Stiffness Transfer Matrix Method (STMM) for stable dispersion curves solution in anisotropic composites

Kamal, Ayman; Giurgiutiu, Victor

doi:10.1117/12.2044789

Cited by 23 publications

(27 citation statements)

References 19 publications

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“…Figure 2 compares the results obtained from LPM with those obtained by TMM for the case of lamb and SH modes in a single plate. As can be observe in Fig.2 1 x axis, the lamb and SH wave are coupled and the SH0 mode has some degree of dispersion.it can also be found that the velocity of the lamb waves tend to abate with increasing the propagation angel.…”

Section: Numerical Examplesmentioning

confidence: 58%

“…Consider the general case of a layer structure of infinite extent in the the 1 x and 3 x directions and thickness H in the 2 x direction, as given in Fig. 1.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…Composite materials play an important role in many structural components, such as auto parts, boat hulls, and aircraft structures [1].In recent years, much attention has been paid to nondestructive testing method for composite. Ultrasonic guided waves is effective way to detect the presence of structure defect such as damage, disbands and delaminations.…”

Section: Introductionmentioning

confidence: 99%

“…There are many methods to investigate the propagation characteristics of guided waves in composite laminates. These method include the Transfer matrix method (TMM) [3,4], the Global matrix method (GMM) [5], the scattering matrix method(SMM) [6], the stiffness transfer matrix method(STMM) [1], reverberation-ray matrix method(RMMM) [7,8], the finite element method (FEM) [9][10][11], and the semi-analysis finite element method (SAFE) [12]. Guided waves propagation can then be found by imposing appropriate boundary.…”

Section: Introductionmentioning

confidence: 99%

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Modelling guided waves in anisotropic plates using the Legendre polynomial method

Zheng

2017

MATEC Web Conf.

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Abstract.A numerical method to compute phase dispersion curve in unidirectional laminate is described. The basic feature of the proposed method is the expansion of fields quantities in single layer on different polynomial bases. The Legendre polynomial method avoid to solve the transcendental dispersion equation of guided wave. Guided waves that have very close propagation constants are calculated with great accuracy. Numerical solution of dispersion relation are calculated for guided waves propagation in orthotropic unidirectional fiber composites. The validation of the polynomial approach is depicted by a comparison between the associated solution and those obtained using Transfer matrix method.

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Section: Numerical Examplesmentioning

confidence: 58%

“…Consider the general case of a layer structure of infinite extent in the the 1 x and 3 x directions and thickness H in the 2 x direction, as given in Fig. 1.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modelling guided waves in anisotropic plates using the Legendre polynomial method

Zheng

2017

MATEC Web Conf.

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“…Besides, this approach has the same dimension and is only slightly more computationally efficient in comparison with the transfer matrix method (Giurgiutiu, 2008). This approach is used by Kamal and Giurgiutiu (2014) in case of the multilayered anisotropic composites. The authors also verify the stiffness matrix method with the use of the transfer matrix method, program DISPRESE and the semi-analytical finite element method (Sorohan et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

Determination of Dispersion Curves for Composite Materials with the Use of Stiffness Matrix Method

Barski

Pająk

2017

Acta Mechanica Et Automatica

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Elastic waves used in Structural Health Monitoring systems have strongly dispersive character. Therefore it is necessary to determine the appropriate dispersion curves in order to proper interpretation of a received dynamic response of an analyzed structure. The shape of dispersion curves as well as number of wave modes depends on mechanical properties of layers and frequency of an excited signal. In the current work, the relatively new approach is utilized, namely stiffness matrix method. In contrast to transfer matrix method or global matrix method, this algorithm is considered as numerically unconditionally stable and as effective as transfer matrix approach. However, it will be demonstrated that in the case of hybrid composites, where mechanical properties of particular layers differ significantly, obtaining results could be difficult. The theoretical relationships are presented for the composite plate of arbitrary stacking sequence and arbitrary direction of elastic waves propagation. As a numerical example, the dispersion curves are estimated for the lamina, which is made of carbon fibers and epoxy resin. It is assumed that elastic waves travel in the parallel, perpendicular and arbitrary direction to the fibers in lamina. Next, the dispersion curves are determined for the following laminate [0°, 90°, 0°, 90°, 0°, 90°, 0°, 90°] and hybrid [Al, 90°, 0°, 90°, 0°, 90°, 0°], where Al is the aluminum alloy PA38 and the rest of layers are made of carbon fibers and epoxy resin.

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Viscoelastic rheological models for guided acoustic waves: Single mode at high frequency and second harmonic generation of Lamb and SH modes

Takali

Othmani

2022

Math Methods in App Sciences

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The previous published work by Othmani et al. invites a further useful discussion on how the viscoelastic rheological model affects the second harmonic and single modes of guided waves. However, this paper has two main objectives.The first objective is to establish a simple relationship between the Rayleigh waves velocity (V R ), fundamental Lamb modes (A 0 and S 0 ), and the shear wave velocity (V S ) in unidirectional viscoelastic carbon-epoxy at high frequency. The second objective is to study the second harmonic Lamb modes. Numerical codes based on Legendre polynomial and Newton-Raphson methods are developed and implemented to predict dispersion and attenuation curves. The second harmonic generation was investigated with the hysteretic and Kelvin-Voigt viscoelastic models. Results showed that rheological models have a much larger effect on the attenuation curves than the ones on the dispersion trajectories. Additionally, the optimal angles of Lamb and SH modes in unidirectional carbon-epoxy under Snell-Descartes law was investigated. The present numerical results may render as a useful message for the rheological community.

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Stiffness Transfer Matrix Method (STMM) for stable dispersion curves solution in anisotropic composites

Cited by 23 publications

References 19 publications

Modelling guided waves in anisotropic plates using the Legendre polynomial method

Modelling guided waves in anisotropic plates using the Legendre polynomial method

Determination of Dispersion Curves for Composite Materials with the Use of Stiffness Matrix Method

Viscoelastic rheological models for guided acoustic waves: Single mode at high frequency and second harmonic generation of Lamb and SH modes

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