Model Updating of a Euler-Bernoulli Beam Using the Response Method

Abstract

In this study, the computational model is updated using an analytical model instead of an experimental one. Continuous and discrete parameter models of a Euler–Bernoulli beam are constructed analytically and computationally. To construct the computational models, Ansys™ software is employed, and 1-D beam elements are chosen to get the finite element model of a cantilever beam. To get analytical solutions for the continuous and discrete parameter models, a state-space representation is employed. In the first step, only mass and stiffness matrices are considered to model the beam. Eigenfrequencies and eigenvectors of the beam are calculated. The analytical and computational eigenfrequencies of continuous and discrete parameter models are compared. In the seconds step, non-proportional viscous damping and non-proportional structural damping matrices are introduced into the analytical discrete parameter model. Then, the frequency response functions of the model are generated. The damping matrices are identified using the generated frequency response functions. The damping matrices used in the analytical model, and the damping matrices identified using the frequency response functions are compared. It is observed that the assigned damping matrices and the identified damping matrices are identical, which shows that the computational model can be accurately updated provided the FRFs are available.

Keywords

• Frequency Response Function
• Model Updating
• Structural Damping
• Viscous Damping

References

1. Mottershead J.E., Friswell M.I., 1993. Model updating in structural dynamics: a survey. Journal of Sound and Vibration, 167, 347-375.
2. Baruch M., 1978. Optimization procedure to correct stiffness and flexibility matrices using vibration tests. AIAA Journal, 16, 1208-1210.
3. Berman A., Nagy E.J., 1983. Improvement of a large analytical model using test data. AIAA Journal, 21, 1168-1173.
4. Wei F-S., 1990. Analytical dynamic model improvement using vibration test data. AIAA Journal, 28, 175-177.
5. Friswell M.I., Inman D., Pilkey D., 1998. Direct updating of damping and stiffness matrices. AIAA Journal, 36, 491-493.
6. Imregun M., Visser W.J., Ewins D.J., 1995. Finite element model updating using frequency response function data – 1: Theory and initial investigation. Journal of Mechanical Science and Technology, 9, 187–202.
7. Lin R-M., Ewins D., 1990. Model updating using FR data. Paper presented at the 15th International Seminar on Modal Analysis, pp.141-162.
8. Kwon K.S., Lin R.M., 2005. Robust finite element model updating Taguchi method. Journal of Sound and Vibration, 280, 77-99.

9. Jacquelin E., Adhikari S., Fiswell M.I., 2012. A second-moment approach for direct probabilistic model updating in structural dynamics. Mechanical Systems and Signal Processing, 29, 262-283.
10. Sipple J.D., Sanayei M., 2014. Finite element model updating using frequency response functions and numerical sensitivities. Structural Control and Health Monitoring, 21, 784–802.
11. Pradhan S., Modak S., 2012. Normal response function method for mass and stiffness matrix updating using complex FRFs. Mechanical Systems and Signal Processing, 32, 232-250.
12. Arora V., 2014. FE model updating method incorporating damping matrices for structural dynamic modifications. Structural Engineering and Mechanics, 52, 261-274.
13. Matta E., Stefano A., 2012. Robust finite element model updating of a large-scale benchmark building structure. Structural Engineering and Mechanics, 43, 371-394.
14. Adhikari S., 2001. Damping models for structural vibration. Doctoral dissertation, University of Cambridge, Cambridge, England.
15. Salamon R., Kamiński H., Fritzkowski P., 2020. Estimation of parameters of various damping models in planar motion of a pendulum. Meccanica, 1-23.
16. Shadan F., Khoshnoudian F., Inman D.J., Esfandiari A., 2018. Experimental validation of a FRF-based model updating method. Journal of Vibration and Control, 24, 1570–1583.
17. Shadan F., Khoshnoudian F., Esfandiari A., 2016. A frequency response‐based structural damage identification using model updating method. Structural Control and Health Monitoring, 23, 286-302.
18. Zin M.M., Rani M.A., Yunus M.A., Sani M.S.M., Wan Iskandar Mirza W.I.I., Mat Isa A.A. 2018. Frequency response function (FRF) based updating of a laser spot welded structure. In AIP Conference Proceedings (Vol. 1952, No. 1, p. 020055). AIP Publishing LLC.
19. Natke H.G., 1988. Updating computational models in the frequency domain based on measured data: a survey. Probabilistic Engineering Mechanics, 3, 28-35.
20. Lu Y., Zhenguo T., 2004. A two-level neural network approach for dynamic FE model updating including damping. Journal of Sound and Vibration, 275, 931-952.
21. Lepoittevin G., Gerald K., 2011. Finite element model updating of vibrating structures under free–free boundary conditions for modal damping prediction., Mechanical Systems and Signal Processing, 25, 2203-2218.
22. Oktav A., 2020. Identification of non-proportional structural damping using experimental modal analysis data. Journal of Measurements in Engineering, 8, 34-45.