Supersonic Flutter of Functionally Graded Plates in a Thermal Environment

2006 ◽  
Author(s):  
H. M. Navazi ◽  
H. Haddadpour
Keyword(s):  
Differential Equations ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Equations Of Motion ◽  
Time Integration ◽  
Analytical Investigation ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Numerical Time Integration ◽  
Flutter Margin

In this paper, an analytical investigation intended to determine the flutter margin of supersonic functionally graded panels is carried out. For this purpose, piston theory aerodynamics has been employed to model quasi-steady aerodynamic loading. The material properties of the plate are assumed to be graded continuously across the panel thickness. The variation of temperature-dependent thermoelastic properties follows a simple power-law distribution in terms of the volume fraction of the constituent materials. The effects of compressive in-plane loads and static pressure differential are studied. Both uniform and through the thickness nonlinear temperature distributions are also considered. Hamilton’s principle is used to determine the coupled partial differential equations of motion. Using Galerkin’s method, the derived equations are transformed into a set of coupled ordinary differential equations, and then solved by numerical time integration. Some examples comparing the flutter margin of FG panels with that of plates made of pure metals and pure ceramics are presented. The results of the present study are compared with those of the previous works, where finite element method was used. It is shown that the use of functionally graded materials can yield an increase or decrease of the aeroelastic stability in the supersonic flow for different regions.

Nonlinear vibrations of fluid-filled functionally graded cylindrical shell considering a time-dependent lateral load and static preload

2015 ◽  
Vol 230 (1) ◽  
pp. 102-119 ◽  
Author(s):  
Frederico Martins Alves da Silva ◽  
Roger Otávio Pires Montes ◽  
Paulo Batista Gonçalves ◽  
Zenón José Guzmán Nuñez Del Prado
Keyword(s):  
Cylindrical Shell ◽  
Shell Thickness ◽  
Nonlinear Vibrations ◽  
Volume Fraction ◽  
Perturbation Technique ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Time Dependent ◽  
Nonlinear Frequency ◽  
Power Law Distribution

In the recent years, functionally gradient materials (FGMs) have gained considerable attention with possible applications in several engineering fields, especially in a high-temperature or hazardous environment. In this work, the nonlinear vibrations of a simply supported fluid-filled functionally graded cylindrical shell subjected to a lateral time-dependent load and axial static preload are analyzed. To model the shell, the Donnell nonlinear shell theory is used. The fluid is assumed to be incompressible, nonviscous, and irrotational. A new function to describe the variation in the volume fraction of the constituent material through the shell thickness is proposed, extending the concept of sandwich structures to a functionally graded material. Material properties are graded along the shell thickness according to the proposed volume fraction power law distribution. A consistent reduced order model derived from a perturbation technique is used to describe the displacements of the shell and, the Galerkin method is applied to derive a set of coupled nonlinear ordinary differential equations of motion. Results show the influence of the variation of the two constituent materials along the shell thickness, internal fluid, static preload, and shell geometry on the natural frequencies, nonlinear frequency–amplitude relation, resonance curves, and bifurcation scenario of the FG cylindrical shell.

Effect of In-Plane Load and Thermal Environment on Buckling and Vibration Behavior of Two-Dimensional Functionally Graded Tapered Timoshenko Nanobeam

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Roshan Lal ◽  
Chinika Dangi
Keyword(s):  
Thermal Environment ◽  
Slenderness Ratio ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Functionally Graded ◽  
Two Dimensional ◽  
Power Law Distribution ◽  
Energy Principle

Abstract In this work, buckling and vibration characteristics of two-dimensional functionally graded (FG) nanobeam of nonuniform thickness subjected to in-plane and thermal loads have been analyzed within the frame work of Timoshenko beam theory. The beam is tapered by linear variation in thickness along the length. The temperature-dependent material properties of the beam are varying along thickness and length as per a power-law distribution and exponential function, respectively. The analysis has been presented using Eringen’s nonlocal theory to incorporate the size effect. Hamilton’s energy principle has been used to formulate the governing equations of motion. These resulting equations have been solved via generalized differential quadrature method (GDQM) for three combinations of clamped and simply supported boundary conditions. The effect of in-plane load together with temperature variation, nonuniformity parameter, gradient indices, nonlocal parameter, and slenderness ratio on the natural frequencies is illustrated for the first three modes of vibration. The critical buckling loads in compression have been computed by putting the frequencies equal to zero. A significant contribution of in-plane load on mechanical behavior of two-directional functionally graded nanobeam with nonuniform cross section has been noticed. Results are in good accordance.

