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1.
The dynamic von Karman equations are used for nonlinear analysis of a thin circular plate made of a functionally graded material.
The thickness of the plate is constant and the properties of the functionally graded material depend on temperature and vary
throughout the thickness. It is assumed that the plate oscillates with large amplitudes. The forces and moments in the plate
are determined in solving the equations for harmonic vibrations. Relevant results are obtained in the case of stead-state
free vibrations. These results indicate that the volume fraction has a strong effect on the forces, moments, and material
properties
Published in Prikladnaya Mekhanika, Vol. 44, No. 6, pp. 134–144, June 2008.
An erratum to this article can be found at 相似文献
2.
《International Journal of Solids and Structures》2005,42(23):6101-6121
A postbuckling analysis is presented for a simply supported, shear deformable functionally graded plate with piezoelectric actuators subjected to the combined action of mechanical, electrical and thermal loads. The temperature field considered is assumed to be of uniform distribution over the plate surface and through the plate thickness and the electric field considered only has non-zero-valued component EZ. The material properties of functionally graded materials (FGMs) 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, and the material properties of both FGM and piezoelectric layers are assumed to be temperature-dependent. The governing equations are based on a higher order shear deformation plate theory that includes thermo-piezoelectric effects. The initial geometric imperfection of the plate is taken into account. Two cases of the in-plane boundary conditions are considered. A two step perturbation technique is employed to determine buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, geometrically mid-plane symmetric FGM plates with fully covered or embedded piezoelectric actuators under different sets of thermal and electric loading conditions. The effects played by temperature rise, volume fraction distribution, applied voltage, the character of in-plane boundary conditions, as well as initial geometric imperfections are studied. 相似文献
3.
Niels Olhoff 《International Journal of Solids and Structures》1974,10(1):93-109
The thickness function of a simply supported rectangular plate is determined such that the fundamental natural frequency of transverse vibrations attains an optimum value. The volume of the solid plate, its size, and data pertaining to its material properties, are assumed to be given.The problem consists of determining the deflection function corresponding to the optimal plate thickness function from a non-linear, fourth order partial differential eigenvalue problem, derived by variational analysis.Second and higher order normal derivatives of the deflection function are singular along the boundary of the domain. This behaviour is investigated analytically, and taken into account in a finite difference formulation of the problem, which is solved numerically by successive iterations. 相似文献
4.
This paper presents an investigation on the nonlinear dynamic response of carbon nanotube-reinforced composite (CNTRC) plates resting on elastic foundations in thermal environments. Two configurations, i.e., single-layer CNTRC plate and three-layer plate that is composed of a homogeneous core layer and two CNTRC surface sheets, are considered. The single-walled carbon nanotube (SWCNT) reinforcement is either uniformly distributed (UD) or functionally graded (FG) in the thickness direction. The material properties of FG-CNTRC plates are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The motion equations are based on a higher-order shear deformation theory with a von Kármán-type of kinematic nonlinearity. The thermal effects are also included and the material properties of CNTRCs are assumed to be temperature-dependent. The equations of motion that includes plate-foundation interaction are solved by a two-step perturbation technique. Two cases of the in-plane boundary conditions are considered. Initial stresses caused by thermal loads or in-plane edge loads are introduced. The effects of material property gradient, the volume fraction distribution, the foundation stiffness, the temperature change, the initial stress, and the core-to-face sheet thickness ratio on the dynamic response of CNTRC plates are discussed in detail through a parametric study. 相似文献
5.
《International Journal of Solids and Structures》2005,42(18-19):5224-5242
A two-dimensional solution is presented for bending analysis of simply supported functionally graded ceramic–metal sandwich plates. The sandwich plate faces are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity and Poisson’s ratio of the faces are assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic ceramic material. Several kinds of sandwich plates are used taking into account the symmetry of the plate and the thickness of each layer. We derive field equations for functionally graded sandwich plates whose deformations are governed by either the shear deformation theories or the classical theory. Displacement functions that identically satisfy boundary conditions are used to reduce the governing equations to a set of coupled ordinary differential equations with variable coefficients. Numerical results of the sinusoidal, third-order, first-order and classical theories are presented to show the effect of material distribution on the deflections and stresses. 相似文献
6.
Post-buckling behaviour of sandwich plates with functionally graded material (FGM) face sheets under uniform temperature rise loading is considered. It is assumed that the plate is in contact with a Pasternak-type elastic foundation during deformation, which acts in both compression and tension. The derivation of equations is based on the first-order shear deformation plate theory. Thermomechanical non-homogeneous properties of FGM layers vary smoothly by the distribution of power law across the thickness, and temperature dependency of material constituents is taken into account. Using the non-linear von-Karman strain-displacement relations, the equilibrium and compatibility equations of imperfect sandwich plates with FGM face sheets are derived. The boundary conditions for the plate are assumed to be simply supported in all edges. The governing equations are reduced to two coupled equation in terms of stress function and lateral deflection. Employing the single mode approach combined with Galerkin technique, an approximate closed-form solution is presented to calculate the critical buckling temperature and post-buckling equilibrium path of the plate. Presented numerical examples contain the influences of power law index, sandwich plate geometry, geometrical imperfection, temperature dependency, and the elastic foundation coefficients. 相似文献
7.
