DYNAMIC STABILITY CHARACTERISTICS OF FUNCTIONALLY GRADED PLATES UNDER ARBITRARY PERIODIC LOADS

2013 ◽  
Vol 13 (06) ◽  
pp. 1350026 ◽  
Author(s):  
CHUN-SHENG CHEN ◽  
CHIH-WEN CHEN ◽  
WEI-REN CHEN
Keyword(s):  
Layer Thickness ◽  
Dynamic Load ◽  
Volume Fraction ◽  
Dynamic Instability ◽  
Plate Thickness ◽  
Excitation Frequency ◽  
Frequency Instability ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Periodic Load

The dynamic instability of functionally graded material (FGM) plates under an arbitrary periodic load is studied. The properties of the functionally graded plates (FGPs) are assumed to vary continuously across the plate thickness according to a simple power law. With the derived Mathieu equations, the dynamic instability regions of the FGPs are determined by using the Bolotin's method. The in-plane periodic load is taken to be a combination of periodic axial and bending stress in the example problems. The influences of the volume fraction index, layer thickness ratio, static and dynamic load on the dynamic instability of ceramic-FGM-metal plates are discussed. The results reveal that the excitation frequency, instability region and dynamic instability index of these plates are significantly affected by the static load, dynamic load, volume fraction index and layer thickness.

Hygrothermal Effects on Dynamic Instability of Hybrid Composite Plates

2017 ◽  
Vol 17 (01) ◽  
pp. 1750001 ◽  
Author(s):  
Chun-Sheng Chen ◽  
An-Hung Tan ◽  
Jin-Yih Kao ◽  
Wei-Ren Chen
Keyword(s):  
Layer Thickness ◽  
Hybrid Composite ◽  
Volume Fraction ◽  
Dynamic Instability ◽  
Composite Plates ◽  
Thickness Ratio ◽  
Fiber Volume ◽  
Periodic Load ◽  
Moisture Concentration ◽  
Layer Thickness Ratio

The dynamic characteristics of hybrid composite plates under an arbitrary periodic load in hygrothermal environments are investigated. The material properties of the plate are assumed to be dependent on the temperature and moisture. The governing equations of motion of the Mathieu-type are established based on the Galerkin method with reduced eigenfunction transforms. The periodic stress is taken to be a combination of the pulsating axial and bending stress in the example problems. Based on Bolotin’s method, the dynamic instability behaviors of hybrid composite plates are determined. The effects of layer thickness ratio, fiber volume fraction, temperature rise, moisture concentration and dynamic load on the instability regions of hybrid composite plates are studied, along with the dynamic instability index discussed. The results reveal that the layer thickness ratio and hygrothermal conditions have a significant impact on the dynamic instability of hybrid composite plates.

BUCKLING ANALYSIS OF FUNCTIONALLY GRADED PLATES UNDER MECHANICAL LOADING USING HIGHER ORDER FUNCTIONALLY GRADED STRIP

2013 ◽  
Vol 13 (06) ◽  
pp. 1350033 ◽  
Author(s):  
M. H. SHERAFAT ◽  
H. R. OVESY ◽  
S. A. M. GHANNADPOUR
Keyword(s):  
Volume Fraction ◽  
Plate Theory ◽  
Load Capacity ◽  
Plate Thickness ◽  
Higher Order ◽  
Functionally Graded ◽  
Biaxial Compression ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Ceramic Phase

This paper is concerned with buckling analyses of rectangular functionally graded plates (FGPs) under uniaxial compression, biaxial compression and combined compression and tension loads. It is assumed that the plate is a mixture of metal and ceramic that its properties changes as afunction according to the simple power law distribution through the plate thickness. The fundamental eigen-buckling equations for rectangular plates of functionally graded material (FGM) are obtained by discretizing the plate into some finite strips, which are developed on the basis of the higher order plate theory (HOPT). The solution is obtained by the minimization of the total potential energy. Numerical results fora variety of FGPs are given, and compared with the available results, wherever possible. The effects of thickness ratio, variation of the volume fraction of the ceramic phase through the thickness, aspect ratio, boundary conditions and also load distribution on the buckling load capacity of FGM plates are determined and discussed. It is found that the buckling behavior of FGM plates is particularly influenced by application of HOPT, especially when the plates are thick.

