Identifying the temperature effect on the vibrations of functionally graded cylindrical shells with porosities

Non-Local Buckling Analysis of Functionally Graded Nanoporous Metal Foam Nanoplates

“…We consider three different types of porosity distribution, namely, (1) uniform distribution (UD); (2) non-uniform distribution 1 (NUD1) (symmetric); and (3) non-uniform distribution 2 (NUD2) (asymmetric), as shown in Figure 1. It is clear that NUD1 and NUD2 exhibit graded characteristics like functionally graded materials [37][38][39][40][41]. In the case of UD, the elasticity modulus E and shear modulus G are constant along the thickness of the nanoplate.…”

“…where m and n are the mode numbers, α = mπ/l a and β = nπ/l b . Substituting Equations (44) and 45into Equations (41) and (42), the following matrix form can be obtained:…”

Analytical Modeling of Buckling Behavior of Porous FGM Cylindrical Shell Embedded within an Elastic Foundation

“…Now we present some research works based on plates theories to model porous materials, Medani et al (2019) [24] examined the behavior of porous plates made of sandwich polymer and reinforced by functionally graded carbon nanotubes, Kaddari et al (2020) [25] developed a new theory based on quasi-3D hyperbolic shear deformation to discuss the statics and free vibration of FGP plates embedded in Kerr-type elastic foundation, Jena et al (2020) [26] used Navier's technique and shifted Chebyshev polynomial-based Rayleigh-Ritz method to study the vibration of a FGP beam resting on Kerr foundation and Tran et al (2020) [27] analyzed a free vibration of the FGP plates embedded in an elastic foundation. The use of shell theories to model porous materials is not used much in the literature, Ebrahimi et al (2019) [28] used an analytical method to analyze the vibration of an embedded cylindrical shell made of porous metal foam, they studied the influence of different models of porosity distribution, Jouneghani et al (2017) [29] analyzed the free vibration of porous FGM doubly-curved shells using the first-order shear deformation theory, Wang et al (2018) [30] identified the effect of temperature and that of porosities on the vibrations of FG cylindrical shells and Keddouri et al (2019) [31] introduced a new displacement based high-order shear deformation theory to study the static behavior of FG sandwich plate taking into account a new expression of porosity distribution. For researchers in the literature, the theoretical researches on dynamic and stability of porous FGM beams, plates or shells are very interesting.…”

Nonlinear vibration of full-filled fluid corrugated sandwich functionally graded cylindrical shells

“…By using the differential quadrature method instead of Fourier series solutions, the free vibration behavior of cylindrical shells on different boundary conditions was investigated by Sadeghi and Alibeigloo (2019). The vibration behavior of FGM cylindrical shells with porosities and metal foam cylindrical shells reinforced by graphene platelets was investigated by Wang et al (2018b, 2019b). Zeng et al (2019) studied the size-dependent flexoelectric effect on the natural frequency and the nonlinear electromechanical behavior of cylindrical nanoshells based on the modified couple stress theory.…”