Exact solution of the bending vibration problem of FGM beams with variation of material properties

Optimal location of piezoelectric actuators for active vibration control of thin axially functionally graded beams

“…In their work, natural frequencies are determined by Fredholm integral equations. The Mathematica solver was used as the tools for programming of derived new equations of the FGM beam finite element with spatially varying material properties including several features as the effects of the large axial forces, shear forces and elastic foundation (Aminbgahai et al 2012;Murin et al 2010Murin et al , 2013. Huang et al (2013) presented a new approach to calculate the frequencies of axially functionally graded Timoshenko beams with non uniform cross section.…”

Dynamics of a functionally graded material axial bar: Spectral element modeling and analysis

“…Many studies have been devoted to the static and dynamic analysis of FGM beams [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], FGM axial bars [19], FGM torsional bars [20], FGM plates [21], and FGM annular circular plates and disks [22,23]. In these studies, the material properties of one-dimensional (1-D) FGM structures were assumed to vary across the thickness (or radial) direction only [1][2][3][4][5][6][7][8][9]20], in the axial direction only [10][11][12]19], or in both the axial and thickness (or radial) directions [13,14].…”

Thermo-Elasticity in Shell Structures Made of Functionally Graded Materials

“…Mahi et al [4] consider free vibrations of symmetric FGM beams subjected to an initial thermal stress. In case of combined variations of material properties in transverse and longitudinal directions, many achievements are due to Murin et al [5,6,7]. The amount of literature dealing with FGM shells is also overwhelming.…”