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

被引：0
作者：
Chein-Shan Liu
机构：
[1] National Taiwan University,Department of Civil Engineering
来源：
Acta Mechanica | 2012年 / 223卷
关键词：
Heat Mass Transf; Conjugate Gradient Method; Numerical Error; Differential Quadrature; Differential Quadrature Method;
D O I：
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中图分类号：
学科分类号：
摘要：
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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页码：2207 / 2223
页数：16
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