fractional coefficients, but fictitious modes may be caused by numerical computation. Structural and fictitious modes can be effectively separated by using a different-order constructed stabilization diagram. Modal identification can be implemented by solving the eigenproblem of the companion matrix yielded from least-square estimation. Numerical simulations, including a full model of sedan and one-half railway vehicle in the form of a linear 2D model, as well as the experimental testing of an actual plate, confirm the validity and robustness of the proposed parametric-estimation method for a system with modal interference under noisy conditions.
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Abbreviations
- [H (ω)]:
-
Frequency response function matrix
- [A ω]:
-
Common denominator polynomial matrix
- [B ω]:
-
Numerator polynomial matrix
- ⊗:
-
Kronecker product
- M :
-
Mass matrix
- K :
-
Stiffness matrix
- C :
-
Damping matrix
- m :
-
Polynomial order
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Acknowledgments
This research was supported in part by the Ministry of Science and Technology of Taiwan under the Grant MOST 107-2221-E-020-010-. The author wishes to thank anonymous reviewers for their valuable comments and suggestions in revising the paper.
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Recommended by Associate Editor Junhong Park
C. S. Lin received his Ph.D. from the Department of Aeronautics and Astronautics of National Cheng Kung University, Taiwan, in 2011. He joined the Faculty of National Pingtung University of Science and Technology, Taiwan, in 2016 where he is currently an Assistant Professor at the Department of Vehicle Engineering. His research interests are random vibration and modal analysis.
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Lin, CS. Frequency-domain approach for the parametric identification of structures with modal interference. J Mech Sci Technol 33, 4081–4091 (2019). https://doi.org/10.1007/s12206-019-0803-2
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DOI: https://doi.org/10.1007/s12206-019-0803-2