Effect of thermal environment on free vibration and buckling of partially cracked isotropic and FGM micro plates based on a non classical Kirchhoff's plate theory: An analytical approach

2017 ◽  
Vol 131-132 ◽  
pp. 155-170 ◽  
Author(s):  
P.V. Joshi ◽  
Ankur Gupta ◽  
N.K. Jain ◽  
R. Salhotra ◽  
A.M. Rawani ◽  
...  
Keyword(s):  
Free Vibration ◽  
Analytical Approach ◽  
Thermal Environment ◽  
Plate Theory ◽  
Micro Plates

Differential Quadrature Free Vibration Analysis of Functionally Graded Thin Annular Sector Plates in Thermal Environments

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
S. H. Mirtalaie
Keyword(s):  
Free Vibration ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Plate Theory ◽  
Differential Quadrature Method ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Differential Quadrature ◽  
Annular Sector

In this paper, the free vibration behavior of functionally graded (FG) thin annular sector plates in thermal environment is studied using the differential quadrature method (DQM). The material properties of the FG plate are assumed to be temperature dependent and vary continuously through the thickness, according to the power-law distribution of the volume fraction of the constituents. The nonlinear temperature distribution along the thickness direction of the plate is considered. Based on the classical plate theory, the governing differential equations of motion of the plate are derived and solved numerically using DQM. The natural frequencies of thin FG annular sector plates in thermal environment under various combinations of clamped, free, and simply supported boundary conditions (BCs) are presented for the first time. To ensure the accuracy of the method, the natural frequencies of a pure metallic plate are calculated and compared with those existing in the literature for the homogeneous plate where the results are in good agreement. The effects of temperature field, BCs, volume fraction exponent, radius ratio, and the sector angle on the free vibrations of the FG-plate are examined.

Closed-form Analytical Solutions for Free Vibration of Rectangular Functionally Graded Thin Plates in Thermal Environment

2018 ◽  
Vol 10 (03) ◽  
pp. 1850025 ◽  
Author(s):  
Y. F. Xing ◽  
Z. K. Wang ◽  
T. F. Xu
Keyword(s):  
Free Vibration ◽  
Closed Form ◽  
Analytical Solutions ◽  
Thermal Environment ◽  
Plate Theory ◽  
Normal Modes ◽  
Functionally Graded ◽  
Thin Plates ◽  
Numerical Comparison ◽  
Fg Plates

Based on classical small deflection plate theory, the governing equation of functionally graded (FG) plates in thermal environment is derived by using Hamilton’s principle. Closed-form analytical solutions are obtained via separation-of-variable method for free vibration of rectangular FG thin plates with simply supported, clamped and guided edges, especially for the plates with two adjacent clamped edges in thermal environment. The normal modes and frequencies are in an elegant and explicit closed form. Comprehensive numerical comparison and results in dimensionless form validate the present method and reveal a few physical phenomena.

scholarly journals Bending, Free Vibration, and Buckling Analysis of Functionally Graded Porous Micro-Plates Using a General Third-Order Plate Theory

2019 ◽  
Vol 3 (1) ◽  
pp. 15 ◽  
Author(s):  
Semsi Coskun ◽  
Jinseok Kim ◽  
Houssam Toutanji
Keyword(s):  
Free Vibration ◽  
Material Properties ◽  
Plate Theory ◽  
Functionally Graded ◽  
Length Scale ◽  
Thickness Direction ◽  
Third Order ◽  
Micro Plates ◽  
Material Length Scale ◽  
Material Length

Static bending, free vibration and buckling of functionally graded porous micro-plates are investigated using a general third order plate theory. In addition, analytical solutions are obtained using the Navier method. The effect of the material length scale factor and the variation of material property through the thickness direction of plates are considered as well as porosity effects. Three different porosity distributions are considered and the effects of porosity variations are examined in the framework of a general third order plate theory. Numerical results show that the effect of each distribution of porosity is distinguished due to coupling between the heterogeneity of the material properties and the variation of porosity.

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 Nonlinear free vibration of rotating FG trapezoidal microplates in thermal environment

2022 ◽  
Vol 170 ◽  
pp. 108614
Author(s):  
Amin Ghorbani Shenas ◽  
Sima Ziaee ◽  
Parviz Malekzadeh
Keyword(s):  
Free Vibration ◽  
Thermal Environment ◽  
Nonlinear Free Vibration

scholarly journals A Unified Analysis for the Free Vibration of the Sandwich Piezoelectric Laminated Beam with General Boundary Conditions under the Thermal Environment

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Guohua Gao ◽  
Ningze Sun ◽  
Dong Shao ◽  
Yongqiang Tao ◽  
Wei Wu
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Thermal Environment ◽  
Search Algorithm ◽  
Golden Section ◽  
Shear Deformation Theory ◽  
Simulation Software ◽  
Elastic Boundary ◽  
Piezoelectric Beam ◽  
Elastic Boundary Conditions

This article mainly analyzes the free vibration characteristic of the sandwich piezoelectric beam under elastic boundary conditions and thermal environment. According to the first-order shear deformation theory and Hamilton’s principle, the thermo-electro-elastic coupling equations of the sandwich piezoelectric beam are obtained. Meanwhile, elastic boundary conditions composed of an array of springs are introduced, and the displacement variables and external potential energy of the beam are expressed as wave functions. By using the method of reverberation-ray matrix to integrate and solve the governing equations, a search algorithm based on golden-section search is introduced to calculate the required frequency parameters. A series of numerical results are compared with those reported in literature studies and obtained by simulation software to verify the correctness and versatility of the search algorithm. In addition, three parametric research cases are proposed to investigate the frequency parameters of sandwich piezoelectric beams with elastic restraint conditions, material parameters, thickness ratio, different temperature rises, and external electric potential.

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