scholarly journals Dynamic stability of functionally graded plate under in-plane compression

2005 ◽  
Vol 2005 (4) ◽  
pp. 411-424 ◽  
Author(s):  
Andrzej Tylikowski
Keyword(s):  
Asymptotic Stability ◽  
Power Law ◽  
Volume Fraction ◽  
Direct Method ◽  
Functionally Graded ◽  
Time Dependent ◽  
Power Law Distribution ◽  
Graded Materials ◽  
Plane State ◽  
The Stability

Functionally graded materials have gained considerable attention in the high-temperature applications. A study of parametric vibrations of functionally graded plates subjected to in-plane time-dependent forces is presented. Moderately large deflection equations taking into account a coupling of in-plane and transverse motions are used. Material properties are graded in the thickness direction of the plate according to volume fraction power law distribution. An oscillating temperature causes generation of in-plane time-dependent forces destabilizing the plane state of the plate equilibrium. The asymptotic stability and almost-sure asymptotic stability criteria involving a damping coefficient and loading parameters are derived using Liapunov's direct method. Effects of power law exponent on the stability domains are studied.

Vibrational behavior of beams made of functionally graded materials by using a mixed formulation

2020 ◽  
Vol 234 (18) ◽  
pp. 3650-3666 ◽  
Author(s):  
Souhir Zghal ◽  
Fakhreddine Dammak
Keyword(s):  
Functionally Graded Materials ◽  
Power Law ◽  
Transverse Shear ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Mixed Formulation ◽  
Shear Stresses ◽  
Power Law Distribution ◽  
Graded Materials ◽  
Vibrational Behavior

This paper investigates the vibrational behavior of beams made of functionally graded materials using a mixed formulation. Unlike the other high order shear deformation theories (HSDTs), the proposed formulation is elaborated within a double field of displacements and stresses which offers the possibility of the development of low order linear elements with enhanced accuracy. As well as, the effect of the transverse shear strains and the zero condition of the transverse shear stresses on the top and bottom surfaces are verified. The material characteristics of the beams are described via a power law distribution in order to take into account the continuous variation of the volume fraction of its constituents along the thickness direction. Numerical simulations are conducted to show the influence of power law index, slenderness ratios, and boundary conditions on natural frequencies of functionally graded beams. Results demonstrate the efficiency and the applicability of the model based on a refined mixed formulation and its ability to predict the vibrational behavior of functionally graded beams with good accuracy.

Deformation Modeling of an FGM Plate under External Force

2012 ◽  
Vol 622-623 ◽  
pp. 246-253
Author(s):  
A.R. Mortazavi Moghaddam ◽  
M.T. Ahmadian ◽  
M. Sarkeshi ◽  
A. Kheradpisheh
Keyword(s):  
Material Property ◽  
Power Law ◽  
Volume Fraction ◽  
Infinite Plate ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Graded Materials ◽  
Plate Deformation ◽  
Deformation Response ◽  
Number Of Layers

Deformation modeling of an infinite plate of functionally graded materials (FGMs) loaded by normal force to the plate surface is studied. The material properties of FGM plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The governing equations are based on stress-strain relation and the equilibrium force equation. Keeping generality, FGM plate has been assumed as a multilayer with linear material property in each layer while arbitrary exponential material property through the thickness. A plate made of Aluminum and Alumina is considered as an example to illustrate the effects of the volume fraction exponent and number of layers on the plate deformation response. Effects of number of layers on the accuracy of the plate behavior under external load are examined. Results indicate that at every certain power-law (M), there exist a number of layers beyond which no variation can be detected on the plate deformation response.

scholarly journals Vibration and Buckling Analysis of Cylindrical Shells Made of Functionally Graded Materials under Combined Static and Periodic Axial Forces

2010 ◽  
Vol 19 (2) ◽  
pp. 096369351001900 ◽  
Author(s):  
F. Ebrahimi ◽  
H.A. Sepiani
Keyword(s):  
Transverse Shear ◽  
Volume Fraction ◽  
Cylindrical Shells ◽  
Shear Deformation Theory ◽  
Deformation Mode ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Graded Materials ◽  
Axial Forces ◽  
Graded Material

In this study, a formulation for the free vibration and buckling of cylindrical shells made of functionally graded material (FGM) subjected to combined static and periodic axial loadings are presented. The properties are temperature dependent and graded in the thickness direction according to a volume fraction power law distribution. The analysis is based on two different methods of first-order shear deformation theory (FSDT) considering the transverse shear strains and the rotary inertias and the classical shell theory (CST). The results obtained show that the effect of transverse shear and rotary inertias on vibration and buckling of functionally graded cylindrical shells is dependent on the material composition, the temperature environment, the amplitude of static load, the deformation mode, and the shell geometry parameters.

