Modal analysis of the FGM beams with effect of the shear correction function

Free vibrations of thin functionally graded plates with microstructure

“…These results are also compared with results obtained by the finite element method. The effect of the shear correction function is considered in modal analysis of the functionally graded beams with longitudinal and transversal varying material properties by Murín et al [17]. The shear correction function is calculated from the shear strain energy equation including spatial Poisson's ratio variations and results are verified by the finite element method.…”

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].…”

“…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]. In the literature, various solution methods have been applied to static and dynamic analyses of FGM structures; these include analytical methods [1][2][3][4]15,[20][21][22], the Rayleigh-Ritz method [16], the modal analysis method [10,14], power series expansion methods [11,19], the differential quadrature method [14], the dynamic stiffness method [23], the finite element method (FEM) [5][6][7][8][9]12,17,18], and the spectral element method [24].…”

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.…”