Abstract
This paper treats a solution for the ill-posed (inverse) load determination problem for a time-varying load on a beam. The ill-posed nature of the problem causes numerical instability. Conventional numerical approach for solutions results in arbitrarily large errors in solution. The Tikhonov regularization method, which is a non-iterative stabilization technique, has been widely adopted for overcoming the ill-posed nature (or numerical instability). However, in this paper, we introduce an “iterative” regularization method, specifically, the iterated Tikhonov regularization method. The iterated method is applied to the present load determination problem. The result of the iterative method is compared with that of the (non-iterative) Tikhonov regularization. The rate of convergence for the introduced iterative method turned out to be very fast. The accuracy and applicability of the introduced method are examined through a numerical experiment.
Similar content being viewed by others
References
B. T. Wang and C. H. Chiu, Determination of unknown impact force acting on a simply supported beam, Mechanical System and Signal Processing 17 (2003) 683–704.
H. Inoue, N. Ikeda, K. Kishimoto, T. Shibuya and T. Koizumi, Inverse analysis of the magnitude and direction of impact force, JSME International Journal Series A 38 (1995) 84–91.
R. Hashemi and M. H. Kargarnovin, Vibration base identification of impact force using genetic algorithm, International Journal of Mechanical Systems Science and Engineering 1 (2007) 204–210.
F. E. Gunawan, H. Homma and Y. Kanto, Two-step B-splines regularization method for solving an ill-posed problem of impact-force reconstruction, Journal of Sound and Vibration 297 (2006) 200–214.
F. E. Gunawan, H. Homma and Y. Morisawa, Impact-Force estimation by quadratic spline approximation, Journal of Solid Mechanics and Materials Engineering 2 (2008) 1092–1103.
A. A. Cardi, D. E. Adams and S. Walsh, Ceramic body armor single impact force identification on a compliant torso using acceleration response mapping, Structural health monitoring 5 (2006) 355–372.
L. Meirovitch, Analytical Methods in Vibrations. London, UK: The MacMillan Company (1967).
A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems. Springer (1996).
A. N. Tikhonov, Solution of incorrectly formulated problems and the regularization method. Sov. Doklady 4 (1963) 1035–1038.
P. C. Hansen, Analysis of discrete ill-posed problems by means of the L-curve, SIAM Review 34 (1992) 561–580.
T. S. Jang, H. G. Sung, S. L. Han and S. H. Kwon, Inverse determination of the loading source of the infinite beam on elastic foundation, Journal of Mechanical Science and Technology 22 (2008) 2350–2356.
T. S. Jang, H. S. Choi and T. Kinoshita, Numerical experiments on an ill-posed inverse problem for a given velocity around a hydrofoil by iterative and noniterative regularizations, Journal of Marine Science and Technology 5 (2000) 107–111.
Author information
Authors and Affiliations
Corresponding author
Additional information
This paper was recommended for publication in revised form by Associate Editor Jeonghoon Yoo
Taek Soo Jang, the corresponding author of the paper, is by birth a Korean, with Naval Architecture and Ocean Engineering Ph.D degree from Seoul National University, who worked at the department of Naval Architecture and Ocean Engineering in Pusan National University from 2003 until now. His main field of research has been the optimization theory, water wave motion and inverse problem with special focus on ocean-related fields
Rights and permissions
About this article
Cite this article
Jang, T.S., Han, S.L. Numerical experiments on determination of spatially concentrated time-varying loads on a beam: an iterative regularization method. J Mech Sci Technol 23, 2722–2729 (2009). https://doi.org/10.1007/s12206-009-0735-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12206-009-0735-3