scholarly journals Vibration Analysis of a Three-Layered FGM Cylindrical Shell Including the Effect Of Ring Support

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 587-600
Author(s):  
Madiha Ghamkhar ◽  
Muhammad Nawaz Naeem ◽  
Muhammad Imran ◽  
Constantinos Soutis
Keyword(s):  
Functionally Graded Material ◽  
Volume Fraction ◽  
Ritz Method ◽  
Frequency Equation ◽  
Functionally Graded ◽  
Physical Parameters ◽  
Ring Support ◽  
Mathematical Expressions ◽  
Graded Material ◽  
The Impact

Abstract In this work, we study vibrations of three-layered cylindrical shells with one ring support along its length. Nature of material of the central layer is a functionally graded material (FGM) type. The considered FGM is of stainless steel and nickel. The internal and external layers are presumed to be made of isotropic material i.e., aluminum. The functionally graded material composition of the center layer is assorted by three volume fraction laws (VFL) which are represented by mathematical expressions of polynomial, exponential and trigonometric functions. The implementation of Rayleigh-Ritz method has been done under the Sanders’ shell theory to obtain the shell frequency equation. Natural frequencies (NFs) are attained for the present model problem under six boundary conditions. Use of characteristic beam functions is made for the estimation of the dependence of axial modals. The impact of layer material variations with ring support is considered for many ring positions. Also the effect of volume fraction laws is investigated upon vibration characteristics. This investigation is performed for various physical parameters. Numerous comparisons of values of shell frequencies have been done with available models of such types of results to verify accuracy of the present formulation and demonstrate its numerical efficiency.

Frequency analysis of functionally graded material cylindrical shells with various volume fraction laws

2007 ◽  
Vol 221 (12) ◽  
pp. 1483-1495 ◽  
Author(s):  
S H Arshad ◽  
M N Naeem ◽  
N Sultana
Keyword(s):  
Frequency Analysis ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Cylindrical Shells ◽  
Ritz Method ◽  
Frequency Equation ◽  
Functionally Graded ◽  
Edge Conditions ◽  
Graded Material ◽  
Love’S Thin Shell Theory

In the current paper a frequency analysis is performed for functionally graded material (FGM) circular cylindrical shells. A comparative study of shell frequencies is given for algebraic polynomial, exponential, and trigonometric volume fraction laws. An FGM shell considered here is structured from two materials. Love's thin shell theory is utilized for strain-displacement and curvature-displacement relations. The Rayleigh-Ritz method is employed to derive the frequency equation in the form of eigenvalue problem. Natural frequencies are evaluated for a shell with simply supported edge conditions. The axial modal dependence is approximated by circular trigonometric functions. Theoretical results are compared with those available in the literature for the validity of the present methodology.

scholarly journals S1-ZGV Modes of a Linear and Nonlinear Profile for Functionally Graded Material Using Power Series Technique

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
M. Zagrouba ◽  
M. S. Bouhdima ◽  
M. H. Ben Ghozlen
Keyword(s):  
Power Series ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Graded Materials ◽  
Graded Material ◽  
Zero Group ◽  
The Impact ◽  
Power Series Technique ◽  
Series Technique

The present work deals with functionally graded materials (FGM) isotropic plates in the neighborhood of the first-order symmetric zero group velocity (S1-ZGV) point. The mechanical properties of functionally graded material (FGM) are assumed to vary continuously through the thickness of the plate and obey a power law of the volume fraction of the constituents. Governing equations for the problem are derived, and the power series technique (PST) is employed to solve the recursive equations. The impact of the FGM basic materials properties on S1-ZGV frequency of FGM plate is investigated. Numerical results show that S1-ZGV frequency is comparatively more sensitive to the shear modulus. The gradient coefficient p does not affect the linear dependence of ZGV frequency fo as function of cut-off frequency fc; only the slope is slightly varied.

