Green's function coupled with perturbation approach to a dynamic problem for a functionally graded steel beam

Hamza Hameed , Sadia Munir , F. D. Zaman , Shahbaz Ahmad

Abstract

Functionally graded beams are very useful materials in structural and design engineering. In this article, we study an analytical approach to analyze the dynamic response of functionally graded beams using Green's function coupled with a perturbation method. Functionally graded materials are characterized by their continuous variation in composition and properties, which provide superior performance under mechanical and thermal loads compared to traditional homogeneous materials. The Green's function method is employed to establish a fundamental solution for the governing differential equations of beam model, capturing the effects of graded material along the beam's length. The perturbation technique is then applied to handle the non-homogeneous nature of the beam, allowing for an accurate approximation of the solution in the presence of small variations in material properties. The effectiveness of the proposed method is demonstrated through several benchmark problems, highlighting its capability to address complex boundary conditions and varying material distributions. The results show that this combined approach offers significant improvements in computational efficiency and accuracy compared to conventional numerical methods. The findings of this research provide a robust analytical tool for engineers and researchers to predict the behavior of graded materials in various applications, contributing to the optimization and design of advanced structural components. The solutions of such problems are also computed and displayed in graphical forms.

Key Words

Euler−Bernoulli beam; functionally graded beams; Green

Address

Hamza Hameed — 1)Advanced Materials Science Laboratory, Computer Science Department, Green International University, Lahore, Pakistan 2)Software Engineering Department, Superior University, Lahore, Pakistan 3)Faculty of Science & Technology, University of Central Punjab, Lahore, Pakistan 4)Abdus Salam School of Mathematical Sciences, Government College University, Lahore-54000, Pakistan
Sadia Munir — Abdus Salam School of Mathematical Sciences, Government College University, Lahore-54000, Pakistan
F. D. Zaman — 1)Abdus Salam School of Mathematical Sciences, Government College University, Lahore-54000, Pakistan 2)School of Mathematics, University of Witwatersrand, Johannesburg, South Africa
Shahbaz Ahmad — Abdus Salam School of Mathematical Sciences, Government College University, Lahore-54000, Pakistan

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