On the High-Temperature Free Vibration Analysis of Elastically Supported Functionally Graded Material Plates Under Mechanical In-PlaneForce Via GDQR

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Roshan Lal ◽  
Rahul Saini
Keyword(s):  
Mechanical Properties ◽  
Plate Theory ◽  
Elastic Equilibrium ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Effect Of Temperature ◽  
Axisymmetric Vibration ◽  
Thickness Direction ◽  
Classical Plate Theory ◽  
Linear Temperature

In this article, the effect of Pasternak foundation on free axisymmetric vibration of functionally graded circular plates subjected to mechanical in-plane force and a nonlinear temperature distribution (NTD) along the thickness direction has been investigated on the basis of classical plate theory. The plate material is graded in thickness direction according to a power-law distribution and its mechanical properties are assumed to be temperature-dependent (TD). At first, the equation for thermo-elastic equilibrium and then equation of motion for such a plate model have been derived by Hamilton's principle. Employing generalized differential quadrature rule (GDQR), the numerical values of thermal displacements and frequencies for clamped and simply supported plates vibrating in the first three modes have been computed. Values of in-plane force parameter for which the plate ceases to vibrate have been reported as critical buckling loads. The effect of temperature difference, material graded index, in-plane force, and foundation parameters on the frequencies has been analyzed. The benchmark results for uniform and linear temperature distributions (LTDs) have been computed. A study for plates made with the material having temperature-independent (TI) mechanical properties has also been performed as a special case. Comparison of results with the published work has been presented.

Nonlinear Static and Dynamic Thermal Buckling Analysis of Spiral Stiffened Functionally Graded Cylindrical Shells with Elastic Foundation

2019 ◽  
Vol 11 (01) ◽  
pp. 1950005 ◽  
Author(s):  
Alireza Shaterzadeh ◽  
Kamran Foroutan ◽  
Habib Ahmadi
Keyword(s):  
Elastic Foundation ◽  
Plate Theory ◽  
Cylindrical Shells ◽  
Thermal Buckling ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Thickness Direction ◽  
Classical Plate Theory ◽  
Linear Temperature ◽  
Nonlinear Static

In this paper, an analytical method is used to study the nonlinear static and dynamic thermal buckling analysis of imperfect spiral stiffened functionally graded (SSFG) cylindrical shells. The SSFG cylindrical shell is surrounded by a linear and nonlinear elastic foundation. The proposed linear model is based on the two-parameter elastic foundation (Winkler and Pasternak). A three-parameter elastic foundation with hardening/softening cubic nonlinearity is used for nonlinear model. The material properties are temperature dependent and assumed to be continuously graded in the thickness direction. Also, for thermal buckling analysis, the uniform and linear temperature distribution in thickness direction is considered. The SSFG cylindrical shells are considered with various angles for spiral stiffeners. The strain–displacement relations are obtained based on the von Kármán nonlinear equations and the classical plate theory of shells. The smeared stiffener technique and the Galerkin method are applied to solve the nonlinear problem. In order to find the nonlinear dynamic thermal buckling responses, the fourth-order Runge–Kutta method is used. To validate the results, comparisons are made with those available in literature and good agreements are shown. The effects of various geometrical and material parameters are investigated on the nonlinear static and dynamic thermal buckling response of SSFG cylindrical shells.

Exact Relationships between Eigenvalues of FGM Circular Plates Based on RPT and those of Isotropic Homogeneous Circular Plates Based on CPT

2007 ◽  
Vol 353-358 ◽  
pp. 3002-3005
Author(s):  
Lian Sheng Ma ◽  
Lei Wu
Keyword(s):  
Eigenvalue Problem ◽  
Plate Theory ◽  
Functionally Graded ◽  
Classical Solutions ◽  
Transverse Shear Deformation ◽  
Axisymmetric Vibration ◽  
Circular Plates ◽  
Third Order ◽  
Classical Plate Theory ◽  
Graded Material

Based on the mathematical similarity of the eigenvalue problem of the Reddy’s third-order plate theory (RPT) and the classical plate theory (CPT), relationships between the solutions of axisymmetric vibration or buckling of functionally graded material (FGM) circular plates based on RPT and those of isotropic homogeneous circular plates based on CPT are presented, from which one can easily obtain the RPT solutions of axisymmetric vibration or buckling of FGM circular plates expressed in terms of the well-known CPT solutions of isotropic circular plates without much tedious mathematics. Effects of rotary inertia are not considered in the present analysis. The relationships obtained from the present analysis may be used to check the validity, convergence and accuracy of numerical results of FGM plates based on RPT, and also show clearly the intrinsic features of the effect of transverse shear deformation on the classical solutions.