BI-STABLE ANALYSES OF LAMINATED FGM SHELLS

2012 ◽  
Vol 12 (02) ◽  
pp. 311-335 ◽  
Author(s):  
X. Q. HE ◽  
L. LI ◽  
S. KITIPORNCHAI ◽  
C. M. WANG ◽  
H. P. ZHU
Keyword(s):  
Power Law ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Optimum Combination ◽  
Thickness Direction ◽  
Power Law Distribution ◽  
Deployable Structures ◽  
Graded Material ◽  
Two Parameter

Based on an inextensional two-parameter analytical model for cylindrical shells, bi-stable analyses were carried out on laminated functionally graded material (FGM) shells with various layups of fibers. Properties of FGM shells are functionally graded in the thickness direction according to a volume fraction power law distribution. The effects of constituent volume fractions of FGM matrix are examined on the curvature and twist of laminated FGM shells. The results reveal that the optimum combination of constituents of FGM matrix can be obtained for the maximum twist of FGM shells with antisymmetric layups, which helps the design of deployable structures. The effects of Young's modulus of fibers and the symmetry of layups on bi-stable behaviors are also discussed in detail.

Characteristics of Power Law and Sigmoid FGMs Models in Thermal Effect

2016 ◽  
Vol 829 ◽  
pp. 90-94
Author(s):  
Seok Hyeon Kang ◽  
Ji Hwan Kim
Keyword(s):  
Power Law ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Temperature Dependent ◽  
Graded Materials ◽  
Virtual Work Principle ◽  
Temperature Dependent Properties

In thermal environment, vibration behavior of Functionally Graded Materials (FGMs) plates is investigated, and the materials are developed with mixing ceramic and metal. Present study is based on the first-order shear deformation theory of plate. Then, mixture methods such as Power law (P-) and Sigmoid (S-) models are chosen. According to a volume fraction, the material properties are assumed to vary continuously through the thickness direction and to be temperature dependent properties. Further, thermal effects are considered as uniform temperature rise and one dimensional heat transfer. For the structure analysis, FEM is used to obtain the natural frequencies based on the virtual work principle.

scholarly journals Nonlinear postbuckling of eccentrically stiffened functionally graded plates and shallow shells

2011 ◽  
Vol 33 (3) ◽  
pp. 131-147 ◽  
Author(s):  
Dao Huy Bich ◽  
Vu Hoai Nam ◽  
Nguyen Thi Phuong
Keyword(s):  
Volume Fraction ◽  
Geometrical Nonlinearity ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Power Law Distribution ◽  
Governing Equations ◽  
Shallow Shells ◽  
The Stability ◽  
The Galerkin Method ◽  
Rich Side

The paper deals with the formulation of governing equations of eccentrically stiffened functionally graded plates and shallow shells based upon the classical shell theory and the smeared stiffeners technique taking into account geometrical nonlinearity in Von Karman-Donnell sense. Material properties are assumed to be temperature-independent and graded in the thickness direction according to a simple power law distribution in terms of the volume fraction of constituents. The shells are reinforced by eccentrically longitudinal and transversal stiffeners made of full metal or full ceramic depending on situation of stiffeners at metal-rich side or ceramic-rich side of the shell respectively. Obtained governing equations can be used in research on nonlinear postbuckling of mentioned above structures. By use of the Galerkin method an approximated analytical solution to the nonlinear stability problem of reinforced FGM plates and shallow shells is performed. The postbuckling load-deflection curves of the shells are investigated and analytical expressions of the upper and lower buckling loads are presented. A comparison of the effectiveness of stiffeners in enhancing the stability of FGM plates and shallow shells is given.