Three-dimensional buckling analyses of cracked functionally graded material plates via the MLS-Ritz method

2019 ◽  
Vol 134 ◽  
pp. 189-202 ◽  
Author(s):  
C.S. Huang ◽  
H.T. Lee ◽  
P.Y. Li ◽  
K.C. Hu ◽  
C.W. Lan ◽  
...  
Keyword(s):  
Functionally Graded Material ◽  
Ritz Method ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Graded Material

FE Analysis of Functionally Graded Material Plate during Debonding Case with Different Boundary Conditions

2014 ◽  
Vol 627 ◽  
pp. 57-60 ◽  
Author(s):  
Wasim M.K. Helal ◽  
Dong Yan Shi
Keyword(s):  
Boundary Conditions ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Maximum Shear Stress ◽  
Functionally Graded ◽  
Von Mises Stress ◽  
Sigmoid Function ◽  
Different Boundary Conditions ◽  
Graded Material ◽  
The Relationship

Functionally graded materials (FGMs) have become helpful in our engineering applications. Analysis of functionally graded material (FGM) plate during debonding case with different boundary conditions is the main purpose of this investigation. Elastic modulus (E) of functionally graded (FG) plate is assumed to vary continuously throughout the height of the plate, according the volume fraction of the constituent materials based on a modified sigmoid function, but the value of Poisson coefficient is constant. In this research, the finite element method (FEM) is used in order to show the shape of a plate made of FGM during debonding case with different boundary conditions. In the present investigation, the displacement value applied to the FGM plate is changed in order to find the relationship between the maximum von Mises stress and the displacement. Also, the relationship between the maximum shear stress and the displacement is carried out in the present work. The material gradient indexes of the FGM plate are changed from 1 to 10. The stress distributions around the debonding zone with all the material gradient indexes of the FGM plate are investigated in this work.

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.

Effects of piezoelectric rings on electro-elasto-dynamic behaviour of functionally graded cylindrical shell

2016 ◽  
Vol 28 (2) ◽  
pp. 272-289 ◽  
Author(s):  
Mohammadreza Saviz
Keyword(s):  
Finite Element ◽  
Cylindrical Shell ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Virtual Work ◽  
Electrical Potential ◽  
Axial Direction ◽  
Functionally Graded ◽  
Radial Coordinate ◽  
Graded Material

A layer-wise finite element approach is adopted to analyse the hollow cylindrical shell made of functionally graded material with piezoelectric rings as sensor/actuator, under dynamic load. The mechanical properties of the substrate are regulated by volume fraction as a function of radial coordinate. The thickness of functionally graded material shell and piezo-rings is divided into mathematical sub-layers and then the general layer-wise laminate theory is formulated through introducing piecewise continuous approximations across the thickness, accounting for any discontinuity in derivatives of the displacement at the interface between the ring and cylinder. The virtual work statement including structural and electrical potential energies yields the three-dimensional governing equations which are reduced to two-dimensional differential equations, using layer-wise method. For axisymmetric case, the resulted equations are solved with one-dimensional finite element method in the axial direction. By assembling stiffness and mass matrices, the required stress and displacement continuities at each interface and between the two adjacent elements are forced. The results for free vibration and static loading are applied to study the convergence and verified by comparing them to solutions of similar existing problems. The induced deformation by piezoelectric actuators as well as the effect of rings on functionally graded material shell is investigated.

On modal analysis of axially functionally graded material beam under hygrothermal effect

2019 ◽  
Vol 234 (5) ◽  
pp. 1085-1101 ◽  
Author(s):  
Pankaj Sharma ◽  
Rahul Singh ◽  
Muzamal Hussain
Keyword(s):  
Modal Analysis ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Axial Direction ◽  
Functionally Graded ◽  
Element Analysis ◽  
Hygrothermal Effect ◽  
Graded Material ◽  
Eigen Frequencies ◽  
Axially Functionally Graded Material

This investigation focuses on the modal analysis of an axially functionally graded material beam under hygrothermal effect. The material constants of the beam are supposed to be graded smoothly along the axial direction under both power law and sigmoid law distribution. A finite element analysis with COMSOL Multiphysics® (version 5.2) package is used to find the Eigen frequencies of the beam. The accuracy of the technique is authenticated by relating the results with the prior investigation for reduced case. The effects of moisture changes, temperature, and volume fraction index, length-to-thickness ratio on the Eigen frequencies are investigated in detail. It is believed that the present investigation may be useful in the design of highly efficient environmental sensors for structural health monitoring perspective.

