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A B-spline Finite Element Method for Structural Damping Beam Vibration Problem

Author

Listed:
  • Jing Zhu
  • Zhe Yin

Abstract

Beam structures are widely applied in civil engineering, mechanical engineering, and architectural design. The beam vibration equation with damping terms can better describe the specific properties of beams. In this paper, the cubic B-spline finite element method is used to solve the vibration problems of damping beams with a firmly supported edge at both ends, a simply supported edge at both ends, and a firmly supported edge at the left end and a simply supported edge at the right end. Moreover, the treatment methods of B-spline basis functions in the finite element space when solving problems under different boundary conditions are presented. By discretizing both the first and second time derivatives via the central difference scheme, the fully discrete scheme is derived, and a detailed analysis of the error estimation is conducted. Finally, the effectiveness of this method is verified through numerical examples, and the theoretical results are tested.

Suggested Citation

  • Jing Zhu & Zhe Yin, 2025. "A B-spline Finite Element Method for Structural Damping Beam Vibration Problem," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 17(5), pages 1-10, December.
    • Handle: RePEc:ibn:jmrjnl:v:17:y:2025:i:5:p:10
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    References listed on IDEAS

    as
    1. Shams Ul Arifeen & Sirajul Haq & Farhan Golkarmanesh, 2022. "Computational Study of Multiterm Time‐Fractional Differential Equation Using Cubic B‐Spline Finite Element Method," Complexity, John Wiley & Sons, vol. 2022(1).
    2. Shams Ul Arifeen & Sirajul Haq & Farhan Golkarmanesh & Jesus M. Munoz-Pacheco, 2022. "Computational Study of Multiterm Time-Fractional Differential Equation Using Cubic B-Spline Finite Element Method," Complexity, Hindawi, vol. 2022, pages 1-15, November.
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      JEL classification:

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

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