Free vibration of FGM layered beams by various theories and finite elements

A quasi-3D theory for vibration and buckling of functionally graded sandwich beams

“…five natural frequencies are given in Table 3 along with results of Bui et al [2] using 3D finite element model (ANSYS) and meshfree method as well as of Mashat et al [17] using the Carrera Unified Formulation (TE8 zz and E4-4 2 ). It can be seen that the solutions obtained from the proposed theory are in excellent agreement with those obtained from previous results, especially with CUF model, which included the stretching effect.…”

“…Carrera et al [15] developed Carrera Unified Formulation (CUF) using various refined beam theories (polynomial, trigonometric, exponential and zig-zag), in which non-classical effects including the stretching effect were automatically taken into account. Recently, he and his co-workers also used CUF to investigate the free vibration of laminated beam [16] and FG layered beams [17]. As far as authors are aware, there is no work available using the quasi-3D theories to study vibration and buckling of FG sandwich beams in a unitary manner.…”

An analytical method for the vibration and buckling of functionally graded beams under mechanical and thermal loads

“…Due to the excellent properties in mechanical and thermal behaviours, a wide range of application for functionally graded (FG) structures can be found in different fields, leading to the intensive study in many types of FG structures in the last three decades. Chebyshev collocation method, finite element method and differential quadrature method [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. For analytical approaches, a Navier solution has been widely used to study various mechanical behaviours of simply supported beams [16][17][18][19][20].…”

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].…”