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Smart Structures and Systems Volume 26, Number 3, September 2020 , pages 361-371 DOI: https://doi.org/10.12989/sss.2020.26.3.361 |
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Exact solution for nonlinear vibration of clamped-clamped functionally graded buckled beam |
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Abdellatif Selmi
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| Abstract | ||
| Exact solution for nonlinear behavior of clamped-clamped functionally graded (FG) buckled beams is presented. The effective material properties are considered to vary along the thickness direction according to exponential-law form. The in-plane inertia and damping are neglected, and hence the governing equations are reduced to a single nonlinear fourth-order partial-integraldifferential equation. The von Karman geometric nonlinearity has been considered in the formulation. Galerkin procedure is used to obtain a second order nonlinear ordinary equation with quadratic and cubic nonlinear terms. Based on the mode of the corresponding linear problem, which readily satisfy the boundary conditions, the frequencies for the nonlinear problem are obtained using the Jacobi elliptic functions. The effects of various parameters such as the Young's modulus ratio, the beam slenderness ratio, the vibration amplitude and the magnitude of axial load on the nonlinear behavior are examined. | ||
| Key Words | ||
| buckled beam; exact solution; functionally graded material; nonlinear vibration | ||
| Address | ||
| (1) Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia; (2) Ecole Nationale d'Ingenieurs de Tunis (ENIT), Civil Engineering Laboratory. B.P. 37, Le belvedere 1002, Tunis, Tunisia. | ||