A new conjugate gradient method for solving multi-source dynamic load identification problem
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A new conjugate gradient method for solving multi-source dynamic load identification problem Linjun Wang • Xu Han • Youxiang Xie
Received: 19 August 2012 / Accepted: 25 November 2012 / Published online: 12 December 2012 Ó Springer Science+Business Media Dordrecht 2012
Abstract In this paper, a new conjugate gradient method is suggested to estimate the multi-source dynamic loads acting on a surface of 3D plate. The algorithm reconstructs the distribution functions of the dynamic loads by the displacement responses at two receiving points. The dynamic Green’s function and response function of dynamic forces excitation are obtained by finite element method. Under linear and time-invariant supposition, the response at a receiving point on the structure can be expressed as a convolution integral of the desired unknown force and the corresponding Green’s function, where the continuous convolution functions are spatially and temporally discretized by trapezium formula. The preset method is suggested to identify the dynamic loads by L. Wang (&) College of Mechanical and Material Engineering, China Three Gorges University, Yichang 443002, Hubei, People’s Republic of China e-mail: [email protected] X. Han State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Automotive Engineering, Hunan University, Changsha 410082, Hunan, People’s Republic of China e-mail: [email protected] Y. Xie College of Mathematics and Econometrics, Hunan University, Changsha 410082, Hunan, People’s Republic of China e-mail: [email protected]
minimizing the error functions. Finally, the multisource dynamic loads are successfully identified by the proposed method, and the performance of numerical simulations is superior to Landweber iteration method, which demonstrates the efficiency and robustness of the proposed method. Keywords Inverse problems Multi-source dynamic load identification Finite element method Conjugate gradient method
1 Introduction In many practical engineering problems, such as structural strength analysis, health monitoring, fault diagnosis, vibration isolation, and so on, the knowledge of the dynamic loads acting on the structure is always required and important. There are many applications in which it is difficult or impossible to directly measure the dynamic forces acting on a structure, but it is possible to measure the response of the structure on which the unknown dynamic forces act. In fact, many works have shown that it is feasible to identify the forces acting on it by a structure’s response. There are numerous studies about force reconstruction by frequency domain technique (Stevens 1987; Fabunmi 1986; Lee and Park 1995; Hillary and Ewins 1984). Liu and Sheppard (2006) adopted
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the singular value decomposition method to locate the small singular value affected by the noisy response. Liu and Han (2003) presented an inverse procedure for identifying both concentrated and extended line load using Green’s function and Heaviside step function in time domain (Liu
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