Complete guided wave modes in piezoelectric cylindrical structures with fan-shaped cross section using the modified double orthogonal polynomial series method
“…Viscoelastic plate described in Cartesian coordinate system (X, Y, Z) occupies the region 0 ≤ Z ≤ H, as shown in Figure 1. Numerical codes based on Legendre polynomial 1,9–12 and Newton–Raphson 1,16 methods are developed and implemented to modeling dispersion and attenuation curves. The associated algorithm that summarizes the different numerical steps used by polynomial and Newton–Raphson methods is presented below, …”
Section: Viscoelastic Structures Design and The Use Of Slowness Curvesmentioning
confidence: 99%
“…[3][4][5][6][7] Consequently, one part of dispersion and attenuation curves may be missed. 8 To overcome these drawbacks, Legendre polynomial method 1,[9][10][11][12] has been proposed to calculate the guided waves in complex viscoelastic structures and that poses several advantages of effectiveness and numerically stability over traditional matrix method.…”
mentioning
confidence: 99%
“…Instead, the second objective is to study second harmonic Lamb modes. Numerical codes based on Legendre polynomial 1,[9][10][11][12] and Newton-Raphson 1,16 methods are developed and implemented to predict dispersion and attenuation curves with both hysteretic and Kelvin-Voigt viscoelastic models. Second harmonic generation is calculated to determine the double frequency Lamb modes accompanying the propagation of the primary mode.…”
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.
“…Viscoelastic plate described in Cartesian coordinate system (X, Y, Z) occupies the region 0 ≤ Z ≤ H, as shown in Figure 1. Numerical codes based on Legendre polynomial 1,9–12 and Newton–Raphson 1,16 methods are developed and implemented to modeling dispersion and attenuation curves. The associated algorithm that summarizes the different numerical steps used by polynomial and Newton–Raphson methods is presented below, …”
Section: Viscoelastic Structures Design and The Use Of Slowness Curvesmentioning
confidence: 99%
“…[3][4][5][6][7] Consequently, one part of dispersion and attenuation curves may be missed. 8 To overcome these drawbacks, Legendre polynomial method 1,[9][10][11][12] has been proposed to calculate the guided waves in complex viscoelastic structures and that poses several advantages of effectiveness and numerically stability over traditional matrix method.…”
mentioning
confidence: 99%
“…Instead, the second objective is to study second harmonic Lamb modes. Numerical codes based on Legendre polynomial 1,[9][10][11][12] and Newton-Raphson 1,16 methods are developed and implemented to predict dispersion and attenuation curves with both hysteretic and Kelvin-Voigt viscoelastic models. Second harmonic generation is calculated to determine the double frequency Lamb modes accompanying the propagation of the primary mode.…”
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.
Traditional finite element methods for the phononic crystals (PCs) with fluid-structure interaction (FSI) are generally based on the deterministic methodology. However, the uncertainty between the design and the manufactural values of the PCs and the uncertainty from the material properties deviation are always unavoidable, which may give rise to the discrepancy of the physical responses. This paper presents a hybrid uncertain mass-redistributed finite element method (HUMR-FEM) to quantitatively describe the uncertainty of the PCs. The MR-FEM is proposed to deal the PCs with FSI to minimize dispersion error, and the hybrid uncertainty is treated as the random uncertainty type with bounded distribution parameters instead of a precise one. The uncertainty model can be transformed into the deterministic computation of the extreme bounds of the statistical characteristics. The influences of the hybrid uncertainty on the physical responses including the band structures and mode shape of the PCs with FSI are investigated. The accuracy and efficiency of the proposed method are validated through several numerical examples including different materials combinations and lattice forms.
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