Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ESTIMATION ALGORITHM FOR PHYSICAL PARAMETERS IN A SHALLOW ARCH

  • Gutman, Semion (Department of Mathematics University of Oklahoma) ;
  • Ha, Junhong (School of Liberal Arts Korea University of Technology and Education) ;
  • Shon, Sudeok (School of Architectural Engineering Korea University of Technology and Education)
  • Received : 2020.04.29
  • Accepted : 2020.08.31
  • Published : 2021.05.01
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Abstract

Design and maintenance of large span roof structures require an analysis of their static and dynamic behavior depending on the physical parameters defining the structures. Therefore, it is highly desirable to estimate the parameters from observations of the system. In this paper we study the parameter estimation problem for damped shallow arches. We discuss both symmetric and non-symmetric shapes and loads, and provide theoretical and numerical studies of the model behavior. Our study of the behavior of such structures shows that it is greatly affected by the existence of critical parameters. A small change in such parameters causes a significant change in the model behavior. The presence of the critical parameters makes it challenging to obtain good estimation. We overcome this difficulty by presenting the Parameter Estimation Algorithm that identifies the unknown parameters sequentially. It is shown numerically that the algorithm achieves a successful parameter estimation for models defined by arbitrary parameters, including the critical ones.

Keywords

Acknowledgement

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (NRF-2019R1F1A1058327).

References

  1. J. M. Ball, Initial-boundary value problems for an extensible beam, J. Math. Anal. Appl. 42 (1973), 61-90. https://doi.org/10.1016/0022-247X(73)90121-2
  2. J. M. Ball, Stability theory for an extensible beam, J. Differential Equations 14 (1973), 399-418. https://doi.org/10.1016/0022-0396(73)90056-9
  3. Q. Bi and H.H. Dai, Analysis of non-linear dynamics and bifurcations of a shallow arch subjected to periodic excitation with internal resonance, J. Sound Vibration 233 (2000), no. 4, 553-567. https://doi.org/10.1006/jsvi.1999.2813
  4. J. Chen and Y. Li, Effects of elastic foundation on the snap-through buckling of a shallow arch under a moving point load, ntern. J. Solids Structures 43 (2006), no. 14, 4220-4237. https://doi.org/10.1016/j.ijsolstr.2005.04.040
  5. E. Emmrich and M. Thalhammer, A class of integro-differential equations incorporating nonlinear and nonlocal damping with applications in nonlinear elastodynamics: existence via time discretization, Nonlinearity 24 (2011), no. 9, 2523-2546. https://doi.org/10.1088/0951-7715/24/9/008
  6. S. Gutman and J. Ha, Uniform attractor of shallow arch motion under moving points load, J. Math. Anal. Appl. 464 (2018), no. 1, 557-579. https://doi.org/10.1016/j.jmaa.2018.04.025
  7. S. Gutman, J. Ha, and S. Lee, Parameter identification for weakly damped shallow arches, J. Math. Anal. Appl. 403 (2013), no. 1, 297-313. https://doi.org/10.1016/j.jmaa.2013.02.047
  8. J. Ha, S. Gutman, S. Shon, and S. Lee, Stability of shallow arches under constant load, Intern. J. Non-Linear Mech. 58 (2014), 120-127. https://doi.org/10.1016/j.ijnonlinmec.2013.08.004
  9. W. Lacarbonara and G. Rega, Resonant non-linear normal modes. II. Activation/orthogonality conditions for shallow structural systems, Internat. J. Non-Linear Mech. 38 (2003), no. 6, 873-887. https://doi.org/10.1016/S0020-7462(02)00034-3
  10. J. Lin and J. Chen, Dynamic snap-through of a laterally loaded arch under prescribed end motion, Intern. J. Solids Structures 40 (2003), no. 18, 4769-4787. https://doi.org/10.1016/S0020-7683(03)00181-1
  11. J.-L. Lions, Optimal control of systems governed by partial differential equations, Translated from the French by S. K. Mitter. Die Grundlehren der mathematischen Wissenschaften, Band 170, Springer-Verlag, New York, 1971.