《International Journal of Solids and Structures》2006,43(18-19):5468-5484
This paper deals with the derivation of a finite element model for the static analysis of functionally graded (FG) plates integrated with a layer of piezoelectric fiber reinforced composite (PFRC) material. The layer of PFRC material acts as the distributed actuator of the FG plates. The Young’s modulus of the FG plate is assumed to vary exponentially along the thickness of the plate while the Poisson’s ratio is assumed to be constant over the domain of the plate. The finite element model has been verified with the exact solutions for both thick and thin plates. Emphasis has been placed on investigating the effect of variation of piezoelectric fiber angle in the PFRC layer on its actuating capability of the FG plates. The finite element solutions also revealed that the activated PFRC layer is more effective in controlling the deformations of the FG plates when the layer is attached to the surface of the FG plate with minimum stiffness than when it is attached to the surface of the same with maximum stiffness. 相似文献
8.
9.
This paper deals with the nonlinear forced vibration of FGM rectangular plate with a boundary of two edges clamped opposite and the other two free. The plate is subjected to transversal and in-plane excitations. The present research treats the material properties of the FGM plates as temperature-dependent and graded continuously throughout the thickness direction, following the volume fraction of the constituent materials according to the power law. The temperature is assumed to be constant in the plane and varied only in the thickness direction of the plate. In the framework of geometrical nonlinearity the plate is modeled and the equations of motion are obtained on Hamilton's principle. With the help of Galerkin discretization, the nonlinear ordinary differential equations describing transverse vibration of the plate are proposed. By the numerical method, the nonlinear dynamical responses of the FGM plate with two clamped opposite and two free edges are analyzed. 相似文献
10.
11.
Thermoelastic buckling behavior of thick rectangular plate made of functionally graded materials is investigated in this article.
The material properties of the plate are assumed to vary continuously through the thickness of the plate according to a power-law
distribution. Three types of thermal loading as uniform temperature raise, nonlinear and linear temperature distribution through
the thickness of plate are considered. The coupled governing stability equations are derived based on the Reddy’s higher-order
shear deformation plate theory using the energy method. The resulted stability equations are decoupled and solved analytically
for the functionally graded rectangular plates with two opposite edges simply supported subjected to different types of thermal
loading. A comparison of the present results with those available in the literature is carried out to establish the accuracy
of the presented analytical method. The influences of power of functionally graded material, plate thickness, aspect ratio,
thermal loading conditions and boundary conditions on the critical buckling temperature of aluminum/alumina functionally graded
rectangular plates are investigated and discussed in detail. The critical buckling temperatures of thick functionally graded
rectangular plates with various boundary conditions are reported for the first time and can be served as benchmark results
for researchers to validate their numerical and analytical methods in the future. 相似文献
12.
In this paper, the wave propagation and dynamic response of the rectangular FGM plates with completed clamped supports under impulse load are analyzed. The effective material properties of functionally graded materials (FGMs) for the plate are assumed to vary continuously through the plate thickness and be distributed according to a volume fraction power law along the plate thickness. Considering the effects of transverse shear deformation and rotary inertia, the governing equations of the wave propagation in the functionally graded plate are derived by using the Hamilton’s principle. A complete discussion of dispersion of the FGM plates is given. Using the dispersion relation and integral transforms, exact integral solutions for the FGM plates under impulse load are obtained. The influence of volume fraction distributions on wave propagation and dynamic response of the FGM plates is analyzed. 相似文献
13.
In this paper, free vibration of a circular plate composed of a transversely isotropic functionally graded piezoelectric material (FGPM) placed in a uniform magnetic field is investigated. Material properties are assumed to depend on the thickness of the circular plate and they are expressed as the same exponential function of h. The problem of free vibration for the transversely isotropic FGPM circular plate with clamped and simply supported boundary conditions is solved by means of the state space method. Numerical examples and some useful discussions are given to demonstrate the significant influence of material inhomogeneity, and adopting a certain value of the graded index can optimize structures of the circular plate. This will be of particular importance in modern engineering design. 相似文献
14.
A. Allahverdizadeh R. Oftadeh M. J. Mahjoob A. Soleimani H. Tavassoli 《Archive of Applied Mechanics (Ingenieur Archiv)》2012,82(7):907-918
In this paper, the nonlinear vibration of a thin circular functionally graded material plates is studied. The plate thickness is constant, and the material properties of the plate are assumed to vary continuously through the thickness. The governing equations and boundary conditions are extracted. The assumed-time-mode method is used to analyze these equations. The time variable is eliminated by assuming a harmonic response for nonlinear vibration and using Kantorovich time averaging technique. Utilizing shooting and Runge–Kutta methods, the set of first-order nonlinear differential equations are solved. The effect of volume fraction index in free and forced vibration response and jump phenomenon is studied. The results show that jump phenomenon occur according to volume fraction index and uniform temperature in the special frequencies of forced vibration response. 相似文献
15.
