Free vibration of functionally graded quadrilateral microplates in thermal environment

Shenas, Amin Ghorbani; Malekzadeh, P.

doi:10.1016/j.tws.2016.05.001

Cited by 53 publications

(16 citation statements)

References 32 publications

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“…It should be noted in Eq. (8) that the thermal effect is assumed to be only accounted for in the classical stress [60,61]. When the coupled thermoelastic problems and thickness stretching effect are considered, the high-order stresses corresponding to the dilatation gradient tensor p i should be modified.…”

Section: Modified Strain Gradient Theory (Mst)mentioning

confidence: 99%

“…For example, Ansari et al [60] presented an investigation on the linear thermal buckling of FG microplates based on the first-order plate theory. Shenas and Malekzadeh [61] discussed the influence of thermal environment on the free vibration behavior of quadrilateral FG microplates by using the Chebyshev-Ritz method. Emami and Alibeigloo [62] also adopted the first-order plate theory and analytical approach to study the thermoelastic damping behavior of FG microplates, in which the coupled thermoelasticity was investigated together with the size effect.…”

Section: Introductionmentioning

confidence: 99%

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Post-buckling of functionally graded microplates under mechanical and thermal loads using isogeomertic analysis

Thai

et al. 2017

Engineering Structures

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The present study uses the isogeometric analysis (IGA) to investigate the post-buckling behavior of functionally graded (FG) microplates subjected to mechanical and thermal loads. The modified a strain gradient theory with three length scale parameters is used to capture the size effect. The Reddy third-order shear deformation plate theory with the von Kámán nonlinearity (i.e., small strains and moderate rotations) is employed to describe the kinematics of the microplates. Material variations in the thickness direction of the plate are described using a rule of mixtures. In addition, material properties are assumed to be either temperature-dependent or temperature-independent. The governing equations are derived using the principle of virtual work, which are then discretized using the IGA approach, whereby a C 2-continuity requirement is fulfilled naturally and efficiently. To trace the post-buckling paths, Newton's iterative technique is utilized. Various parametric studies are conducted to examine the influences of material variations, size effects, thickness ratios, and boundary conditions on the post-buckling behavior of microplates.

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Section: Modified Strain Gradient Theory (Mst)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Post-buckling of functionally graded microplates under mechanical and thermal loads using isogeomertic analysis

Thai

et al. 2017

Engineering Structures

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“…where ∆T is the temperature change in the z-direction, which can be derived by Equations (5)- (7). The governing equations of the motion system for the FGM rectangular plates can be derived by substituting Equations (14)- (16) into Equation (13); the following equations regarding the forces N ij and moment resultants M ij can be stated as:…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Malekzadeh [14,15] analyzed the natural frequencies of FGM plates considering the effect of temperature change employing the differential quadrature method and discussed the effects of different boundary conditions, temperature change, and the volume fraction index. Shenas [16] computed the free vibration of FG quadrilateral microplates subjected to thermal loads by the Chebyshev-Ritz method and concluded that the free frequencies increased monotonically with the temperature drops. Shi [17] chose 3D elasticity theory to compute the vibration characteristics of FGM annular plates employing the Chebyshev-Ritz algorithm and analyzed the influences of various mixed boundary conditions, the material graded index, and temperature rise on the eigenfrequencies.…”

Section: Introductionmentioning

confidence: 99%

Novel Semi-Analytical Solutions for the Transient Behaviors of Functionally Graded Material Plates in the Thermal Environment

et al. 2019

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The primary objective of this article is to present a semi-analytical algorithm for the transient behaviors of Functionally Graded Materials plates (FGM plates) considering both the influence of in-plane displacements and the influence of temperature changes. Based on the classical plate theory considering the effect of in-plane displacements, the equilibrium equations of the motion system are derived by Hamilton’s principle. Here, we propose a novel, accurate, and efficient semi-analytical method that incorporates the Fourier series expansion, the Laplace transforms, and its numerical inversion and the Differential Quadrature Method (DQM) to simulate the transient behaviors. This paper validates the proposed method by comparisons with semi-analytical natural frequency results and those from the literature. Expressly, the results of dynamic response also agree well with those generated by the Navier’s method and Finite Element Method (FEM). A convergence study that utilizes the different numbers of sampling points shows that the process can converge quickly, and a few sampling points can achieve high accuracy. The effects of various boundary conditions at the ends, material graded index, and temperature change are further investigated. From the detailed parametric study, it is seen that the peak displacement increases as the edge degrees of freedom, the gradient index of the material, and temperature change increase.

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“…He et al [35] presented a sizedependent four-variable re ned plate model for functionally graded micro-plates based on modi ed couple stress theory. Shenas and Malekzadeh [36] investigated free vibration of functionally graded quadrilateral micro plates in thermal environment. Thus, according to the available literature, no analytical expressions for nonlinear frequencies of FG micro plates have been derived so far.…”

Section: Introductionmentioning

confidence: 99%

An explicit solution for the size-dependent large amplitude transverse vibration of thin functionally graded micro-plates

Setoodeh

Rezaei

2017

Scientia Iranica

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Abstract. In this article, an analytical solution to the moderately large amplitude transverse vibration of thin Functionally Graded Micro-Plates (FGMPs) is presented based on a practical approach. The size-dependent nonlinear governing equation is obtained in conjunction with the Kirchho 's plate and modi ed couple stress theories. The material properties of Functionally Graded (FG) micro-plates vary according to the Reddy's model. The employed non-classical theory contains one material length-scale parameter to capture the size e ects. The highly nonlinear governing equation is solved by means of homotopy analysis method so as to obtain accurate analytic approximations. Both of simply supported and clamped micro-plates with immovable edges are considered. The comparison made between the present results and those of earlier studies con rms the reliability and e ectiveness of the present formulation for the design purpose. Furthermore, the e ects of di erent parameters, such as material gradient index, length-scale parameter, and aspect ratio, on the nonlinear frequency ratio are investigated.

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Free vibration of functionally graded quadrilateral microplates in thermal environment

Cited by 53 publications

References 32 publications

Post-buckling of functionally graded microplates under mechanical and thermal loads using isogeomertic analysis

Post-buckling of functionally graded microplates under mechanical and thermal loads using isogeomertic analysis

Novel Semi-Analytical Solutions for the Transient Behaviors of Functionally Graded Material Plates in the Thermal Environment

An explicit solution for the size-dependent large amplitude transverse vibration of thin functionally graded micro-plates

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