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 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.

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 Multiple zero group velocity Lamb modes in an anisotropic plate: propagation along different crystallographic axes

2019 ◽  
Vol 97 (10) ◽  
pp. 1064-1074
Author(s):  
Soufien Karous ◽  
Souhail Dahmen ◽  
Mohamed Shili Bouhdima ◽  
Morched Ben Amor ◽  
Christ Glorieux
Keyword(s):  
Group Velocity ◽  
Lamb Waves ◽  
Iodic Acid ◽  
Transverse Waves ◽  
Cutoff Frequencies ◽  
Crystallographic Planes ◽  
Zero Group ◽  
Crystallographic Axes ◽  
Symmetric And Antisymmetric Modes ◽  
Lamb Mode

This paper studies the propagation of symmetric and antisymmetric Lamb waves along a 1 mm thick iodic acid plate (HIO3) in the 1–50 MHz frequency range. The Lamb mode propagation along three crystallographic planes was theoretically investigated, for two mutually orthogonal propagation directions. Several frequencies were found that correspond to Lamb modes with zero group velocity (ZGV) and non-null phase velocity values. The first symmetric Lamb mode, S1, was found to possess only one ZGV point, regardless of the propagation direction; higher order symmetric and antisymmetric modes with up to four ZGV points were found, depending on the propagation plane. The dependence of the ZGV frequencies on each elastic constant (c11, c13, c33, c55) of the HIO3 plate material was also investigated by changing the constant values by 5% and 10%. It was found that c33 and c55 affect the number of the ZGV points, while c11 and c13 affect the frequency of the ZGV points. The existence and frequencies of the ZGV points are strongly dependent on the proximity of standing longitudinal and transverse waves at nearby cutoff frequencies.

scholarly journals Imaging gigahertz zero-group-velocity Lamb waves

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Qingnan Xie ◽  
Sylvain Mezil ◽  
Paul H. Otsuka ◽  
Motonobu Tomoda ◽  
Jérôme Laurent ◽  
...  
Keyword(s):  
Group Velocity ◽  
Lamb Waves ◽  
Zero Group

Geometrically nonlinear dynamic response and vibration of shear deformable eccentrically stiffened functionally graded material cylindrical panels subjected to thermal, mechanical, and blast loads

2018 ◽  
Vol 22 (3) ◽  
pp. 658-688 ◽  
Author(s):  
Nguyen Dinh Duc ◽  
Ngo Duc Tuan ◽  
Pham Hong Cong ◽  
Ngo Dinh Dat ◽  
Nguyen Dinh Khoa
Keyword(s):  
Dynamic Response ◽  
Functionally Graded Material ◽  
Material Properties ◽  
Nonlinear Dynamic ◽  
Functionally Graded ◽  
Blast Loads ◽  
Temperature Dependent ◽  
Nonlinear Dynamic Response ◽  
Cylindrical Panels ◽  
Graded Material

Based on the first order shear deformation shell theory, this paper presents an analysis of the nonlinear dynamic response and vibration of imperfect eccentrically stiffened functionally graded material (ES-FGM) cylindrical panels subjected to mechanical, thermal, and blast loads resting on elastic foundations. The material properties are assumed to be temperature-dependent and graded in the thickness direction according to simple power-law distribution in terms of the volume fractions of the constituents. Both functionally graded material cylindrical panels and stiffeners having temperature-dependent properties are deformed under temperature, simultaneously. Numerical results for the dynamic response of the imperfect ES-FGM cylindrical panels with two cases of boundary conditions are obtained by the Galerkin method and fourth-order Runge–Kutta method. The results show the effects of geometrical parameters, material properties, imperfections, mechanical and blast loads, temperature, elastic foundations and boundary conditions on the nonlinear dynamic response of the imperfect ES-FGM cylindrical panels. The obtained numerical results are validated by comparing with other results reported in the open literature.

Stochastic Extended Finite Element Implementation for Natural Frequency of Cracked Functionally Gradient and Bi-Material Structures

2020 ◽  
pp. 2150044
Author(s):  
Ahmed Raza ◽  
Himanshu Pathak ◽  
Mohammad Talha
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Material Properties ◽  
Perturbation Technique ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Extended Finite Element ◽  
Material Interface ◽  
Level Set Function ◽  
Graded Material

In this work, stochastic perturbation-based vibration characteristics of cracked bi-material and functionally graded material (FGM) domain with uncertain material properties are investigated using the extended finite element method. The level set function is implemented to track the geometrical discontinuities. The partition of unity-based extrinsic enrichment technique is employed to model the crack and material interface. The exponential law is used to model the graded material properties of FGM. The First-order perturbation technique (FOPT) is implemented to predict the standard deviation of natural frequency for the given uncertainties in the material properties. The numerical results are presented to show the effect of geometrical discontinuities and material randomness on vibration characteristics.

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