Acta Mechanica Sinica

, Volume 30, Issue 5, pp 687–692 | Cite as

Artificial boundary conditions for Euler-Bernoulli beam equation

Research Paper


In a semi-discretized Euler-Bernoulli beam equation, the non-nearest neighboring interaction and large span of temporal scales for wave propagations pose challenges to the effectiveness and stability for artificial boundary treatments. With the discrete equation regarded as an atomic lattice with a three-atom potential, two accurate artificial boundary conditions are first derived here. Reflection coefficient and numerical tests illustrate the capability of the proposed methods. In particular, the time history treatment gives an exact boundary condition, yet with sensitivity to numerical implementations. The ALEX (almost EXact) boundary condition is numerically more effective.


Euler-Bernoulli beam Artificial boundary condition Wave propagation 


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.HEDPS, CAPT, and LTCS, College of EngineeringPeking UniversityBeijingChina
  2. 2.Department of Civil and Materials EngineeringUniversity of Illinois at ChicagoChicagoUSA

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