Finite Element Formulation for the Large-Amplitude Vibrations of FG Beams

Abstract

On the basis of Euler-Bernoulli beam theory, the large-amplitude free vibration analysis of functionally graded beams is investigated by means of a finite element formulation. The von Kármán type nonlinear strain-displacement relationship is employed where the ends of the beam are constrained to move axially. The material properties are assumed to be graded in the thickness direction according to the powerlaw and sigmoid distributions. The finite element method is employed to discretize the nonlinear governing equations, which are then solved by the direct numerical integration technique in order to obtain the nonlinear vibration frequencies of functionally graded beams with different boundary conditions. The influences of powerlaw index, vibration amplitude, beam geometrical parameters and end supports on the free vibration frequencies are studied. The present numerical results compare very well with the results available from the literature where possible.

Sonlu Eleman Modelleme Tekni̇kleri̇ni̇n Ki̇ri̇şleri̇n Di̇nami̇k Anali̇zi̇ne Etki̇si̇

“…Euler-Bernoulli and Timoshenko cross-ply beams are investigated to determine the natural frequencies by Madenci and Ozutok [13] using the Gâteaux differential approach and finite element. Javid and Hemmatnezhad [14] have studied the large-amplitude oscillations of heterogeneous Euler-Bernoulli beams by employing the von Karman type nonlinear strain-displacement relationship. Vo et al [15] have examined the vibration and buckling behaviors of functionally-graded sandwich beams.…”

Archive of Mechanical Engineering

“…Rezaiee-Pajand and Hozhabrossadati [7] provided analytical solutions for FGM double beam systems connected by massspring system. Javid and Hemmatnezhad [8] used finite element method to perform nonlinear free vibration analysis on FGM beams and direct numerical integration technique was used to determine the natural frequencies. Chen et al [9] investigated the thermal buckling behaviour of such beams using transformed-section method.…”