Investigation of the mechanical properties on the large amplitude free vibrations of the functionally graded material sandwich plates

2017 ◽  
Vol 21 (3) ◽  
pp. 895-916 ◽  
Author(s):  
Sid Ahmed Belalia
Keyword(s):  
Mechanical Properties ◽  
Functionally Graded Material ◽  
Large Amplitude ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Nonlinear Frequency ◽  
Graded Material

In this paper, the geometrically nonlinear formulation based on von Karman’s assumptions is employed to study the large amplitude free vibrations of functionally graded materials sandwich plates. The functionally graded material sandwich plate is made up of two layers of power-law functionally graded material face sheet and one layer of ceramic homogeneous core. A hierarchical finite element is employed to define the model, taking into account the effects of the transverse shear deformation and the rotatory inertia. The equations of motion for the nonlinear vibration of the functionally graded material sandwich plates are obtained using Lagrange’s equations. Employing the harmonic balance method, the equations of motion are converted from time domain to frequency domain and then solved iteratively using the linearized updated mode method. Results for linear and nonlinear frequency parameters of the simply supported functionally graded material sandwich plates are computed and compared with the published values, and an excellent agreement was found. The influence of the mechanical properties of the functionally graded material, thickness ratio of FGM layers, and volume fraction exponent on the backbone curves and on the nonlinear frequency parameters are investigated. The effects of the material properties of two different types of ceramics on the large amplitude vibration behaviors of the functionally graded material sandwich plates is also presented and discussed for the first time.

Dynamic behaviors of multi-span viscoelastic functionally graded material pipe conveying fluid

2016 ◽  
Vol 231 (17) ◽  
pp. 3181-3192 ◽  
Author(s):  
Jiaquan Deng ◽  
Yongshou Liu ◽  
Zijun Zhang ◽  
Wei Liu
Keyword(s):  
Functionally Graded Material ◽  
Volume Fraction ◽  
Fluid Velocity ◽  
Functionally Graded ◽  
Piping System ◽  
Pipe Conveying Fluid ◽  
Dynamic Behaviors ◽  
Graded Material ◽  
The Stability ◽  
Conveying Fluid

In this paper, the dynamic behaviors of a multi-span viscoelastic functionally graded material pipe conveying fluid are investigated by dynamic stiffness method. The material properties of the functionally graded material pipe are considered as graded distribution along the thickness direction according to a power-law. Several numerical examples are performed to study the effects of volume fraction exponent, fluid velocity, internal pressure, and internal damping on the stability and frequency response of the fluid-conveying functionally graded material pipe. It’s found that the viscoelastic functionally graded material pipe exhibits some special dynamic behaviors and it could increase the stability significantly when compared with the aluminum and steel pipes. The numerical results also demonstrate that by the introduction of the functionally graded material, the stiffness of the piping system could be modulated easily by designing the volume fraction function. Therefore, if the dominant frequency contents of the external loads are known, a preferable design of the functionally graded material pipe to reduce the vibration is possible.

Free Vibration of a Rotating Sandwich Plate with Viscoelastic Core and Functionally Graded Material Constraining Layer

2017 ◽  
Vol 17 (10) ◽  
pp. 1750114 ◽  
Author(s):  
Shince. V. Joseph ◽  
S. C. Mohanty
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Functionally Graded Material ◽  
Rotational Speed ◽  
Sandwich Plate ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Setting Angle ◽  
Viscoelastic Core ◽  
Graded Material

Free vibration analysis of a sandwich plate with viscoelastic material core and functionally graded material (FGM) constraining layer under centrifugal force field is investigated herein. One edge of the sandwich plate is fixed to a rotating hub. The first-order shear deformation theory (FSDT) is used in the finite element modeling of the problem. The effects of strains due to the longitudinal and transverse deformations are also considered in addition to the shear deformation of the core. Various parametric studies are carried out to examine the effects of volume fraction index, setting angle, hub radius and rotational speed on the vibration characteristics of the sandwich plate. It is found that the fundamental frequency of the plate decreases with an increase in the volume fraction index of the FGM layer, viscoelastic core thickness and setting angle. The first mode loss factor increases with respect to the increasing volume fraction index. Increase in rotational speed and hub radius lead to an increase in the natural frequencies and a decrease in the modal loss factors.

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