scholarly journals Analysis of the Vibration Behaviors of Rotating Composite Nano-Annular Plates Based on Nonlocal Theory and Different Plate Theories

2021 ◽  
Vol 12 (1) ◽  
pp. 230
Author(s):  
Haonan Li ◽  
Wei Wang ◽  
Linquan Yao
Keyword(s):  
Thermal Environment ◽  
Plate Theory ◽  
Constitutive Relations ◽  
Rotational Velocity ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Radius Ratio ◽  
Mindlin Plate ◽  
Motion Equations ◽  
Annular Plates

Rotating machinery has significant applications in the fields of micro and nano meters, such as nano-turbines, nano-motors, and biomolecular motors, etc. This paper takes rotating nano-annular plates as the research object to analyze their free vibration behaviors. Firstly, based on Kirchhoff plate theory, Mindlin plate theory, and Reddy plate theory, combined with nonlocal constitutive relations, the differential motion equations of rotating functionally graded nano-annular plates in a thermal environment are derived. Subsequently, the numerical method is used to discretize and solve the motion equations. The effects of nonlocal parameter, temperature change, inner and outer radius ratio, and rotational velocity on the vibration frequencies of the nano-annular plates are analyzed through numerical examples. Finally, the relationship between the fundamental frequencies and the thickness-to-radius ratio of the nano-annular plates of clamped inner and outer rings is discussed, and the differences in the calculation results among the three plate theories are compared.

A New Quasi 3D Nonlocal Plate Theory for Vibration and Buckling of FGM Nanoplates

2017 ◽  
Vol 09 (01) ◽  
pp. 1750008 ◽  
Author(s):  
Mohammed Sobhy ◽  
Ahmed F. Radwan
Keyword(s):  
Thermal Environment ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Nonlocal Parameter ◽  
Nonlocal Theory ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Motion Equations ◽  
Nonlocal Equations ◽  
Power Law Index

This paper presents the analyses of free vibration and buckling of functionally graded (FG) nanoplates in thermal environment by using a new quasi-3D nonlocal hyperbolic plate theory in which both shear and normal strains are included. The nonlocal equations of motion for the present problem are derived from Hamilton’s principle. For simply-supported boundary conditions, Navier’s approach is utilized to solve the motion equations. Eringen’s nonlocal theory is employed to capture the effect of the nonlocal parameter on natural frequency and buckling of the FGM nanoplates. Numerical results of the present formulation are compared with those predicted by other theories available in the open literature to explain the accuracy of the suggested theory that contains the shear deformation and thickness stretching. Other numerical examples are also presented to show the influences of the nonlocal coefficient, power law index and geometrical parameters on the vibration and buckling load of FGM nanoplates.

Dynamical Behaviors of Sinusoidal Nanocomposite Plates Subjected to Thermomechanical Loads

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.

scholarly journals Non-Local Buckling Analysis of Functionally Graded Nanoporous Metal Foam Nanoplates

Coatings ◽  
2018 ◽  
Vol 8 (11) ◽  
pp. 389 ◽  
Author(s):  
Yanqing Wang ◽  
Zhiyuan Zhang
Keyword(s):  
Metal Foam ◽  
Plate Theory ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Local Buckling ◽  
Functionally Graded ◽  
Small Scale ◽  
Refined Plate Theory ◽  
Nanoporous Metal ◽  
Non Local

In this study, the buckling of functionally graded (FG) nanoporous metal foam nanoplates is investigated by combining the refined plate theory with the non-local elasticity theory. The refined plate theory takes into account transverse shear strains which vary quadratically through the thickness without considering the shear correction factor. Based on Eringen’s non-local differential constitutive relations, the equations of motion are derived from Hamilton’s principle. The analytical solutions for the buckling of FG nanoporous metal foam nanoplates are obtained via Navier’s method. Moreover, the effects of porosity distributions, porosity coefficient, small scale parameter, axial compression ratio, mode number, aspect ratio and length-to-thickness ratio on the buckling loads are discussed. In order to verify the validity of present analysis, the analytical results have been compared with other previous studies.

