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A Lie-group adaptive differential quadrature method to identify an unknown force in an Euler–Bernoulli beam equation

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Abstract

We recover an unknown space–time-dependent force in an Euler–Bernoulli beam vibration equation by an effective combination of the Lie-group adaptive method (LGAM) and the differential quadrature method (DQM). The layer-stripping technique is used to simplify this identification problem. The DQM is a feasible tool to semi-discretize the Euler–Bernoulli beam equation into a system of ordinary differential equations (ODEs) in time. Then, we can develop a two-point Lie-group equation to recover the unknown force through a few iterations. The success of the present method hinges on a rationale that the local in time ODEs and the global in time algebraic Lie-group equation have to be self-adapted during the iteration processes. The feasibility, accuracy and efficiency of the present method are assessed by comparing the estimated results with some exact solutions.

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  1. Department of Civil Engineering, National Taiwan University, Taipei, Taiwan

    Chein-Shan Liu

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  1. Chein-Shan Liu
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Correspondence to Chein-Shan Liu.

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Liu, CS. A Lie-group adaptive differential quadrature method to identify an unknown force in an Euler–Bernoulli beam equation. Acta Mech 223, 2207–2223 (2012). https://doi.org/10.1007/s00707-012-0707-z

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  • DOI: https://doi.org/10.1007/s00707-012-0707-z

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