scholarly journals Multiparametric Analytical Solution for the Eigenvalue Problem of FGM Porous Circular Plates

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 429 ◽  
Author(s):  
Krzysztof Żur ◽  
Piotr Jankowski
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Special Functions ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Circular Plates ◽  
Classical Plate Theory ◽  
Coupled Equations

Free vibration analysis of the porous functionally graded circular plates has been presented on the basis of classical plate theory. The three defined coupled equations of motion of the porous functionally graded circular/annular plate were decoupled to one differential equation of free transverse vibrations of plate. The one universal general solution was obtained as a linear combination of the multiparametric special functions for the functionally graded circular and annular plates with even and uneven porosity distributions. The multiparametric frequency equations of functionally graded porous circular plate with diverse boundary conditions were obtained in the exact closed-form. The influences of the even and uneven distributions of porosity, power-law index, diverse boundary conditions and the neglected effect of the coupling in-plane and transverse displacements on the dimensionless frequencies of the circular plate were comprehensively studied for the first time. The formulated boundary value problem, the exact method of solution and the numerical results for the perfect and imperfect functionally graded circular plates have not yet been reported.

Free vibration analysis of imperfect functionally graded sandwich plates: analytical and experimental investigation

2021 ◽  
Vol 111 (2) ◽  
pp. 49-65
Author(s):  
E.K. Njim ◽  
S.H. Bakhy ◽  
M. Al-Waily
Keyword(s):  
Free Vibration ◽  
Power Law ◽  
Vibration Analysis ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Slenderness Ratio ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Classical Plate Theory

Purpose: This paper develops a new analytical solution to conduct the free vibration analysis of porous functionally graded (FG) sandwich plates based on classical plate theory (CPT). The sandwich plate made of the FGM core consists of one porous metal that had not previously been taken into account in vibration analysis and two homogenous skins. Design/methodology/approach: The analytical formulations were generated based on the classical plate theory (CPT). According to the power law, the material properties of FG plates are expected to vary along the thickness direction of the constituents. Findings: The results show that the porosity parameter and the power gradient parameter significantly influence vibration characteristics. It is found that there is an acceptable error between the analytical and numerical solutions with a maximum discrepancy of 0.576 % at a slenderness ratio (a/h =100), while the maximum error percentage between the analytical and experimental results was found not exceeding 15%. Research limitations/implications: The accuracy of analytical solutions is verified by the adaptive finite elements method (FEM) with commercial ANSYS 2020 R2 software. Practical implications: Free vibration experiments on 3D-printed FGM plates bonded with two thin solid face sheets at the top and bottom surfaces were conducted. Originality/value: The novel sandwich plate consists of one porous polymer core and two homogenous skins which can be widely applied in various fields of aircraft structures, biomedical engineering, and defense technology. This paper presents an analytical and experimental study to investigate the free vibration problem of a functionally graded simply supported rectangular sandwich plate with porosities. The objective of the current work is to examine the effects of some key parameters, such as porous ratio, power-law index, and slenderness ratio, on the natural frequencies and damping characteristics.

scholarly journals Exact Analytical Solution for Free Axisymmetric and Non-Axisymmetric Vibrations of FGM Porous Circular Plates

2018 ◽  
Author(s):  
Krzysztof Kamil Żur ◽  
Piotr Jankowski
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Special Functions ◽  
Plate Theory ◽  
Exact Analytical Solution ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Circular Plates ◽  
Classical Plate Theory ◽  
Coupled Equations

Free vibration analysis of the porous functionally graded circular plates has been presented on the basis of classical plate theory. The three defined coupled equations of motion of the porous functionally graded circular/annular plate were decoupled to one differential equation of free transverse vibrations of plate. The one universal general solution was obtained as linear combination of the multiparametric special functions for the functionally graded circular and annular plates with even and uneven porosity distributions. The multiparametric frequency equations of functionally graded porous circular plate with diverse boundary conditions were obtained in the exact closed-form. The influences of the even and uneven distributions of porosity, power-law index, diverse boundary conditions and the negligibled effect of the coupling in-plane and transverse displacements on the dimensionless frequencies of the circular plate were comprehensively studied for the first time. The formulated boundary value problem, the exact method of solution and the numerical results for the perfect and imperfect functionally graded circular plates have not yet been reported.

scholarly journals Static Analysis of Functionally Graded Plate Using Nonlinear Classical Plate Theory with Von-Karman Strains

