A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation

Shahsavari, Davood; Shahsavari, Maryam; Li, Li; Karami, Behrouz

doi:10.1016/j.ast.2017.11.004

Cited by 234 publications

(79 citation statements)

References 58 publications

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“…It can be seen that the present results agree well with the results of the authors using analytical methods [5,14,17] and are more accurate than those using the original MITC3 element and FEM [6]. In addition, from Table 2, it is obvious that the relative error of the present results compared to [18] is less than 2%. In [18], they used a new quasi-3D hyperbolic theory to investigate the free vibration of the FGP plate resting on the EF.…”

Section: Accuracy Of the Proposed Methodssupporting

confidence: 87%

“…In addition, from Table 2, it is obvious that the relative error of the present results compared to [18] is less than 2%. In [18], they used a new quasi-3D hyperbolic theory to investigate the free vibration of the FGP plate resting on the EF. ese results are the basis to analyze the free vibration of FGP plates on the EFTIM.…”

Section: Accuracy Of the Proposed Methodsmentioning

confidence: 58%

“…where λ pr and λ re are nondimensional frequencies of present method and nondimensional frequencies in [17,18], respectively. e results of the convergence of the first two nondimensional frequencies of the plate in the case of fully simple support (SSSS) plate and a fully clamped (CCCC) plate with h/a � 0.1, K 1 � 100, K 2 � 10, respectively, are shown in Figure 5.…”

Section: Accuracy Of the Proposed Methodsmentioning

confidence: 99%

“…Substituting equations (12) and (18) into equation 11, the weak formulation for the free vibration of the FGP plate is finally obtained as…”

Section: Weak Form Equationsmentioning

confidence: 99%

“…Ferreira et al [17] presented bending and free vibration analyses of the FGP plates on the Winkler-Pasternak foundation by using radial basis functions. Shahsavari et al [18] used a new quasi-3D hyperbolic theory for the free vibration analysis of the FGP plates resting on the EF. Zenkour and Radwan [19] proposed an exact analytical approach for free vibration analysis of laminated composite and Sandwich plates resting on the EF using a four-unknown plate theory.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

An Edge-Based Smoothed Finite Element for Free Vibration Analysis of Functionally Graded Porous (FGP) Plates on Elastic Foundation Taking into Mass (EFTIM)

Tran

Pham

Nguyen-Thoi

2020

Mathematical Problems in Engineering

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In this paper, free vibration analysis of the functionally graded porous (FGP) plates on the elastic foundation taking into mass (EFTIM) is presented. The fundamental equations of the FGP plate are derived using Hamilton’s principle. The mixed interpolation of the tensorial components (MITC) approach and the edge-based smoothed finite element method (ES-FEM) is employed to avoid the shear locking as well as to improve the accuracy for the triangular element. The EFTIM is a foundation model based on the two-parameter Winkler–Pasternak model but added a mass parameter of foundation. Materials of the plate are FGP with a power-law distribution and maximum porosity distributions in the forms of cosine functions. Some numerical examples are examined to demonstrate the accuracy and reliability of the proposed method in comparison with those available in the literature.

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Section: Accuracy Of the Proposed Methodssupporting

confidence: 87%

Section: Accuracy Of the Proposed Methodsmentioning

confidence: 58%

Section: Accuracy Of the Proposed Methodsmentioning

confidence: 99%

“…Substituting equations (12) and (18) into equation 11, the weak formulation for the free vibration of the FGP plate is finally obtained as…”

Section: Weak Form Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An Edge-Based Smoothed Finite Element for Free Vibration Analysis of Functionally Graded Porous (FGP) Plates on Elastic Foundation Taking into Mass (EFTIM)

Tran

Pham

Nguyen-Thoi

2020

Mathematical Problems in Engineering

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Assessment of non‐polynomial shear deformation theories for the free vibration and transient analysis of plates with functionally‐graded materials supported on an elastic foundation

et al. 2023

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In this article, various non‐polynomial higher‐order shear deformation theories are applied for the first time to analyze the free vibration and transient responses of plates with functionally graded material (FGM) supported on an elastic foundation. The shear deformation theories account for the non‐linear variation of the transverse shear strains with various warping functions, namely trigonometric, inverse hyperbolic, and inverse trigonometric ones. These models also inherently satisfy the traction‐free boundary conditions of transverse shear stresses at the top and bottom surfaces of the plates and do not require any shear correction factor. A two‐parameter model, namely Winkler‐Pasternak's elastic foundation model, is utilized to develop the interaction between the FGM plates and the elastic medium. The governing equations of motion are obtained using Hamilton's principle and solved analytically using Navier's solution scheme. Furthermore, the transient responses of the plates are obtained using Newmark's average acceleration method. The applicability of the present theories is established by solving several numerical problems and validating the results with the solutions available in the literature. The effects of various parameters like span‐thickness ratios, aspect ratios, gradation coefficients, mechanical loads, and foundation stiffness on the fundamental frequencies and the transient responses of the plates are thoroughly investigated. The comparison of the results reveals the efficiency of the non‐polynomial functions, and the capability of efficient prediction of the structural responses of the FGM plates at a similar computational cost compared to established models in the literature. Furthermore, the results show that the stiffness of the elastic foundation can tweak the stiffness characteristics of the FGM plate resulting in significant changes in the natural frequencies and more controlled displacement‐time responses.

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Nonlinear thermomechanical vibration of initially stressed functionally graded plates with porosities

Anh,

Van Thinh,

Van Tung

2023

Z Angew Math Mech

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The large‐amplitude vibration of initially stressed functionally graded material (FGM) rectangular plates with porosities is investigated in this paper. All edges of the plate are simply supported and uncompressed edges are tangentially restrained. Initial stresses are caused by in‐plane compressive load acting on freely movable edges or thermally induced forces at restrained edges. Pores present in FGM through even and uneven distributions. Material properties are assumed to be temperature‐dependent and, due to the presence of the pores, the effective properties of FGM are determined using a modified rule of mixture. Governing equations in terms of deflection and stress function are established based on the classical plate theory taking into account von Kármán nonlinearity and initial geometric imperfection. These equations are solved using approximate analytical solutions along with the Galerkin method to obtain a time differential equation containing quadratic and cubic nonlinear terms. Nonlinear frequencies are determined by means of numerical integration employing the fourth‐order Runge–Kutta scheme. Parametric studies are carried out to analyze the effects of material and geometry properties, porosity volume fraction and distribution, pre‐existent compressive and thermal loads, imperfection and degree of tangential constraints of unloaded edges on the natural frequencies and nonlinear to linear frequency ratio of FGM plates.

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A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation

Cited by 234 publications

References 58 publications

An Edge-Based Smoothed Finite Element for Free Vibration Analysis of Functionally Graded Porous (FGP) Plates on Elastic Foundation Taking into Mass (EFTIM)

An Edge-Based Smoothed Finite Element for Free Vibration Analysis of Functionally Graded Porous (FGP) Plates on Elastic Foundation Taking into Mass (EFTIM)

Assessment of non‐polynomial shear deformation theories for the free vibration and transient analysis of plates with functionally‐graded materials supported on an elastic foundation

Nonlinear thermomechanical vibration of initially stressed functionally graded plates with porosities

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