Free and forced vibration analysis of FG beam considering temperature dependency of material properties

Abstract

This paper presents a finite element method (FEM) free and forced lateral vibration analysis of beams made of functionally graded materials (FGMs). The temperature dependency of material properties along with damping had not previously been taken into account in vibration analysis. In the present study, the material properties were assumed to be temperature-dependent, and were graded in the thickness direction according to a simple power law distribution of the volume fractions of the constituents. The natural frequencies were obtained for functionally graded (FG) beams with various boundary conditions. First, an FG beam was assumed to be isotropic (metal rich) and the results were compared with the analytical solution and the results for ANSYS and NASTRAN software. Finally, dynamic responses were obtained for damped and un-damped systems. Numerical results were obtained to show the influences of the temperature dependency of the materials properties, the boundary conditions, the volume fraction distribution (the index of power law, N) and the geometrical parameters.

Non-linear forced vibration analysis of higher-order shear-deformable functionally graded material beam in thermal environment subjected to harmonic excitation and resting on non-linear elastic foundation

“…41 Xiang and Yang 40 studied the dynamic response of laminated FGM Timoshenko beam subjected to through-thickness steady-state heat conduction and a harmonic distributed load. Azadi 41 reported the forced vibration analysis of Euler-Bernoulli FGM beam in thermal environment under harmonic point load. In recent years, forced vibration analyses of FGM nanobeams are reported in the literature, [42][43][44][45] , where Ansari et al 43 involves analysis considering through-thickness linear thermal gradient and El-Borgi et al 44 and Barati and Zenkour 45 considered that the FGM beam is resting on elastic foundation.…”

“…Forced vibration analyses of FGM beams under high-temperature environment are reported in Xiang and Yang 40 and Azadi. 41 Xiang and Yang 40 studied the dynamic response of laminated FGM Timoshenko beam subjected to through-thickness steady-state heat conduction and a harmonic distributed load. Azadi 41 reported the forced vibration analysis of Euler–Bernoulli FGM beam in thermal environment under harmonic point load.…”

Quasi-3D beam models for the computation of eigenfrequencies of functionally graded beams with arbitrary boundary conditions

“…A combined Fourier series -Galerkin method for the analysis of FG beams have been proposed by Zhu and Sankar [35]. Azadi [36] dealt with the free and forced vibration analysis of FG beam considering temperature dependency of material properties. Pradhan and Chackraverty [37] investigated the effects of different shear deformation theories on the free vibration of functionally graded beams.…”

Dynamic response of functionally graded beams in a thermal environment under a moving load

“…It can be concluded from the free vibration behavior of FG beams in thermal environment that the initial thermal stresses has significant effect on the dynamic behavior of FG beams [23][24][25][26][27]. Hence, in this work, the dynamic response of FG beams under moving load is investigated by considering the influence of thermal environment.…”