Vibrational behavior of rotating pre-twisted functionally graded microbeams in thermal environment

Abstract The sandwich structures are three- or multilayered structures such that their mechanical properties are better than each single layer. In the current research, a three-layered cylindrical shell including a functionally graded porous core and two reinforced nanocomposite face sheets resting on the Pasternak foundation is used as model to provide a comprehensive understanding of vibrational behavior of such structures. The core is made of limestone, while the epoxy is utilized as the top and bottom layers’ matrix phase and also it is reinforced by the graphene nanoplatelets (GNPs). The pattern of the GNPs dispersion and the pores distribution play a crucial role at the continuous change of the layers’ properties. The sinusoidal shear deformation shells theory and the Hamilton’s principle are employed to derive the equations of motion for the mentioned cylindrical sandwich shell. Ultimately, the impacts of the model’s geometry, foundation moduli, mode number, and deviatory radius on the vibrational behavior are investigated and discussed. It is revealed that the natural frequency and rotation angle of the sandwich shell are directly related. Moreover, mid-radius to thickness ratio enhancement results in the natural frequency reduction. The results of this study can be helpful for the future investigations in such a broad context. Furthermore, for the pipe factories current study can be effective at their designing procedure.

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Bifurcation and chaos of thin circular functionally graded plate in thermal environment

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2011.06.012 ◽

2011 ◽

Vol 44 (9) ◽

pp. 739-750 ◽

Cited By ~ 12

Author(s):

Hu Yuda ◽

Zhang Zhiqiang

Keyword(s):

Thermal Environment ◽

Functionally Graded ◽

Functionally Graded Plate ◽

Bifurcation And Chaos

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Dynamical Behaviors of Sinusoidal Nanocomposite Plates Subjected to Thermomechanical Loads

International Journal of Applied Mechanics ◽

10.1142/s1758825121500691 ◽

2021 ◽

Author(s):

Vu Ngoc Viet Hoang ◽

Dinh Gia Ninh

Keyword(s):

Thermal Environment ◽

Plate Theory ◽

Micromechanical Model ◽

Functionally Graded ◽

Geometrical Parameters ◽

Rectangular Plates ◽

Sine Function ◽

Classical Plate Theory ◽

Wolfram Mathematica ◽

Number Of Cycles

In this paper, a new plate structure has been found with the change of profile according to the sine function which we temporarily call as the sinusoidal plate. The classical plate theory and Galerkin’s technique have been utilized in estimating the nonlinear vibration behavior of the new non-rectangular plates reinforced by functionally graded (FG) graphene nanoplatelets (GNPs) resting on the Kerr foundation. The FG-GNP plates were assumed to have two horizontal variable edges according to the sine function. Four different configurations of the FG-GNP plates based on the number of cycles of sine function were analyzed. The material characteristics of the GNPs were evaluated in terms of two models called the Halpin–Tsai micromechanical model and the rule of mixtures. First, to verify this method, the natural frequencies of new non-rectangular plates made of metal were compared with those obtained by the Finite Element Method (FEM). Then, the numerical outcomes are validated by comparing with the previous papers for rectangular FGM/GNP plates — a special case of this structure. Furthermore, the impacts of the thermal environment, geometrical parameters, and the elastic foundation on the dynamical responses are scrutinized by the 2D/3D graphical results and coded in Wolfram-Mathematica. The results of this work proved that the introduced approach has the advantages of being fast, having high accuracy, and involving uncomplicated calculation.

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