Static Analysis of Moderately Thick Functionally Graded Plates With Various Boundary Conditions

2010 ◽  
Author(s):  
Nastaran Shahmansouri ◽  
Mohammad Mohammadi Aghdam ◽  
Kasra Bigdeli
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Closed Form Solution ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Various Boundary Conditions ◽  
Fg Plates ◽  
Ode Systems

The present study investigates static analyses of moderately thick FG plates. Using the First Order Shear Deformation Theory (FSDT), functionally graded plates subjected to transversely distributed loading with various boundary conditions are studied. Effective mechanical properties which vary from one surface of the plate to the other assumed to be defined by a power law form of distribution. Different ceramic-metal sets of materials are studied. Solution of the governing equations, including five equilibrium and eight constitutive equations, is obtained by the Extended Kantorovich Method (EKM). The system of thirteen Partial Differential Equations (PDEs) in terms of displacements, rotations, force and moment resultants are considered as multiplications of separable function of independent variables x and y. Then by successful utilization of the EKM these equations are converted to a double set of ODE systems in terms of x and y. The obtained ODE systems are then solved iteratively until final convergence is achieved. Closed form solution is presented for these ODE sets. It is shown that the method is very stable and provides fast convergence and highly accurate predictions for both thin and moderately thick plates. Comparison of the normal stresses at various points of rectangular plates and deflection of mid-point of the plate are presented and compared with available data in the literature. The effects of the volume fraction exponent n on the behavior of the normalized deflection, moment resultants and stresses of FG plates are also studied. To validate data for analysis fully clamped FG plates, another analysis was carried out using finite element code ANSYS. Close agreement is observed between predictions of the EKM and ANSYS.

Transient Vibroacoustic Analysis of Functionally Graded Plates

2021 ◽  
pp. 1-36
Author(s):  
Avnish Mahendra Pandey ◽  
K. V. Nagendra Gopal
Keyword(s):  
Volume Fraction ◽  
Free Field ◽  
Shear Deformation Theory ◽  
Structural Response ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
The Finite Element Method ◽  
Time Marching ◽  
The Time Domain ◽  
Vibroacoustic Response

Abstract This paper presents the vibroacoustic response of pure functionally graded plates under transient loading of mechanical nature. The functionally graded plate is modelled using the conventional first-order shear deformation theory to incorporate the effects of transverse shear and rotary inertia. The mid-surface variables are determined using the finite element method. Transient structural response is determined using Newmark Beta time marching scheme and the acoustic pressure in the free field is obtained using the time-domain Rayleigh integral. The effective material properties of the FG plate and the transient response of both the structural and acoustic fields have been computed in MATLAB. The influence of the volume fraction index, thickness ratio and boundary conditions of pure FG plate on its transient vibroacoustic response is investigated by a detailed parametric study.

Nonlinear Analysis of a Thin Circular Functionally Graded Plate and Large Deflection Effects on the Forces and Moments

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
A. Allahverdizadeh ◽  
A. Rastgo ◽  
M. H. Naei
Keyword(s):  
Nonlinear Analysis ◽  
Large Deflection ◽  
Volume Fraction ◽  
Plate Thickness ◽  
Functionally Grade ◽  
Functionally Graded ◽  
Governing Equations ◽  
Temperature Dependent ◽  
Harmonic Vibrations ◽  
Graded Material

