Vol. 5, No. 1, 2010

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ISSN: 1559-3959
Exact closed-form solution of the dynamic coupled thermoelastic response of a functionally graded Timoshenko beam

Mostafa Abbasi, Mehdy Sabbaghian and M. Reza Eslami

Vol. 5 (2010), No. 1, 79–94
Abstract

We present the analytical solution for a beam made of a functionally graded material based on first-order shear deformation theory and subjected to lateral thermal shock loads. The beam is assumed to be graded across the thickness direction. The material properties across the thickness direction follow the volume fraction of the constitutive materials in power law form. The solution is obtained under the coupled thermoelastic assumption. The equation of motion and the conventional coupled energy equation are simultaneously solved to obtain the transverse deflection and temperature distribution in the beam. The governing partial differential equations are solved using the finite Fourier transformation method. Using the Laplace transform, the unknown variables are obtained in the Laplace domain. Applying the analytical Laplace inverse method, the solution in the time domain is derived. Results are presented for different power law indices and the coupling coefficients for a beam with simply supported boundary conditions. The results are validated with data reported in the literature.

Keywords
functionally graded material, thermal shock, first-order shear deformation theory, coupled thermoelasticity, finite Fourier transformation method
Milestones
Received: 12 March 2009
Revised: 19 September 2009
Accepted: 21 September 2009
Published: 19 April 2010
Authors
Mostafa Abbasi
Mechanical Engineering Department
Amirkabir University of Technology
424 Hafez Avenue
Tehran 15914
Iran
http://www.mostafabbasi.ir
Mehdy Sabbaghian
Mechanical Engineering Department
Louisiana State University
Baton Rouge, LA 70803
United States
M. Reza Eslami
Mechanical Engineering Department
Amirkabir University of Technology
424 Hafez Avenue
Tehran 15914
Iran
http://me.aut.ac.ir/M.Eslami.htm