2018 ◽  
Vol 23 (3) ◽  
pp. 707-726 ◽  
Author(s):  
S.J. Singh ◽  
S.P. Harsha
Keyword(s):  
Plate Theory ◽  
Functionally Graded ◽  
Complex Nature ◽  
Thickness Direction ◽  
Complex Solution ◽  
Functionally Graded Plate ◽  
Classical Plate Theory ◽  
Bending Analysis ◽  
Von Karman ◽  
Non Linear

Abstract The present study is based on the nonlinear bending analysis of an FGM plate with Von-Karman strain based on the non-linear classical plate theory (NLCPT) with in-plane displacement and moderate rotation. Non-linear bending analysis based on stresses and transverse deflections is then carried out for the plate for the complex solution obtained using an analytical method viz. Navier’s method. The equations of motion and boundary conditions are obtained using the Principle of Minimum Potential Energy (PMPE) method and material property is graded in thickness direction according to simple power-law distribution in terms of volume fractions of the constituents. The effect of the span-to-thickness ratio and FGM exponent on the maximum central deflection and stresses are studied. The results show that the response is transitional with respect to ceramic and metal and the complex solution predicts the real behavior of stresses and deflections in the functionally graded plate. The functionally graded plate is found to be more effective for moderately thick and thick plates, which is inferred by a complex nature of the solution. For FGM plates, the transverse deflection is in-between to that of metal and ceramic rich plates. The complex nature of the solution also gives information about the stress distribution in the thickness direction.

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 Free Vibration Analysis of a Thermally Loaded Porous Functionally Graded Rotor–Bearing System

2020 ◽  
Vol 10 (22) ◽  
pp. 8197
Author(s):  
Prabhakar Sathujoda ◽  
Aneesh Batchu ◽  
Bharath Obalareddy ◽  
Giacomo Canale ◽  
Angelo Maligno ◽  
...  
Keyword(s):  
Temperature Distribution ◽  
Power Law ◽  
Inner Core ◽  
Volume Fraction ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Linear Temperature ◽  
Volume Fractions ◽  
Rotor Bearing ◽  
Bearing System

The present work deals with natural and whirl frequency analysis of a porous functionally graded (FG) rotor–bearing system using the finite element method (FEM). Stiffness, mass and gyroscopic matrices are derived for porous and non-porous FG shafts by developing a novel two-noded porous FG shaft element using Timoshenko beam theory (TBT), considering the effects of translational inertia, rotatory inertia, gyroscopic moments and shear deformation. A functionally graded shaft whose inner core is comprised of stainless steel (SS) and an outer layer made of ceramic (ZrO2) is considered. The effects of porosity on the volume fractions and the material properties are modelled using a porosity index. The non-linear temperature distribution (NLTD) method based on the Fourier law of heat conduction is used for the temperature distribution in the radial direction. The natural and whirl frequencies of the porous and non-porous FG rotor systems have been computed for different power law indices, volume fractions of porosity and thermal gradients to investigate the influence of porosity on fundamental frequencies. It has been found that the power law index, volume fraction of porosity and thermal gradient have a significant influence on the natural and whirl frequencies of the FG rotor–bearing system.

Superharmonic and Subharmonic Resonances of Spiral Stiffened Functionally Graded Cylindrical Shells under Harmonic Excitation

2019 ◽  
Vol 19 (10) ◽  
pp. 1950114 ◽  
Author(s):  
Habib Ahmadi ◽  
Kamran Foroutan
Keyword(s):  
Multiple Scales ◽  
Plate Theory ◽  
Cylindrical Shells ◽  
Harmonic Excitation ◽  
Functionally Graded ◽  
Classical Plate Theory ◽  
Geometrical Properties ◽  
Hardening Nonlinearity ◽  
Subharmonic Resonances ◽  
Theory Of Shells

This paper presents the superharmonic and subharmonic resonances of spiral stiffened functionally graded (SSFG) cylindrical shells under harmonic excitation. The stiffeners are considered to be externally or internally added to the shell. Also, it is assumed that the material properties of the stiffeners are continuously graded in the thickness direction. In order to model the stiffeners, the smeared stiffener technique is used. Within the context of the classical plate theory of shells, the von Kármán nonlinear equations are derived for the shell and stiffeners based on Hooke’s law and the relations of stress-strain. Using Galerkin’s method, the equation of motion is discretized. The superharmonic and subharmonic resonances are analyzed by the method of multiple scales. The influence of the material parameters and various geometrical properties on the superharmonic and subharmonic resonances of SSFG cylindrical shells is investigated. Considering these results, the hardening nonlinearity behavior and jump value of cylindrical shell is less and more than others, when the angle of stiffeners is [Formula: see text] and [Formula: see text], respectively.

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