Numerical study of S1 zero group velocity Lamb modes for nonlinear functionally graded materials

2016 ◽  
Vol 94 (11) ◽  
pp. 1189-1194 ◽  
Author(s):  
Mouldi Zagrouba ◽  
Mohamed Shili Bouhdima
Keyword(s):  
Group Velocity ◽  
Lamb Waves ◽  
Numerical Study ◽  
Poisson Ratio ◽  
Functionally Graded ◽  
Convergence Criteria ◽  
Graded Materials ◽  
Graded Material ◽  
Zero Group ◽  
The Impact

This paper presents detailed theoretical investigation of the first-order symmetric zero group velocity (S1-ZGV) modes propagating in functionally graded material (FGM) plates. Governing equations for the Lamb waves are derived and the power series technique (PST) is employed to solve the recursive equations associated with any power law and its gradient coefficient. The convergence criteria relative to PST have been discussed. Then, the dispersion curves are obtained on the basis of PST. Additionally, the impact of the FGM base materials and the gradient coefficient on S1-ZGV frequency is investigated. Numerical results show that S1-ZGV frequency is comparatively more sensitive to the shear modulus than to the Lamé parameter λ. Additionally, the variations of S1-ZGV frequency as a function of the Poisson ratio of various FGM plates are clarified.

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.

The power series technique and detection of zero-group velocity Lamb waves in a functionally graded material plate

2012 ◽  
Vol 90 (2) ◽  
pp. 159-164 ◽  
Author(s):  
M.S. Bouhdima ◽  
M. Zagrouba ◽  
M.H. Ben Ghozlen
Keyword(s):  
Power Series ◽  
Group Velocity ◽  
Material Properties ◽  
Lamb Waves ◽  
Functionally Graded ◽  
Minimum Frequency ◽  
Graded Material ◽  
Zero Group ◽  
Power Series Technique ◽  
Series Technique

This paper presents a technique for measuring the variation of the material properties along the thickness in a functionally graded material (FGM) plate. To investigate the propagation behavior of Lamb waves in a thermal stress relaxation type FGM plate with material parameters that vary continuously along the thickness, the power series technique, which has been proved to have good convergence and high precision, is employed for theoretical derivations. The method exploits the resonance at the minimum frequency of the S1 - zero group velocity (ZGV) mode. At this minimum frequency (f0), the group velocity vanishes, whereas the phase velocity remains finite. The numerical results also reveal differences between the ZGV frequency in the FGM plate and the corresponding frequency in a homogenous plate. In terms of results, we find that the in-plane and out-plane displacements are different between Al-rich and Si-rich surfaces. The plots of the involved stresses within the plate are added to check the performed calculations. Besides, the study covers the sensitivity of S1-ZGV resonance frequency to the FGM character and any slight variation of the plate thickness. All these results give theoretical guidance not only for experimental measurement of material properties but also for nondestructive evaluation using an ultrasonic wave generation device.

scholarly journals Thermoelastic analysis of FGM hollow cylinder for variable parameters and temperature distributions using FEM

2020 ◽  
Vol 9 (1) ◽  
pp. 256-264
Author(s):  
Dinkar Sharma ◽  
Ramandeep Kaur
Keyword(s):  
Stress Field ◽  
Hollow Cylinder ◽  
Numerical Study ◽  
Axial Stress ◽  
Circumferential Stress ◽  
Functionally Graded ◽  
Gradient Index ◽  
Variable Parameters ◽  
Graded Material ◽  
Governing Differential Equation

AbstractThis paper presents, numerical study of stress field in functionally graded material (FGM) hollow cylinder by using finite element method (FEM). The FGM cylinder is subjected to internal pressure and uniform heat generation. Thermoelastic material properties of FGM cylinder are assumed to vary along radius of cylinder as an exponential function of radius. The governing differential equation is solved numerically by FEM for isotropic and anistropic hollow cylinder. Additionally, the effect of material gradient index (β) on normalized radial stresses, normalized circumferential stress and normalized axial stress are evaluated and shown graphically. The behaviour of stress versus normalized radius of cylinder is plotted for different values of Poisson’s ratio and temperature. The graphical results shown that stress field in FGM cylinder is influenced by some of above mentioned parameters.

scholarly journals Group and Phase Velocity of Love Waves Propagating in Elastic Functionally Graded Materials

2015 ◽  
Vol 40 (2) ◽  
pp. 273-281 ◽  
Author(s):  
Piotr Kiełczyński ◽  
Marek Szalewski ◽  
Andrzej Balcerzak ◽  
Krzysztof Wieja
Keyword(s):  
Group Velocity ◽  
Half Space ◽  
Functionally Graded Materials ◽  
Integral Formula ◽  
Liouville Problem ◽  
Elastic Half Space ◽  
Functionally Graded ◽  
Love Waves ◽  
Graded Materials ◽  
Sturm Liouville

