Investigation of guided waves propagation in orthotropic viscoelastic carbon–epoxy plate by Legendre polynomial method

Othmani, Cherif; Dahmen, Souhail; Njeh, Anouar; Ghozlen, Mohamed Hédi Ben

doi:10.1016/j.mechrescom.2016.03.007

Cited by 35 publications

(50 citation statements)

References 12 publications

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“…, and H j m are the corresponding elements of these matrices, which can be obtained by equation (8) Note that in equation (11), once we specify a fixed value of v, it does not have the structure of a general eigenvalue problem in k. In previous research works, 12,13 equation (11) was transformed into an eigenvalue problem with eigenvalue v. For a propagating wave, it is simple to specify real k and then solve for v. But for an evanescent wave, it is useless because the wavenumber is complex, which involves a multivariable search. To deal with this problem, we develop a new solution procedure to recast the equation again in the form of a general eigenvalue problem, as shown below.…”

Section: Mathematics and Formulation Of The Problemmentioning

confidence: 99%

“…7 There are also many methods taking FGM as a continuous gradient medium to be proposed for analyzing guided waves in FGM structures, such as the Wentzel-Kramers-Brillouin method, 8 power series method, 9 reverberation-ray matrix method, 10 state vector method, 11 and orthogonal polynomial series method. 12,13 Such methods have been successfully applied to computing, two-dimensional (2D), and less often three-dimensional (3D), dispersion curves for guided waves. Recently, the guided waves in nanostructures and functionally graded nanostructures have also been extensively investigated.…”

Section: Introductionmentioning

confidence: 99%

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Properties of circumferential non-propagating waves in functionally graded piezoelectric cylindrical shells

Zhang

et al. 2019

Advances in Mechanical Engineering

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Each guided elastic wave mode is composed of propagating and non-propagating branches. Non-propagating branches associated with complex wavenumbers are substantially different from the propagating ones. Accurate calculation of the transcendental dispersion equation for complex wavenumbers and arbitrary ranges of frequencies is usually very difficult, especially for demanding cases such as those involving composite materials and curved structures. In this article, an extended Legendre orthogonal polynomial method is presented to determine non-propagating waves in a functionally graded piezoelectric cylindrical shell. The extended Legendre orthogonal polynomial method can obtain complete solutions without the tedious iterative search. Results are compared with those published earlier to validate the extended Legendre orthogonal polynomial method, and the convergence of this method is also discussed. Dispersion characteristics of the non-propagating waves in various graded piezoelectric cylindrical shells are studied and three-dimensional dispersion curves are plotted. The effects of piezoelectricity, graded fields, and the mechanical and electrical boundary conditions on dispersion curves are illustrated. The displacement amplitude, stress, and electric potential distributions are also analyzed in detail. Numerical results show that the extended Legendre orthogonal polynomial method is very efficient to retrieve the guided waves of any nature and the modes of all orders.

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Section: Mathematics and Formulation Of The Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Properties of circumferential non-propagating waves in functionally graded piezoelectric cylindrical shells

Zhang

et al. 2019

Advances in Mechanical Engineering

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“…Moreover, although the Legendre polynomial method is quite versatile for guided wave problems, it involves a large amount of numerical integration calculations, resulting in a low computational efficiency. [29][30][31][32][33][34] This paper presents a recursive Legendre polynomial analytical integral (RLPAI) method to determine complete roots of the dispersion equation of guided waves in a rectangular orthotropic composite bar. The RLPAI method does not require the large amount of numerical integration calculations required by traditional polynomial methods, and the computational efficiency increases significantly.…”

Section: Introductionmentioning

confidence: 99%

A Recursive Legendre Polynomial Analytical Integral Method for the Fast and Efficient Modelling Guided Wave Propagation in Rectangular Section Bars of Orthotropic Materials

Zhang¹,

Shao²,

Shao³

2021

The International Journal of Acoustics and Vibration

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Ultrasonic guided waves are widely used in non-destructive testing (NDT), and complete guided wave dispersion, including propagating and evanescent modes in a given waveguide, is essential for NDT. Compared with an infinite plate, the finite lateral width of a rectangular bar introduces a greater density of modes, and the dispersion solutions become more complicated. In this study, a recursive Legendre polynomial analytical integral (RLPAI) method is presented to calculate the dispersion behaviours of guided waves in rectangular bars of orthotropic materials. The existing polynomial method involves a large number of numerical integration steps, and it is often computationally costly to compute these integrals. The presented RLPAI method uses analytical integration instead of numerical integration, thus leading to a significant improvement in the computational speed. The results are compared with those published previously to validate our method, and the computational efficiency is discussed. The full three-dimensional dispersion curves are plotted. The dispersion characteristics of propagating and evanescent waves are investigated in various rectangular bars. The influences of different width-to-thickness ratios on the dispersion curves of four types of low-order modes for a rectangular bar of an orthotropic composite are illustrated.

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“…Vignjevic et al [32] and Destrade [8] attempted to inspect the surface waves as well as shock waves in orthotropic elastic materials. The propagation of surface waves in orthotropic composite structure with irregular interfaces has been studied by Singh and Alam [29] whereas Othmani et al [20] investigated the guided waves propagation in orthotropic viscoelastic carbon-epoxy plate by Legendre polynomial method. Some significant works were studied by Kaushik and Chopra [15] as well as Gogna and Chander [14] based on reflection and transmission of general plane SH-waves at the plane interface between two heterogeneous homogeneous viscoelastic media and anisotropic inhomogeneous viscoelastic half-spaces respectively.…”

Section: Introductionmentioning

confidence: 99%

Generation and Propagation of SH Waves Due to Shearing Stress Discontinuity in Linear Orthotropic Viscoelastic Layered Structure

Singh

Koley

Chaki

2021

Int. J. Appl. Comput. Math

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This present paper deals with the generation and propagation of SH wave due to shearingstress discontinuity at the common interface of a linear orthotropic viscoelastic layer of finite thickness overlying linear orthotropic viscoelastic half-space. Laplace and Fourier transformations in combination with the modified Cagniard-De Hoop method have been adopted as the solution technique for the present problem. The free surface displacement field has been obtained in integral form for four distinct cases of shear-stress discontinuity (Case 1, 2, 3 and 4) at the common interface of stratum and substrate of the layered structure. Numerical computation and graphical demonstration have been carried out to observe the profound effects of various affecting parameters viz. time of disturbance, distance from the source of disturbance, attenuation parameter and angular frequency on free surface displacement field which serve as major highlights of the present study.

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Investigation of guided waves propagation in orthotropic viscoelastic carbon–epoxy plate by Legendre polynomial method

Cited by 35 publications

References 12 publications

Properties of circumferential non-propagating waves in functionally graded piezoelectric cylindrical shells

Properties of circumferential non-propagating waves in functionally graded piezoelectric cylindrical shells

A Recursive Legendre Polynomial Analytical Integral Method for the Fast and Efficient Modelling Guided Wave Propagation in Rectangular Section Bars of Orthotropic Materials

Generation and Propagation of SH Waves Due to Shearing Stress Discontinuity in Linear Orthotropic Viscoelastic Layered Structure

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