A Spectral Taylor Polynomial Solution of Euler-Bernoulli Beam Equation by a Matrix Approach

Özer Tatar; Muhammet Mustafa Bahşı; Mehmet Çevik

EN

A Spectral Taylor Polynomial Solution of Euler-Bernoulli Beam Equation by a Matrix Approach

Abstract

The Euler-Bernoulli beam theory, widely applied in structural engineering, describes the relationship between applied loads and resulting deformations in beams. This study addresses the transverse vibration of beams with simply supported, cantilever, and fixed-fixed boundary conditions using the Taylor matrix method. The governing differential equation, which includes both boundary and initial conditions, is transformed into a matrix form through Taylor series expansion. This matrix approach simplifies the process of solving the Euler-Bernoulli equation, providing an efficient method for analyzing beam vibrations under various support conditions. The accuracy of the Taylor matrix method is validated by comparing it with exact solutions derived through the separation of variables. Numerical examples illustrate that the method yields results closely aligning with the exact solutions, with minimal discrepancies that decrease as the number of terms N in the Taylor series expansion increases. This method shows promise as an accessible and accurate approach for studying mechanical vibrations, especially in engineering applications requiring efficient computational techniques. The findings contribute to the literature on beam theory and demonstrate the applicability of the Taylor matrix method in structural analysis.

Keywords

Taylor matrix method, vibration, Euler-Bernoulli beam, spectral method

References

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Details

Primary Language

English

Subjects

Solid Mechanics, Numerical Methods in Mechanical Engineering

Journal Section

Research Article

Authors

Özer Tatar
0009-0007-9801-2518
Türkiye

Muhammet Mustafa Bahşı
0000-0003-2237-5818
Türkiye

Mehmet Çevik ^*
0000-0002-6366-5566
Türkiye

Publication Date

May 28, 2025

Submission Date

February 26, 2025

Acceptance Date

April 19, 2025

Published in Issue

Year 2025 Volume: 1 Number: 1

IZ

https://izlik.org/JA35LA37RR

APA

Tatar, Ö., Bahşı, M. M., & Çevik, M. (2025). A Spectral Taylor Polynomial Solution of Euler-Bernoulli Beam Equation by a Matrix Approach. Journal of Dynamics, Energy and Utility, 1(1), 1-12. https://izlik.org/JA35LA37RR

AMA

1.Tatar Ö, Bahşı MM, Çevik M. A Spectral Taylor Polynomial Solution of Euler-Bernoulli Beam Equation by a Matrix Approach. JDEU. 2025;1(1):1-12. https://izlik.org/JA35LA37RR

Chicago

Tatar, Özer, Muhammet Mustafa Bahşı, and Mehmet Çevik. 2025. “A Spectral Taylor Polynomial Solution of Euler-Bernoulli Beam Equation by a Matrix Approach”. Journal of Dynamics, Energy and Utility 1 (1): 1-12. https://izlik.org/JA35LA37RR.

EndNote

Tatar Ö, Bahşı MM, Çevik M (May 1, 2025) A Spectral Taylor Polynomial Solution of Euler-Bernoulli Beam Equation by a Matrix Approach. Journal of Dynamics, Energy and Utility 1 1 1–12.

IEEE

[1]Ö. Tatar, M. M. Bahşı, and M. Çevik, “A Spectral Taylor Polynomial Solution of Euler-Bernoulli Beam Equation by a Matrix Approach”, JDEU, vol. 1, no. 1, pp. 1–12, May 2025, [Online]. Available: https://izlik.org/JA35LA37RR

ISNAD

Tatar, Özer - Bahşı, Muhammet Mustafa - Çevik, Mehmet. “A Spectral Taylor Polynomial Solution of Euler-Bernoulli Beam Equation by a Matrix Approach”. Journal of Dynamics, Energy and Utility 1/1 (May 1, 2025): 1-12. https://izlik.org/JA35LA37RR.

JAMA

1.Tatar Ö, Bahşı MM, Çevik M. A Spectral Taylor Polynomial Solution of Euler-Bernoulli Beam Equation by a Matrix Approach. JDEU. 2025;1:1–12.

MLA

Tatar, Özer, et al. “A Spectral Taylor Polynomial Solution of Euler-Bernoulli Beam Equation by a Matrix Approach”. Journal of Dynamics, Energy and Utility, vol. 1, no. 1, May 2025, pp. 1-12, https://izlik.org/JA35LA37RR.

Vancouver

1.Özer Tatar, Muhammet Mustafa Bahşı, Mehmet Çevik. A Spectral Taylor Polynomial Solution of Euler-Bernoulli Beam Equation by a Matrix Approach. JDEU [Internet]. 2025 May 1;1(1):1-12. Available from: https://izlik.org/JA35LA37RR

Abstract

A Spectral Taylor Polynomial Solution of Euler-Bernoulli Beam Equation by a Matrix Approach

Abstract

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References

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