Title: Application of Tikhonov regularisation method in bounded chord subjected to enforcement

Authors: Linjun Wang; Youxiang Xie

Addresses: College of Mechanical and Material Engineering, China Three Gorges University, Yichang, Hubei 443002, China; State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Automotive Engineering, Hunan University, Changsha City 410082, China ' College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, China

Abstract: Inverse problem of identifying initial condition about forced vibration equation of chord is investigated. First, we separate the forward problem into two determinate problems by the superposition principle, and obtain the solution of direct problem by separate variable method and latent function method. Second, discrete it by trapezoidal formula method, and then obtain a severely ill-conditioned linear equation, which is sensitive to the disturbance of the right data. Thirdly, identify the initial condition by Tikhonov regularisation method. The numerical results confirm that this method is feasible and effective.

Keywords: forced vibration equation of chord; Tikhonov regularisation; ill-posed; latent function; superposition principle; bounded chord.

DOI: 10.1504/IJSCOM.2013.058673

International Journal of Service and Computing Oriented Manufacturing, 2013 Vol.1 No.2, pp.141 - 153

Published online: 02 Jul 2014 *

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