Free Vibration Analysis of Functionally Graded Beams Resting on Elastic Foundation in Thermal Environment

2016 ◽  
Vol 16 (07) ◽  
pp. 1550029 ◽  
Author(s):  
P. Zahedinejad
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Differential Quadrature Method ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Various Boundary Conditions

The free vibration of functionally graded (FG) beams with various boundary conditions resting on a two-parameter elastic foundation in the thermal environment is studied using the third-order shear deformation beam theory. The material properties are temperature-dependent and vary continuously through the thickness direction of the beam, based on a power-law distribution in terms of the volume fraction of the material constituents. In order to discretize the governing equations, the differential quadrature method (DQM) in conjunction with the Hamilton’s principle is adopted. The convergence of the method is demonstrated. In order to validate the results, comparisons are made with solutions available for the isotropic and FG beams. Through a comprehensive parametric study, the effect of various parameters involved on the FG beam was studied. It is concluded that the uniform temperature rise has more significant effect on the frequency parameters than the nonuniform case.

An Analytical Solution for Nonlinear Vibrations Analysis of Functionally Graded Plate Using Modified Lindstedt–Poincare Method

2020 ◽  
Vol 12 (01) ◽  
pp. 2050003 ◽  
Author(s):  
S. Hashemi ◽  
A. A. Jafari
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Rectangular Plate ◽  
Volume Fraction ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Published Data ◽  
Power Law Distribution ◽  
Partial Differential

In this research, the nonlinear free vibrations analysis of functionally graded (FG) rectangular plate which simply supported all edges are investigated analytically using modified Lindstedt–Poincare (MLP) method for the first time. For this purpose, with the aid of von Karman nonlinearity strain-displacement relations, the partial differential equations of motion are developed based on first-order shear deformation theory (FSDT). Afterward, by applying Galerkin method, the nonlinear partial differential equations are transformed into the time-dependent nonlinear ordinary differential equations. The nonlinear equation of motion is then solved analytically by MLP method to determine the nonlinear frequencies of the FG rectangular plate. The material properties are assumed to be graded through the direction of plate thickness according to power law distribution. The effects of some system parameters such as vibration amplitude, volume fraction index and aspect ratio on the nonlinear to linear frequency ratio are discussed in detail. To validate the analysis, the results of this paper are compared with both the published data and numerical method, and good agreements are found.

Nonlinear Dynamics of FGM Conical Panel With Initial Imperfection in Thermal Environment

2017 ◽  
Author(s):  
Ming Hui Yao ◽  
Yan Niu ◽  
Wei Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Thermal Environment ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Initial Imperfection ◽  
Harmonic Excitation ◽  
Functionally Graded ◽  
Phase Portraits ◽  
Power Law Distribution ◽  
Geometric Imperfection

In this paper, the nonlinear dynamics of a simply supported functionally graded materials (FGM) conical panel with different forms of initial imperfections is investigated. The conical panel is subjected to the simple harmonic excitation along the radial direction and the parametric excitation in the meridian direction. The small initial geometric imperfection of the conical panel is expressed by the form of the Cosine functions. According to a power-law distribution, the effective material properties are assumed to be graded along the thickness direction. Based on the first-order shear deformation theory and von Karman type nonlinear geometric relationship, the nonlinear equations of motion are established by using the Hamilton principle. The nonlinear partial differential governing equations are truncated by Galerkin’s method to obtain the ordinary differential equations along the radial displacement. The effects of imperfection types, half-wave numbers and amplitudes on the dynamic behaviors are studied by numerical simulation. Maximum Lyapunov exponents, bifurcation diagrams, time histories and phase portraits are obtained to show the dynamic response.

THERMOMECHANICAL STABILITY ANALYSIS OF FUNCTIONALLY GRADED THIN-WALLED CANTILEVER PIPE WITH FLOWING FLUID SUBJECTED TO AXIAL LOAD

2011 ◽  
Vol 11 (03) ◽  
pp. 513-534 ◽  
Author(s):  
M. HOSSEINI ◽  
S. A. FAZELZADEH
Keyword(s):  
Differential Equations ◽  
Axial Force ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Stability Boundary ◽  
Functionally Graded ◽  
Flowing Fluid ◽  
Thin Walled ◽  
The Stability ◽  
Compressive Axial Force

In this study, the thermomechanical stability of functionally graded thin-walled cantilever pipes conveying flow and loading by compressive axial force is investigated. The governing equations of motion and boundary conditions are derived via the Hamilton's variational principle. The thin-walled structure is formulated based on Rayleigh's theory. Moreover, quasi-steady flow pressure loadings and steady surface temperature are considered and the temperature gradient through the wall thickness of the pipe is included. The partial differential equations of the pipe are transformed into a set of ordinary differential equations using the extended Galerkin method. Finally, having solved the resulting thermal-structural-fluid eigenvalue system of equations, the effects of the compressive axial force, fluid speed, fluid mass ratio, volume fraction index of functionally graded materials (FGMs), and temperature change through the thickness of the pipe on the stability boundary are investigated. Numerical comparisons are also performed with the available data in the literature and good agreement is observed.