Nonlinear thermo-mechanical buckling of higher-order shear deformable porous functionally graded material plates reinforced by orthogonal and/or oblique stiffeners

2019 ◽  
Vol 233 (17) ◽  
pp. 6177-6196 ◽  
Author(s):  
Vu Hoai Nam ◽  
Nguyen Thi Phuong ◽  
Dang Thuy Dong ◽  
Nguyen Thoi Trung ◽  
Nguyen Van Tue
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Functionally Graded Material ◽  
Thermal Environment ◽  
Plate Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Shear Deformation Plate Theory ◽  
Graded Material ◽  
Post Buckling

In this paper, an analytical approach for nonlinear buckling and post-buckling behavior of stiffened porous functionally graded plate rested on Pasternak's elastic foundation under mechanical load in thermal environment is presented. The orthogonal and/or oblique stiffeners are attached to the surface of plate and are included in the calculation by improving the Lekhnitskii's smeared stiffener technique in the framework of higher-order shear deformation plate theory. The complex equilibrium and stability equations are established based on the Reddy's higher-order shear deformation plate theory and taken into account the geometrical nonlinearity of von Kármán. The solution forms of displacements satisfying the different boundary conditions are chosen, the stress function method and the Galerkin procedure are used to solve the problem. The good agreements of the present analytical solution are validated by making the comparisons of the present results with other results. In addition, the effects of porosity distribution, stiffener, volume fraction index, thermal environment, elastic foundation… on the critical buckling load and post-buckling response of porous functionally graded material plates are numerically investigated.

scholarly journals Free vibration and buckling of bidirectional functionally graded sandwich plates using an efficient Q9 element

2021 ◽  
Author(s):  
Le Cong Ich ◽  
Tran Quang Dung ◽  
Pham Vu Nam ◽  
Nguyen Dinh Kien
Keyword(s):  
Free Vibration ◽  
Plate Theory ◽  
Functionally Graded ◽  
Mindlin Plate ◽  
Sandwich Plates ◽  
Various Boundary Conditions ◽  
Fundamental Frequencies ◽  
Numerical Result ◽  
Three Phase ◽  
Graded Material

Free vibration and buckling of three-phase bidirectional functionally graded sandwich (BFGSW) plates are studied in this paper for the first time by using an efficient nine-node quadrilateral (Q9) element. The core of the sandwich plates is pure ceramic, while the two skin layers are of a three-phase bidirectional functionally graded material. The element is derived on the basis of the Mindlin plate theory and linked interpolations. Fundamental frequencies and buckling loads are computed for the plates with various boundary conditions. Numerical result shows that convergence of the linked interpolation element is faster compared to the conventional Lagrangian interpolation Q9 element. Numerical investigations are carried out to highlight the influence of the material gradation and the side-to-thickness ratio on the vibration and buckling behaviour of the plates.

Free vibration and buckling analysis of elastically supported transversely inhomogeneous functionally graded nanoplate in thermal environment using Rayleigh–Ritz method

2020 ◽  
pp. 107754632096693
Author(s):  
Piyush P Singh ◽  
Mohammad S Azam
Keyword(s):  
Free Vibration ◽  
Thermal Environment ◽  
Ritz Method ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Small Scale ◽  
Pasternak Foundation ◽  
Differential Model ◽  
Aspect Ratios ◽  
Elastically Supported

In this study, free vibration and buckling behaviors of a functionally graded nanoplate supported by the Winkler–Pasternak foundation using a nonlocal classical plate theory are investigated. Eringen’s nonlocal differential model has been used for considering the small-scale effect. The properties of the functionally graded nanoplate are considered to vary transversely following the power law. The governing vibration and buckling equations of an elastically supported functionally graded nanoplate have been derived using the principle of virtual work, and the solution is obtained using the Rayleigh–Ritz method and characteristic polynomials. The advantage of this method is that it disposes of all the drawbacks regarding edge constraints. The objective of the article is to see the effect of edge constraints, aspect ratios, material property exponent, nonlocal parameter, and foundation parameters on the nondimensionalized frequency and the buckling load of an embedded functionally graded nanoplate in a thermal environment. The study highlights that the nonlocal effect is pronounced for higher modes and/or higher aspect ratios and need to be considered for the analysis of the nanoplate. Further, it is observed that the effect of the Pasternak foundation is prominent on nondimensionalized frequencies and buckling of the functionally graded nanoplate.