Three-Dimensional Flexure of Rectangular Plates Made of Functionally Graded Materials

2005 ◽  
Vol 72 (5) ◽  
pp. 788-791 ◽  
Author(s):  
Isaac Elishakoff ◽  
Cristina Gentilini
Keyword(s):  
Functionally Graded Materials ◽  
Power Law ◽  
Minimum Energy ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Power Law Distribution ◽  
Dimensional Solution ◽  
Energy Principle ◽  
Graded Materials

A three-dimensional solution for the problem of transversely loaded, all-round clamped rectangular plates of arbitrary thickness is presented within the linear, small deformation theory of elasticity. The Ritz minimum energy principle is employed to derive the governing equation of the plate made of functionally graded materials. In theory, if we employ an infinite number of terms in the displacement series, the exact solution can be determined. However, a practical limit always exists due to numerical implementation. The solution has a validity comparable to some higher order theories. A power-law distribution for the mechanical characteristics is adopted to model the continuous variation of properties from those of one component to those of the other. The displacements and stresses of the plate for different values of the power-law exponent are investigated.

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.

scholarly journals Mechanical Property Variation of a Rotating Cantilever FGSW Beam under Parametric Excitation

2019 ◽  
Vol 8 (11) ◽  
pp. 495-499
Keyword(s):  
Shear Modulus ◽  
Power Law ◽  
Parametric Excitation ◽  
Excitation Power ◽  
Functionally Graded ◽  
Timoshenko Beams ◽  
Power Law Distribution ◽  
Property Variation ◽  
Graded Material ◽  
The Stability

We report here the dynamic stability of functionally graded sandwich (FGSW) rotating cantilever Timoshenko beams under parametric excitation. Power law with various indices as well as exponential law were used to find out the properties along the thickness of the FGSW beam. The stability boundaries were established using Floquet’s theory. The equation of motion was governed by Hamilton’s principle and solved by Finite element method. The power index was optimized for uniform variation of shear modulus along the thickness of FGSW beam.The shear modulus variation along the thickness of the FGSW beam was compared both by power law and exponential law.It has been confirmed that the Exponential distribution of constituent phases renders better stability compared to power law distribution of the phases in the functionally graded material(FGM).

Effect of Functionally Graded Materials on Resonances of Bending Shafts Under Time-Dependent Axial Loading

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Arnaldo J. Mazzei ◽  
Richard A. Scott
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Functionally Graded Materials ◽  
Parametric Resonance ◽  
Axial Load ◽  
Volume Fraction ◽  
Axial Loading ◽  
Functionally Graded ◽  
Time Dependent ◽  
Graded Materials

The effect of functionally graded materials (FGMs) on resonances of bending shafts under time-dependent axial loading is investigated. The axial load is taken to be a sinusoidal function of time and the shaft is modeled via an Euler–Bernoulli beam approach (pin-pin boundary conditions). The axial load enters the formulation via a “buckling load type” approach. For generality, two distinct particulate models for the FGM are considered, namely, one involving power law variations and another based on a volume fraction approach, for both Young’s modulus and material density. The spatial dependence in the partial differential equation of motion is suppressed by utilizing Galerkin’s method with homogeneous beam mode shapes. To check the accuracy of this approximation, numerical solutions for the boundary value problem represented by the original partial differential equation are obtained using MAPLE®’s PDE solver. Good agreement (within 5%) was found between the PDE results and the one-mode approximation. The approximation leads to ordinary differential equations that have time-dependent coefficients and are prone to parametric and forced motions instabilities. Hill’s infinite determinant approach is used to study stability. The main focus is on the primary parametric resonance. It was found that in most cases the FGM shafts increase the parametric resonance frequencies substantially, while decreasing the zone thicknesses, both desirable trends. For instance, for an axial load about one-third of the buckling value, an aluminum/silicon carbide shaft, when compared to a pure aluminum shaft, increases the primary parametric resonance by 21% and decreases instabilities by 23%. For one model of FGM, the sensitivity of the results to volume fraction variations is examined and it was found that increasing the volume fraction is not uniformly beneficial. Results for other parametric zones are also presented. Forced resonances are also briefly treated.

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