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Dissipative Numerical Method for a Flexible Euler-Bernoulli Beam with a Force Control in Rotation and Velocity Rotation

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Listed:
  • Bomisso G. Jean Marc
  • Tour'{e} K. Augustin
  • Yoro Gozo

Abstract

In this paper, we study a flexible Euler-Bernoulli beam clamped at one end and subjected to a force control in rotation and velocity rotation. We develop a finite element method, stable and convergent which preserves the property of time decay of energy in the continuous case. We prove firstly the existence and uniqueness of the weak solution. Then, we discretize the system in two steps: in the first step, a semi-discrete scheme is obtained for discretization in space and, in the second step, a fully-discrete scheme is obtained for discretization in time by the Crank-Nicolson scheme. At each step of the discretization, the a-priori error estimates are obtained.

Suggested Citation

  • Bomisso G. Jean Marc & Tour'{e} K. Augustin & Yoro Gozo, 2017. "Dissipative Numerical Method for a Flexible Euler-Bernoulli Beam with a Force Control in Rotation and Velocity Rotation," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 9(4), pages 30-48, August.
    • Handle: RePEc:ibn:jmrjnl:v:9:y:2017:i:4:p:30-48
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    Keywords

    beam equation; Galerkin method; finite element methods; a priori estimates;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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