Free Vibration Analysis of Functionally Graded Skew Plate in Thermal Environment Using Higher Order Theory

2018 ◽  
Vol 10 (01) ◽  
pp. 1850007 ◽  
Author(s):  
Smita Parida ◽  
Sukesh Chandra Mohanty
Keyword(s):  
Free Vibration ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Higher Order ◽  
Functionally Graded ◽  
Transverse Shear Strain ◽  
Power Law Distribution ◽  
Skew Angle

This paper deals with the free vibration of a skew functionally graded material (FGM) plate in the thermal environment. A higher-order shear deformation theory (HOSDT) is employed to develop a finite element model of the plate. The material properties are assumed to be temperature-dependent and are graded along the thickness direction as per simple power law distribution in terms of volume fraction of metal and ceramic constituent phases. The model is based on an eight-noded isoparametric element with seven degrees of freedom (DOFs) per node. The general displacement equation provides C[Formula: see text] continuity. The transverse shear strain undergoes parabolic variation through the thickness of the plate. The governing equations are derived using the Hamilton’s principle. The obtained results are compared with the published results to determine the accuracy of the method. The effects of various parameters like aspect ratio, side-thickness ratio, volume fraction index, boundary conditions and skew angle on the natural frequencies are investigated.

TSDT theory for free vibration of functionally graded plates with various material properties

2021 ◽  
Vol 8 (4) ◽  
pp. 691-704
Author(s):  
M. Janane Allah ◽  
◽  
Y. Belaasilia ◽  
A. Timesli ◽  
A. El Haouzi ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Implicit Algorithm ◽  
Proposed Model ◽  
Graded Material ◽  
Composite Modeling

In this work, an implicit algorithm is used for analyzing the free dynamic behavior of Functionally Graded Material (FGM) plates. The Third order Shear Deformation Theory (TSDT) is used to develop the proposed model. In this contribution, the formulation is written without any homogenization technique as the rule of mixture. The Hamilton principle is used to establish the resulting equations of motion. For spatial discretization based on Finite Element Method (FEM), a quadratic element with four and eight nodes is adopted using seven degrees of freedom per node. An implicit algorithm is used for solving the obtained problem. To study the accuracy and the performance of the proposed approach, we present comparisons with literature and laminate composite modeling results for vibration natural frequencies. Otherwise, we examine the influence of the exponent of the volume fraction which reacts the plates "P-FGM" and "S-FGM". In addition, we study the influence of the thickness on "E-FGM" plates.

Effect of Temperature Gradient on the Mechanical Buckling Resistance of FGM Shallow Arches

2014 ◽  
Author(s):  
M. Bateni ◽  
M. R. Eslami
Keyword(s):  
Temperature Gradient ◽  
Thermal Environment ◽  
Mechanical Load ◽  
Functionally Graded ◽  
Effect Of Temperature ◽  
Power Law Distribution ◽  
Concentrated Load ◽  
Shallow Arches ◽  
Buckling Resistance ◽  
Graded Material

This work presents a closed form investigation on the effect of temperature gradient on the buckling resistance of functionally graded material (FGM) shallow arches. The constituents are assumed to vary smoothly through the thickness of the arch according to the power law distribution and they are assumed to be temperature dependent. The arches subjected to the both uniform distributed radial load and central concentrated load and both boundary supports are supposed to be pinned. The temperature field is approximated by one-dimensional linear gradient through the thickness of the arch and the displacement field approximated by classical arches model. Also, Donnell type kinematics is utilized to extract the suitable strain-displacement relations for shallow arches. Adjacent equilibrium criterion is used to buckling analysis, and, critical bifurcation load is obtain in the complete presence of pre-buckling deformations. Results discloses the usefulness of using the FGM shallow arches in thermal environment because the temperature gradient enhances the buckling resistance of these structures when they are subjected to a lateral mechanical load.

scholarly journals Weight optimisation of functionally graded beams using modified differential evolution

2019 ◽  
Vol 13 (2) ◽  
pp. 48-63 ◽  
Author(s):  
Pham Hoang Anh ◽  
Tran Thuy Duong
Keyword(s):  
Differential Evolution ◽  
Volume Fraction ◽  
Lightweight Design ◽  
Shear Deformation Theory ◽  
Numerical Approach ◽  
Functionally Graded ◽  
Parameter Distribution ◽  
Power Law Distribution ◽  
De Algorithm ◽  
Fgm Beam

In this article, an efficient numerical approach for weight optimisation of functionally graded (FG) beams in the presence of frequency constraints is presented. For the analysis purpose, a finite element (FE) solution based on the first order shear deformation theory (FSDT) is established to analyse the free vibration behaviour of FG beams. A four-parameter power law distribution and a five-parameter trigonometric distribution are used to describe the volume fraction of material constituents in the thickness direction. The goal is to tailor the thickness and material distribution for minimising the weight of FG beams while constraining the fundamental frequency to be greater than a prescribed value. The constrained optimisation problem is effectively solved by a novel differential evolution (DE) algorithm. The validity and efficiency of the proposed approach is demonstrated through two numerical examples corresponding to the four-parameter distribution and the five-parameter distribution.Keywords: FGM beam; lightweight design; frequency constraint; differential evolution.

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