Nonlinear analysis of a thin circular functionally grade plate is formulated in terms of von Karman’s dynamic equations. The plate thickness is constant and temperature-dependent functionally graded material (FGM) properties vary through the thickness of the plate. Forces and moments of the plate, due to large vibration amplitudes, are developed in this paper by solving the governing equations for harmonic vibrations. Corresponding results are illustrated in the case of steady-state free vibration. The results show that the variation of volume fraction index is influential in forces, moments, and FGM properties.

scholarly journals Thermal Free Vibration Analysis of Temperature-Dependent Functionally Graded Plates Using Second Order Shear Deformation

2011 ◽  
Vol 471-472 ◽  
pp. 133-139 ◽  
Author(s):  
Ali Shahrjerdi ◽  
Faizal Mustapha ◽  
S.M. Sapuan ◽  
M. Bayat ◽  
Dayang Laila Abang Abdul Majid ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Vibration Characteristics ◽  
Second Order ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Functionally Graded Plates ◽  
Temperature Dependent

This research has been conducted to approach second-order shear deformation theory (SSDT) to analysis vibration characteristics of Functionally Graded Plates (FGP’s). Material properties in FGP's were assumed to be temperature dependent and graded along the thickness using a simple power law distribution in term of the volume fractions of the constituents. FGP was subjected to a linear and nonlinear temperature rise. The energy method was chosen to derive the equilibrium equations. The solution was based on the Fourier series that satisfy the simply supported boundary condition (Navier's method). Numerical results indicated the effect of material composition, plate geometry, and temperature fields on the vibration characteristics and mode shapes. The results revealed that, the temperature field and volume fraction distribution had significant effect on the vibration of FGPs. It was observed the second order theory was very close to the other shear deformation theorem as reported in the literature.

scholarly journals Study of Dynamic Buckling of FG Plate Due to Heat Flux Pulse

2015 ◽  
Vol 20 (1) ◽  
pp. 19-31 ◽  
Author(s):  
L. Czechowski
Keyword(s):  
Heat Flux ◽  
Volume Fraction ◽  
Plate Thickness ◽  
Fem Analysis ◽  
Dynamic Buckling ◽  
Functionally Graded ◽  
Ceramic Surface ◽  
Power Law Distribution ◽  
Different Shapes ◽  
Newton Raphson

Abstract The paper deals with a FEM analysis of dynamic buckling of functionally graded clamped plates under heat flux loading with huge power. The materials of structures as well as their properties are varying in each layer across the plate thickness formulated by the power law distribution. The heat flux was applied evenly to the whole ceramic surface. The analysis was developed in the ANSYS 14.5 software. The duration of the heat flux loading equal to a period of natural fundamental flexural vibrations of given structures was taken into consideration. To implement large deflections of structures, the Green-Lagrange nonlinear-displacement equations and the incremental Newton-Raphson algorithm were applied. An evaluation of the dynamic response of structures was carried out on basis of the Budiansky-Hutchinson criterion. The studies were conducted for different volume fraction distributions and different shapes of the heat flux loading. The computation results of the heat flux versus maximal plate deflection are shown and discussed.

A New Higher Order Shear Deformation Model for Static Behavior of Functionally Graded Plates

2013 ◽  
Vol 5 (03) ◽  
pp. 351-364 ◽  
Author(s):  
Tahar Hassaine Daouadji ◽  
Abdelouahed Tounsi ◽  
El Abbes Adda Bedia
Keyword(s):  
Shear Stress ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Volume Fraction ◽  
Higher Order ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Deformation Model ◽  
Functionally Graded Plates ◽  
Static Behavior

AbstractIn this paper, a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded plate. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Numerical illustrations concerned flexural behavior of FG plates with Metal-Ceramic composition. Parametric studies are performed for varying ceramic volume fraction, volume fraction profiles, aspect ratios and length to thickness ratios. The validity of the present theory is investigated by comparing some of the present results with those of the classical, the first-order and the other higher-order theories. It can be concluded that the proposed theory is accurate and simple in solving the static behavior of functionally graded plates.

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