Vibration of two-dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams

Shafiei, Navvab; Mirjavadi, Seyed Sajad; Afshari, Behzad Mohasel; Rabby, Samira; Kazemi, Mohammad Taghi

doi:10.1016/j.cma.2017.05.007

Cited by 185 publications

(47 citation statements)

References 87 publications

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“…As can be noted from Equations (9)- (11), the overall mechanical properties of the composite are computed through the well-known rule of mixture, which has been properly modified to take into account the porosity of the medium [31]. The same empirical approach has been recently employed and validated by many authors to describe the porous phase of FGMs [30][31][32][33][34][35]. To the best of the authors' knowledge, the rule of mixture represents a simple homogenization technique that allows us to evaluate in an efficient manner the elastic properties of a graded composite.…”

Section: Functionally Graded Materialsmentioning

confidence: 99%

“…For this purpose, the well-known rule of mixture has been modified to deal with porosities. Since this approach has been validated by other authors, as illustrated in [30][31][32][33][34][35], the same empirical scheme is employed in the present paper to deal with FGM structures. The methodology in hand is also extended to the case of shell structures, since the previous studies are mainly focused on beams and plates with porosities.…”

Section: Introductionmentioning

confidence: 99%

“…For this purpose, various hierarchical refined exponential, polynomial, and trigonometric higher-order beam theories were developed in a generalized manner. An empirical approach has been used in all the aforementioned papers concerning porous and imperfect media to evaluate the overall mechanical properties of the composites at issue [30][31][32][33][34][35]. For this purpose, the well-known rule of mixture has been modified to deal with porosities.…”

Section: Introductionmentioning

confidence: 99%

“…Wattanasakulpong and Chaikittiratana [32] studied the flexural vibration of functionally graded beams based on Timoshenko theory by means of the Chebyshev collocation method. The Timoshenko beam theory was employed by Shafiei et al [33] to investigate the vibrational behavior of two-dimensional functionally graded nano and microbeams including porosities. To this aim, the Eringen's nonlocal elasticity and the modified couple stress theories were employed.…”

Section: Introductionmentioning

confidence: 99%

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Free Vibration Analysis of Functionally Graded Porous Doubly-Curved Shells Based on the First-Order Shear Deformation Theory

et al. 2017

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Due to some technical issues that can appear during the manufacturing process of Functionally Graded Materials (FGMs), it can be extremely difficult to produce perfect materials. Indeed, one of the biggest problems is the presence of porosities. For this purpose, the vibrational behavior of doubly-curved shells made of FGM including porosities is investigated in this paper. With respect to previous research, the porosity has been added to the mechanical model that characterizes the through-the-thickness distribution of the graded constituents and applied to doubly-curved shell structures. Few papers have been published on this topic. In fact, it is easier to find works related to one-dimensional structures and beam models that take account the effect of porosities. The First-order Shear Deformation Theory (FSDT) is considered as the theoretical framework. In addition, the mechanical properties of the constituents vary along the thickness direction. For this purpose, two power-law distributions are employed to characterize their volume fraction. Strain components are established in an orthogonal curvilinear coordinate system and the governing equations are derived according to the Hamilton's principle. Finally, Navier's solution method is used and the numerical results concerning three different types of shell structures are presented.

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Section: Functionally Graded Materialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Free Vibration Analysis of Functionally Graded Porous Doubly-Curved Shells Based on the First-Order Shear Deformation Theory

et al. 2017

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“…The material properties in [13] were assumed to vary in both the thickness and longitudinal directions by a power-law function. Recently, Shafiei et al [17] studied the vibration behavior of 2-D FG nano and microbeams formed from two types of porous FGMs. The generalized differential quadrature method has been employed by the authors to solve the governing equations of motion.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration of Two-Directional FGM Beams Using a Higher-Order Timoshenko Beam Element

Thom

Kien²

2018

JST

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Abstract. Free vibration of two-directional functionally graded material (2-D FGM) beams is studied by the finite element method (FEM). The material properties are assumed to be graded in both the thickness and longitudinal directions by a power-law distribution. Equations of motion based on Timoshenko beam theory are derived from Hamilton's principle. A higher-order beam element using hierarchical functions to interpolate the displacements and rotation is formulated and employed in the analysis. In order to improve the efficiency of the element, the shear strain is constrained to constant. Validation of the derived element is confirmed by comparing the natural frequencies obtained in the present paper with the data available in the literature. Numerical investigations show that the proposed beam element is efficient, and it is capable to give accurate frequencies by a small number of elements. The effects of the material composition and aspect ratio on the vibration characteristics of the beams are examined in detail and highlighted.

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Forced vibrations of functionally graded annular and circular plates by domain‐boundary element method

Eshraghi

Dağ

2020

Z Angew Math Mech

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Axi‐symmetric dynamic response of functionally graded circular and annular Mindlin plates with through‐the‐thickness variations of physical properties is investigated by a new domain‐boundary element formulation. Three governing partial differential equations of motion of the inhomogeneous plate are converted to integral equations by utilizing the static fundamental solutions of the displacement components. These integral equations are then spatially discretized by dividing the entire domain into a number of cells and incorporating suitable shape functions to approximate the variation of unknown parameters across the cells. The resulting set of ordinary differential equations in time are then solved by the Houbolt method. To verify the accuracy of the developed procedure, dynamic responses generated for a homogeneous plate are compared to those calculated through an analytical solution. Different loading conditions such as step, harmonic, and impulsive loadings are considered for generation of numerical results of dynamic responses of functionally graded circular and annular plates. Convergence characteristics and effects of material inhomogeneity, and geometric parameters are extensively investigated. It has been shown that the presented method is a fast and accurate and technique in elastodynamic analysis of functionally graded plates.

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Vibration of two-dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams

Cited by 185 publications

References 87 publications

Free Vibration Analysis of Functionally Graded Porous Doubly-Curved Shells Based on the First-Order Shear Deformation Theory

Free Vibration Analysis of Functionally Graded Porous Doubly-Curved Shells Based on the First-Order Shear Deformation Theory

Free Vibration of Two-Directional FGM Beams Using a Higher-Order Timoshenko Beam Element

Forced vibrations of functionally graded annular and circular plates by domain‐boundary element method

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