Analysis of Thermoelastic Damping of Functionally Graded Material Micro Plate Based on the Mindlin Plate Theory

2020 ◽  
Vol 865 ◽  
pp. 67-71
Author(s):  
Shi Rong Li ◽  
Peng Xiong ◽  
Da Fu Cao
Keyword(s):  
Heat Conduction ◽  
Functionally Graded Material ◽  
Heat Conduction Equation ◽  
Plate Theory ◽  
Functionally Graded ◽  
Conduction Equation ◽  
Mindlin Plate ◽  
Thermoelastic Damping ◽  
Graded Material ◽  
Mindlin Plate Theory

In this paper, thermoelastic damping (TED) in a simply supported rectangular functionally graded material (FGM) micro plate with continuous variation of the material properties along the thickness direction is performed. The equations of motion and the heat conduction equation coupled with the thermal effects are derived based on the Mindlin plate theory and the one-way coupled heat conduction theory, respectively. The heat conduction equation with variable coefficients is solved by using the layer-wise homogenization approach. Analytical solution of TED is obtained by complex frequency method. Numerical results of TED are presented for the rectangular FGM micro plate made of ceramic-metal constituents with the power-law gradient profile. The effects of the shear deformation, the material gradient index, the plate thickness on the TED of the FGM micro plate are studied.

High-frequency vibrations of circular and annular plates with the Mindlin plate theory

2020 ◽  
Vol 90 (5) ◽  
pp. 1025-1038
Author(s):  
Hui Chen ◽  
Rongxing Wu ◽  
Longtao Xie ◽  
Jianke Du ◽  
Lijun Yi ◽  
...  
Keyword(s):  
High Frequency ◽  
Plate Theory ◽  
Mindlin Plate ◽  
Annular Plates ◽  
Mindlin Plate Theory ◽  
High Frequency Vibrations

Nonlocal Buckling Characteristics of Functionally Graded Nano-Plates Subjected to Thermal Loads and Biaxial Linearly Varying Forces

2018 ◽  
Author(s):  
Ma’en S. Sari ◽  
Seyedeh Sepideh Ghaffari ◽  
Samantha Ceballes ◽  
Abdessattar Abdelkefi
Keyword(s):  
Power Law ◽  
Plate Theory ◽  
Constitutive Relations ◽  
Equations Of Motion ◽  
Nonlocal Elasticity Theory ◽  
Functionally Graded ◽  
Thin Plates ◽  
Thermal Loads ◽  
Buckling Loads ◽  
The Difference

The buckling characteristics of thin functionally graded (FG) nano-plates subjected to both thermal loads and biaxial linearly varying forces is investigated. Eringen’s nonlocal elasticity theory is employed to account for the nano-scale phenomena in the plates. Hamilton’s principle and the constitutive relations are used to derive the partial differential governing equations of motion for the thin plates that are modeled using Kirchhoff’s plate theory. The mechanical properties of the FG nano-plates are assumed to vary smoothly across the thickness of the plate following a power law. Three types of thermal loads are presented and the spectral collocation method is utilized to solve for the critical buckling loads. The accuracy of the numerical solution of the proposed model is verified by comparing the results with those available in the literature. A comprehensive parametric study is carried out, and the effects of the nonlocal scale parameter, power law index, aspect ratio, slopes of the axial loads, boundary conditions, assumed temperature distributions, and the difference between the ceramic-rich and metal-rich surfaces on the nonlocal critical buckling loads of the nano-plates are examined. The results reveal that these parameters have significant influence on the stability behavior of the FG nano-plates.

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