Dynamic Stability Analysis of Functionally Graded Timoshenko Beams with Internal Viscous Damping Distribution

Abstract

This paper investigates the dynamic stability of functionally graded material (FGM) beams, using the Timoshenko model with internal viscous damping distribution (DIVD). It is assumed that the material properties change continuously across the thickness direction of the beam, according to the power law function for the FGM (P-FGM). The governing equations of motion were developed by the Lagrange principle. Then, the finite element method was adopted to describe unamortized natural frequencies and the damped eigenfrequencies of the dynamic system. The numerical results were compared with those available in the literature. Illustrative examples were given to show the influence of internal damping distribution, material distribution and slenderness ratio on the dynamic stability margin of FGM Timoshenko beams. The research findings provide new insights into the dynamic stability of the FGM.

Exact Solution for Free Vibration Analysis of FGM Beams

“…Due to the wide application of FGM several studies have been conducted on the mechanical and thermal behavior of FGMs [2][3][4][5][6][7][8][9][10][11][12]. Detailed theoretical and experimental studies have been carried out and published, on the mechanics of rupture [13][14][15], the distribution of thermal stresses [16][17][18][19][20][21][22][23][24], the treatment [25][26][27], etc.…”

Forced Vibration Analysis of Functionally Graded Beams Carrying Moving Harmonic Loads under Random Boundary Conditions

“…Nejad and Hadi [14] used the classical Euler-Bernoulli theory in the vibratory study of FGM beams. Moreover, other researchers [15][16][17] used Timoshenko's theory to study the dynamics of FGM beams.…”