AbstractThis paper presents a theoretical study of the propagation behaviour of surface Love waves in nonhomogeneous functionally graded elastic materials, which is a vital problem in acoustics. The elastic properties (shear modulus) of a semi-infinite elastic half-space vary monotonically with the depth (distance from the surface of the material). Two Love wave waveguide structures are analyzed: 1) a nonhomogeneous elastic surface layer deposited on a homogeneous elastic substrate, and 2) a semi-infinite nonhomogeneous elastic half-space. The Direct Sturm-Liouville Problem that describes the propagation of Love waves in nonhomogeneous elastic functionally graded materials is formulated and solved 1) analytically in the case of the step profile, exponential profile and 1cosh2type profile, and 2) numerically in the case of the power type profiles (i.e. linear and quadratic), by using two numerical methods: i.e. a) Finite Difference Method, and b) Haskell-Thompson Transfer Matrix Method.The dispersion curves of phase and group velocity of surface Love waves in inhomogeneous elastic graded materials are evaluated. The integral formula for the group velocity of Love waves in nonhomogeneous elastic graded materials has been established. The results obtained in this paper can give a deeper insight into the nature of Love waves propagation in elastic nonhomogeneous functionally graded materials.

The Elastic-Viscoelastic Correspondence Principle for Functionally Graded Materials, Revisited

2003 ◽  
Vol 70 (3) ◽  
pp. 359-363 ◽  
Author(s):  
S. Mukherjee ◽  
Glaucio H. Paulino
Keyword(s):  
Functionally Graded Materials ◽  
Functionally Graded Material ◽  
Correspondence Principle ◽  
Functionally Graded ◽  
Graded Materials ◽  
One Dimensional ◽  
Space And Time ◽  
Graded Material ◽  
Nonhomogeneous Materials ◽  
Exponentially Graded

Paulino and Jin [Paulino, G. H., and Jin, Z.-H., 2001, “Correspondence Principle in Viscoelastic Functionally Graded Materials,” ASME J. Appl. Mech., 68, pp. 129–132], have recently shown that the viscoelastic correspondence principle remains valid for a linearly isotropic viscoelastic functionally graded material with separable relaxation (or creep) functions in space and time. This paper revisits this issue by addressing some subtle points regarding this result and examines the reasons behind the success or failure of the correspondence principle for viscoelastic functionally graded materials. For the inseparable class of nonhomogeneous materials, the correspondence principle fails because of an inconsistency between the replacements of the moduli and of their derivatives. A simple but informative one-dimensional example, involving an exponentially graded material, is used to further clarify these reasons.

Incremental Melting and Solidification Process/Mechanical Characterization of Functionally Graded Al-Si Alloys

2008 ◽  
Vol 587-588 ◽  
pp. 400-404
Author(s):  
P. Pinto ◽  
L. Mazare ◽  
Delfim Soares ◽  
F.S. Silva
Keyword(s):  
Mechanical Properties ◽  
Functionally Graded Materials ◽  
Phase Distribution ◽  
Solidification Process ◽  
Functionally Graded ◽  
Graded Materials ◽  
Graded Material ◽  
Gradual Variation ◽  
Melting And Solidification

The Incremental Melting and Solidification Process (IMSP) is a relatively new field for material processing for the production of functionally graded materials. In this process a controlled liquid bath is maintained at the top of the component where new materials are added changing the components composition. Thus, a functionally graded material is obtained with a varying composition along one direction of the component. This paper deals with the influence of one of the process parameters, namely displacement rates between heating coil and mould, in order to evaluate its influence on both metallurgical and mechanical properties of different Al-Si alloys. Hardness and phase distribution, along the main castings axis, were measured. To better assess and characterize the process, two different Al-Si alloys with and without variation of chemical composition along the specimen were analysed. Results demonstrate that a gradual variation of metallurgical and mechanical properties along the component is obtained. It is also shown that Al-Si functionally graded materials can be produced by the incremental melting and solidification process. Results show that the displacement rate is very important on metallurgical and mechanical properties of the obtained alloy.

Задачи о дисперсии волн в неоднородных волноводах: методы решения (обзор). Часть I

2021 ◽  
Vol 27 (2) ◽  
pp. 227-260
Author(s):  
С. И. Жаворонок ◽  
Keyword(s):  
Functionally Graded Materials ◽  
Functionally Graded Material ◽  
Matrix Method ◽  
Degrees Of Freedom ◽  
Normal Wave ◽  
Wave Dispersion ◽  
Functionally Graded ◽  
Graded Materials ◽  
Generalized Fourier Series ◽  
Graded Material

