Nonlinear vibration and buckling of functionally graded porous nanoscaled beams

Abstract

Although many researchers have studied the vibration and buckling behavior of porous materials, the behavior of porous nanobeams is still a needed issue to be studied. This paper is focused on the buckling and nonlinear vibration of functionally graded (FG) porous nanobeam for the first time. Nonlinear Von Kármán strains are put into consideration to study the nonlinear behavior of nanobeam based on the Euler-Bernoulli beam theory. The nonlocal Eringen's theory is used to study the size effects. The mechanical properties of ceramic and metal are used to model the functionally graded material through thickness, and the boundary conditions are considered as clamped-clamped (CC) and simply supportedsimply supported (SS). The generalized differential quadrature method (GDQM) is used in conjunction with the iterative method to solve the equations. The parametric study is done to examine the effects of nonlinearity, porosity, sized effect, FG index, etc., on the vibration and buckling of porous nanobeam.

Special review: Mechanical investigation on failure modes of reticular porous metal foams under different loadings in engineering applications

“…The critical load for buckling of porous beams is studied in (Magnucki and Stasiewicz, 2004), and the buckling load of foam Sandwich panels under different loads is obtained in References (Douville and Grognec, 2013; Jasion et al , 2012). The buckling behavior of porous beams has also been studied in (Mirjavadi et al , 2018). Nonlinear strains are put into consideration to study the nonlinear behavior of porous beam based on Euler–Bernoulli beam theory, and Eringen's nonlocal elasticity theory is used to study the size effects.…”

Examining wave propagation characteristics in metal foam beams: Euler–Bernoulli and Timoshenko models

“…Young's modulus, the shear modulus and the mass density vary smoothly along the thickness direction due to the nonuniform distribution of the metal foams. It is clear that the metal foam structure exhibits graded characteristics like functionally graded materials [30][31][32][33][34].…”

Free vibration analysis of porous beams with gradually varying mechanical properties

“…13,14 Parametric studies are conducted to show the effects of porosity distributions, material, and geometrical parameters on mechanical responses of FGM porous structures. Continuously, and within the context of nonlocal strain gradient theory, recent researches on nanobeams have been investigated by Mirjavadi et al [15][16][17] In these studies, the nonlocal Eringen's theory is used to study the size effects and others geometrical and material parameters on the temporal, vibrational, and buckling responses of FGM nanobeams. For porous case, results reveled that porosities volume fractions, porosities distributions, non-local, and strain gradient coefficients have an influential effect on mechanical behavior of FGM porous nanobeams.…”

“…For porous case, results reveled that porosities volume fractions, porosities distributions, non-local, and strain gradient coefficients have an influential effect on mechanical behavior of FGM porous nanobeams. 15,16 In another research, at micro-scale level, Mirjavadi et al 18 have presented thermal vibration analysis of 2D FGM porous microbeams based on the combination of Timoshenko beam and couple stress theories. The generalized differential quadrature (GDQ) method is utilized for the resolution of the equations of motion and the effect of temperature change, porosity, FG, and AFG power gradient indexes and also micro-scale parameter on the vibration of the microbeams are examined.…”