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The Use of Trigonometric Series for the Study of Isotropic Beam Deflection

Author

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  • Adrian Ioan Botean

    (Mechanical Engineering Department, Faculty of Road Vehicles, Mechatronics and Mechanics, Technical University of Cluj-Napoca, 28 Memorandumului, 400114 Cluj-Napoca, Romania)

Abstract

The average deformed fiber is a continuous and smooth function of the fourth order. The deflection and rotation of beams can be determined by various methods available in the literature. Thus, in this paper, the expression of the average deformed fiber is defined in advance, then it is considered an infinite sum of sinusoidal functions that are successively evaluated using sinusoidal trigonometric series if it is considered a periodic function, or using Fourier series if it is considered a non-periodic function. The method is examined by solving several beam problems. The results indicate that the method can be used with confidence for solving any bending beam problem.

Suggested Citation

  • Adrian Ioan Botean, 2023. "The Use of Trigonometric Series for the Study of Isotropic Beam Deflection," Mathematics, MDPI, vol. 11(6), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1426-:d:1098248
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    Cited by:

    1. Zdeněk Kala, 2024. "Global Sensitivity Analysis of Structural Reliability Using Cliff Delta," Mathematics, MDPI, vol. 12(13), pages 1-18, July.

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