A brief review of the modern state-of-the art and tendencies of further development of various methods of solution of wave dispersion problems in heterogeneous functionally graded elastic waveguides is presented. Main types of functionally graded materials and structures, including gradient thon-walled structures, and their main engineering applications is discussed. The main difficulties of modelling of the stress-strain state of functionally graded shells and plates are pointed, as well as the possible ways to overcome such difficulties. The main theoretical bases of definition of effective constitutive constants of functionally graded materials and their possible estimates used in the practice are considered. Main dependencies of the effective constitutive constants of a functionally graded material on coordinates used for the mathematical modelling of the dynamics are also shown. The statement of the dynamics problem for a functionally graded waveguide and the appropriate statement of the normal wave dispersion problem are pointed. The presented Part I of the review consider some analytical methods of solution of dispersion problems, mainly the matrix ones based on the formulation of the steady dynamics problem in the image space as a first-order ordinary differential equations system. The state vectors corresponding to the useful Cauchy and Stroh formalisms are introduced, and the appropriate governing equations and the boundary conditions on waveguide’s faces are presented. Classical methods for solving the steady dynamics problem for a laminated waveguide are briefly described, which could be a basis for the further approximation of a functionally graded material by a system of layers with constant properties, i.e. the transfer matrix method, its main modifications developed to ensure the stability of calculations, and the global matrix method. Then, the intensively developed last 15 years reverberation matrix method, stiffness matrix method, and the Peano series method are discussed. Some key solutions of the wave dispersion problems for heterogeneous layers are presented; such solutions improve the efficiency of approximation of a functionally graded structure by a laminated one. The implicit solution of the general problem of steady dynamics for a waveguide with arbitrary gradation law is shown. The key features of the discussed matrix methods are pointed briefly as well as their main drawbacks. In the Part II, the main attention will be paid to methods of semi-analytical solution of dispersion problems based on the approximation of a waveguide by an equivalent system with a finite number of degrees of freedom: power series, generalized Fourier series, semi-analytical finite elements. spectral elements, as well as methods based on various theories of plates and shells.

Analytical and numerical investigation of the free vibration of functionally graded materials sandwich beams

2021 ◽  
Vol 2 (110) ◽  
pp. 72-85
Author(s):  
S.H. Bakhy ◽  
M. Al-Waily ◽  
M.A. Al-Shammari
Keyword(s):  
Analytical Solution ◽  
Free Vibration ◽  
Functionally Graded Materials ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Functionally Graded ◽  
Gradient Index ◽  
Sandwich Beams ◽  
Graded Materials ◽  
The Impact

Purpose: In this study, the free vibration analysis of functionally graded materials (FGMs) sandwich beams having different core metals and thicknesses is considered. The variation of material through the thickness of functionally graded beams follows the power-law distribution. The displacement field is based on the classical beam theory. The wide applications of functionally graded materials (FGMs) sandwich structures in automotive, marine construction, transportation, and aerospace industries have attracted much attention, because of its excellent bending rigidity, low specific weight, and distinguished vibration characteristics. Design/methodology/approach: A mathematical formulation for a sandwich beam comprised of FG core with two layers of ceramic and metal, while the face sheets are made of homogenous material has been derived based on the Euler–Bernoulli beam theory. Findings: The main objective of this work is to obtain the natural frequencies of the FG sandwich beam considering different parameters. Research limitations/implications: The important parameters are the gradient index, slenderness ratio, core metal type, and end support conditions. The finite element analysis (FEA), combined with commercial Ansys software 2021 R1, is used to verify the accuracy of the obtained analytical solution results. Practical implications: It was found that the natural frequency parameters, the mode shapes, and the dynamic response are considerably affected by the index of volume fraction, the ratio as well as face FGM core constituents. Finally, the beam thickness was dividing into frequent numbers of layers to examine the impact of many layers' effect on the obtained results. Originality/value: It is concluded, that the increase in the number of layers prompts an increment within the frequency parameter results' accuracy for the selected models. Numerical results are compared to those obtained from the analytical solution. It is found that the dimensionless fundamental frequency decreases as the material gradient index increases, and there is a good agreement between two solutions with a maximum error percentage of no more than 5%.

Additive manufacturing of Inconel625-HSLA Steel functionally graded material by wire arc additive manufacturing

2021 ◽  
Vol 118 (5) ◽  
pp. 502
Author(s):  
Jiarong Zhang ◽  
Xinjie Di ◽  
Chengning Li ◽  
Xipeng Zhao ◽  
Lingzhi Ba ◽  
...  
Keyword(s):  
Additive Manufacturing ◽  
Chemical Composition ◽  
Primary Dendrite ◽  
Hsla Steel ◽  
High Strength ◽  
Phase Evolution ◽  
Functionally Graded ◽  
Graded Materials ◽  
Graded Material ◽  
Wire Arc Additive Manufacturing

Functional graded materials (FGMs) have been widely applied in many engineering fields, and are very potential to be the substitutions of dissimilar metal welding joints due to their overall performance. In this work, the Inconel625-high-strength low-alloy (HSLA) Steel FGM was fabricated by wire arc additive manufacturing (WAAM). The chemical composition distribution, microstructure, phase evolution and mechanical properties of the FGM were examined. With the increasing of HSLA Steel, the chemical composition appeared graded distribution, and the primary dendrite spacing was largest in graded region with 20%HSLA Steel and then gradually decreased. And the main microstructure of the FGM transformed from columnar dendrites to equiaxed dendrites. Laves phase precipitated along dendrites boundary when the content of HSLA Steel was lower than 70% and Nb-rich carbides precipitated when the content of HSLA Steel exceeded to 70%. Microhardness and tensile strength gradually decreased with ascending content of HSLA Steel, and had a drastic improvement (159HV to 228HV and 355Mpa to 733Mpa) when proportion of HSLA Steel increased from 70% to 80%.

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