Modeling of vibration for functionally graded beams

Open Mathematics

Bayram Mustafa¹  Yiğit Gülsemay²  Şahin Ali³ 

[1] Department of Computer Engineering, Istanbul Gelisim University, Istanbul, Turkey;Department of Electrical and Electronics Engineering, Istanbul Kemerburgaz University, Istanbul, Turkey;Vodno Consultancy, 1000 Skopje, Macedonia (the former Yugoslav Republic of);

关键词: adomian decomposition method;    functionally graded beam;    fourier analysis;    orthogonality;    35l35;    74k10;   

DOI  :  10.1515/math-2016-0057

来源: DOAJ

【 摘 要 】

In this study, a vibration problem of Euler-Bernoulli beam manufactured with Functionally Graded Material (FGM), which is modelled by fourth-order partial differential equations with variable coefficients, is examined by using the Adomian Decomposition Method (ADM).The method is one of the useful and powerful methods which can be easily applied to linear and nonlinear initial and boundary value problems. As to functionally graded materials, they are composites mixed by two or more materials at a certain rate. This mixture at a certain rate is expressed with an exponential function in order to try to minimize singularities from transition between different surfaces of materials as much as possible. According to the structure of the ADM in terms of initial conditions of the problem, a Fourier series expansion method is used along with the ADM for the solution of simply supported functionally graded Euler-Bernoulli beams. Finally, by choosing an appropriate mixture rate for the material, the results are shown in figures and compared with those of a standard (homogeneous) Euler-Bernoulli beam.

【 授权许可】

Unknown