Here, thermal gradient effect on vibration of non-homogeneous orthotropic rectangular plate having bi-direction linearly thickness
variations is studied. The non-homogeneity is assumed to arise due to the variation in the density of the plate material.
Rayleigh Ritz method is used to evaluate the fundamental frequencies and deflection function. The two-dimensional thickness
variation is taken as the Cartesian product of linear variations along the two concurrent edges of the plate. Yet the method
used for the solution of present problem provides an approximate solution but it is quite convenient and authentic one. A two-term
deflection function is used. Frequency corresponding to first mode of vibration is calculated for clamped plate for different
values of temperature gradient, taper constants and non-homogeneity constant. In special cases, comparisons have been made
with results that are available in the literature. 相似文献
16.
Wiighted residual solutions are presented for thermal bending of laminated composite plates. The material of each layer is assumed to be clastically and thermoelastically orthotropic and bimodular. The formulations are based on the thermoclastic version of the theory of Whitney-Pagano laminated plate, which includes thickness shear detormations. The results are obtained for deflections and neutral-surface positions and are found to be in good agreement with the closed-form solution. 相似文献
17.
《International Journal of Solids and Structures》2006,43(14-15):4082-4096
Thermal buckling analysis of rectangular functionally graded plates (FGPs) with geometrical imperfections is presented in this paper. The equilibrium, stability, and compatibility equations of an imperfect functionally graded plate are derived using the classical plate theory. It is assumed that the nonhomogeneous mechanical properties of the plate, graded through thickness, are described by a power function of the thickness variable. The plate is assumed to be under three types of thermal loading as uniform temperature rise, nonlinear temperature rise through the thickness, and axial temperature rise. Resulting equations are employed to obtain the closed-form solutions for the critical buckling temperature change of an imperfect FGP. The results are reduced and compared with the results of perfect functionally graded and imperfect isotropic plates. 相似文献
18.
In this article, an analytical solution for buckling of moderately thick functionally graded (FG) sectorial plates is presented.
It is assumed that the material properties of the FG plate vary through the thickness of the plate as a power function. The
stability equations are derived according to the Mindlin plate theory. By introducing four new functions, the stability equations
are decoupled. The decoupled stability equations are solved analytically for both sector and annular sector plates with two
simply supported radial edges. Satisfying the edges conditions along the circular edges of the plate, an eigenvalue problem
for finding the critical buckling load is obtained. Solving the eigenvalue problem, the numerical results for the critical
buckling load and mode shapes are obtained for both sector and annular sector plates. Finally, the effects of boundary conditions,
volume fraction, inner to outer radius ratio (annularity) and plate thickness are studied. The results for critical buckling
load of functionally graded sectorial plates are reported for the first time and can be used as benchmark. 相似文献
19.
Vibrations of nonhomogeneous orthotropic rectangular plates with bilinear thickness variation resting on Winkler foundation 总被引:1,自引:0,他引:1
Free transverse vibrations of nonhomogeneous orthotropic rectangular plates with bilinear thickness variation resting on Winkler
foundation are presented here using two dimensional boundary characteristic orthogonal polynomials in the Rayleigh-Ritz method
on the basis of classical plate theory. Gram-Schmidt process has been used to generate orthogonal polynomials. The nonhomogeneity
of the plate is assumed to arise due to linear variations in elastic properties and density of the plate material with the
in-plane coordinates. The two dimensional thickness variation is taken as the Cartesian product of linear variations along
the two concurrent edges of the plate. Effect of nonhomogeneity parameters, aspect ratio and thickness variation together
with foundation parameter on the natural frequencies has been illustrated for the first three modes of vibration for four
different combinations of clamped, simply supported and free edges correct to four decimal places. Three dimensional mode
shapes for specified plate for all the four boundary conditions have been plotted. A comparison of results in special cases
with published one has been presented. 相似文献
20.
《International Journal of Solids and Structures》2003,40(13-14):3311-3330
Based on the classical nonlinear von Karman plate theory, axisymmetric large deflection bending of a functionally graded circular plate is investigated under mechanical, thermal and combined thermal–mechanical loadings, respectively, and axisymmetric thermal post-buckling behavior of a functionally graded circular plate is also investigated. The mechanical and thermal properties of functionally graded material (FGM) are assumed to vary continuously through the thickness of the plate, and obey a simple power law of the volume fraction of the constituents. Governing equations for the problem are derived, and then a shooting method is employed to numerically solve the equations. Effects of material constant n and boundary conditions on the temperature distribution, nonlinear bending, critical buckling temperature and thermal post-buckling behavior of the FGM plate are discussed in details. 相似文献