Large-amplitude nonlinear free vibrations of functionally graded plates with porous imperfection: A novel approach based on energy balance method

Xie, Ke; Wang, Yuewu; Niu, Hongpan; Chen, Hongyong

doi:10.1016/j.compstruct.2020.112367

Cited by 26 publications

(4 citation statements)

References 64 publications

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“…As tabulated in table 1, an excellent compliance is achieved confirming the validity of the present size-dependent model. Also, in order to show the accuracy of the present solving procedure to predict nonlinear frequency of a plate-type structure, by removing the terms associated with the nonlocal strain gradient continuum elasticity, the frequency ratios of / w w l associated with different dimensionless maximum deflections for a FG composite rectangular plate having constant thickness are tabulated in table 2, and are compared with those predicted by Xie et al [76] using energy balance method. An excellent agreement between two approaches is derived which confirms the accuracy of the current study.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

Nonlinear oscillations of elliptical and sector prefabricated nanoplate-type structures made of functionally graded building material

2021

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The primary goal of this work is to apply for the first time the efficient isogeometric type of numerical solving technique for the geometrically nonlinear large-amplitude oscillations of nanoplates with arbitrary shapes with variable thicknesses incorporating simultaneously strain gradient size and nonlocality dependencies. Microplate thickness variation follows convex, concave, and linear patterns. Accordingly, isogeometric analysis is carried out to obtain precise geometrical description and higher-order efficient smoothness related to thickness variation within an arbitrary shape with no difficulty in meshing. It is assumed that nanoplates are made of functionally graded composite materials with variable material properties at different thicknesses. It is found that changing thickness variation pattern from convex to linear, and finally to concave increases the significance of both nonlocality and strain gradient size effects. Moreover, it is demonstrated that by increasing plate deflection and material gradient index, the contributions of strain gradient and nonlocal stress to the nonlinear frequency of functionally graded composite nanoplates are weakened.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Nonlinear oscillations of elliptical and sector prefabricated nanoplate-type structures made of functionally graded building material

2021

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“…The nonlinear free and forced vibrations of sigmoid FGM thin and thick plates with porosities have been treated in the works of Wang and Zu [29] and Huang et al [30] employing harmonic balance method and improved perturbation technique, respectively. Based on energy balance method and different plate theories, Xie et al [31] looked at the effects of porosities on the nonlinear vibrations of FGM plates. FSDT-based nonlinear FEM was employed in work of Kumar et al [32] dealing with the nonlinear vibration and transient response of skew FGM plates including porosities.…”

Section: Introductionmentioning

confidence: 99%

“…Based on energy balance method and different plate theories, Xie et al. [31] looked at the effects of porosities on the nonlinear vibrations of FGM plates. FSDT‐based nonlinear FEM was employed in work of Kumar et al.…”

Section: Introductionmentioning

confidence: 99%

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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“…Starting with the basic idea from [21], we propose a four-variable refined plate theory to handle the problem without any use of shear correction factors, whose accuracy is verified against other higher-order formulations available from literature involving more variables. The potential of the proposed theoretical formulation for FG sandwich plates reinforced with carbon nanotubes (CNTs) would be of particular interest for different plate components, as commonly encountered in many aerospace, marine and automobile structures [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63], and can be extended to more complicated shell components under different boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Higher-Order Free Vibration Analysis of Porous Functionally Graded Plates

et al. 2021

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The present work analyzes the free vibration response of functionally graded (FG) plates made of Aluminum (Al) and Alumina (Al2O3) with different porosity distributions, as usually induced by a manufacturing process. The problem is tackled theoretically based on a higher-order shear deformation plate theory, while proposing a Navier-type approximation to solve the governing equations for simply-supported plates with different porosity distributions in the thickness direction. The reliability of the proposed theory is checked successfully by comparing the present results with predictions available from literature based on further first-order or higher-order theories. A large parametric study is performed systematically to evaluate the effect of different mechanical properties, such as the material indexes, porosity volume fractions, porosity distributions, and length-to-thickness ratios, on the free vibration response of FG plates, as useful for the design purposes of most engineered materials and composite applications.

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Large-amplitude nonlinear free vibrations of functionally graded plates with porous imperfection: A novel approach based on energy balance method

Cited by 26 publications

References 64 publications

Nonlinear oscillations of elliptical and sector prefabricated nanoplate-type structures made of functionally graded building material

Nonlinear oscillations of elliptical and sector prefabricated nanoplate-type structures made of functionally graded building material

Nonlinear thermomechanical vibration of initially stressed functionally graded plates with porosities

Higher-Order Free Vibration Analysis of Porous Functionally Graded Plates

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