Theoretical analysis of transient waves in a simply-supported Timoshenko beam by ray and normal mode methods

Yu Chi Su, Chien Ching Ma

研究成果: Article同行評審

13 引文 斯高帕斯(Scopus)

摘要

The dynamic transient responses of a simply-supported Timoshenko beam subjected to an impact force are investigated by two theoretical approaches - ray and normal mode methods. The mathematical methodology proposed in this study for the ray method enable us to construct the solution for the interior source problem and to extend to solve the complicated problem for the multi span of the Timoshenko beam. Numerical results based on these two approaches are compared. The comparison in this study indicates that the normal mode method is more computationally efficient than the ray method except for very short time after the impact. The long-time transient responses are easily calculated using the normal mode method. It is shown that the average long-time transient response converges to the corresponding static value. The Timoshenko beam theory is more accurate than the Bernoulli-Euler beam theory because it includes shear and rotary inertia. This study also provides the slender ratio for which the Bernoulli-Euler beam can be used for the transient-response analysis of the displacement. Moreover, the resonant frequencies obtained from finite element calculation based on the three-dimensional model are compared with the results calculated using the Timoshenko beam and Bernoulli-Euler beam theories. It is noted in this study that the resonant frequency can be accurately determined by the Timoshenko beam theory if the slender ratio is larger than 100, and by the Bernoulli-Euler beam theory if the slender ratio is larger than 400.

原文English
頁(從 - 到)535-552
頁數18
期刊International Journal of Solids and Structures
48
發行號3-4
DOIs
出版狀態Published - 2011 2月

All Science Journal Classification (ASJC) codes

  • 建模與模擬
  • 材料科學(全部)
  • 凝聚態物理學
  • 材料力學
  • 機械工業
  • 應用數學

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