Investigation of the coupled Lamb waves propagation in viscoelastic and anisotropic multilayer composites by Legendre polynomial method

Dahmen, Souhail; Amor, Morched Ben; Ghozlen, Mohamed Hédi Ben

doi:10.1016/j.compstruct.2016.06.068

Cited by 35 publications

(18 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These equations remain valid for any material of higher symmetry class, assuming that the direction of propagation is collinear with a principal axis [41]. Solutions to these equations are coupled ω and v ph values: they are obtained using a numerical process based on the dichotomy method to find initial solutions at specific angular frequencies, plus the Newton-Raphson method used to follow these roots as the angular frequency changes [45,49].…”

Section: Fig1mentioning

confidence: 99%

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

et al. 2019

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Fig1mentioning

confidence: 99%

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

et al. 2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…The derivative of the rectangular window function is δfalse(r−afalse)−δfalse(r−bfalse), with δ being a step function. This treatment can automatically introduce the boundary conditions into the wave propagation equations [27,28].…”

Section: Statement Of the Problem And Basic Equationsmentioning

confidence: 99%

Computation of Propagating and Non-Propagating Lamb-Like Wave in a Functionally Graded Piezoelectric Spherical Curved Plate by an Orthogonal Function Technique

et al. 2018

View full text Add to dashboard Cite

Non-propagating waves have great potential for crack evaluation, but it is difficult to obtain the complex solutions of the transcendental dispersion equation corresponding to the non-propagating wave. This paper presents an analytical approach based on the orthogonal function technique to investigate non-propagating Lamb-like waves in a functionally graded piezoelectric spherical curved plate. The presented approach can transform the set of partial differential equations for the acoustic waves into an eigenvalue problem that can give the generally complex wave numbers and the field profiles. A comparison of the obtained results with the well-known ones in plates is provided. The obtained solutions of the dispersion equation are shown graphically in three dimensional frequency-complex wave number space, which aids in understanding the properties of non-propagating waves better. The properties of the guided wave, including real, purely imaginary, and complex branches in various functionally graded piezoelectric spherical curved plates, are studied. The effects of material piezoelectricity, graded fields, and mechanical and electrical boundary conditions on the dispersion characteristics, are illustrated. The amplitude distributions of displacement and electric potential are also discussed, to analyze the specificities of non-propagating waves.

show abstract

“…The model has practical application meaning to metallic and mineral crystals. Dahmen studied coupled Lamb waves propagation in viscoelastic and anisotropic multilayer composites. Based on the Legendre orthogonal polynomial approach, the attenuation of guided waves in damped multilayered arbitrary anisotropic composite laminates is investigated.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of anisotropic half space containing an elliptical inclusion under SH waves

Jiang

Yang

Sun

et al. 2020

Math Methods in App Sciences

View full text Add to dashboard Cite

Based on the methods of complex function, conformal mapping, and multipolar coordinate system, dynamic response of an elliptical inclusion embedded in an anisotropic half space is investigated. In order to find the solution of SH waves, the governing equation is transferred into its normalized form. Then, the scattering wave induced by the inclusion and the standing wave in the inclusion is deduced. Different incident wave angles and the corresponding anisotropy of the half space are considered to obtain the reflected waves. The elliptical inclusion is transferred into a unit circle by conformal mapping method, and then the undetermined coefficients in scattering wave and standing wave are solved by using the continuous condition at the boundary of the inclusion. Subsequently, the dynamic stress concentration factor (DSCF) around the inclusion is calculated and analyzed. Numerical results demonstrate that the distribution of the DSCF is mainly influenced by the incident wave angle and the incident wave number. It is affected by anisotropic parameters as well. KEYWORDSanisotropy, complex function method, dynamic stress concentration factor (DSCF), elliptical inclusion, wave scattering MSC CLASSIFICATION 74J20Math Meth Appl Sci. 2020;43:6888-6902. wileyonlinelibrary.com/journal/mma

show abstract

Investigation of the coupled Lamb waves propagation in viscoelastic and anisotropic multilayer composites by Legendre polynomial method

Cited by 35 publications

References 32 publications

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

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

Computation of Propagating and Non-Propagating Lamb-Like Wave in a Functionally Graded Piezoelectric Spherical Curved Plate by an Orthogonal Function Technique

Dynamic analysis of anisotropic half space containing an elliptical inclusion under SH waves

Contact Info

Product

Resources

About