Mapped orthogonal functions method applied to acoustic waves-based devices

Lefebvre, Jean-Etienne; Yu, Jiangong; Ratolojanahary, F. E.; Elmaimouni, L.; Xü, Wei-Jiang; Gryba, T.

doi:10.1063/1.4953847

Cited by 40 publications

(9 citation statements)

References 49 publications

(62 reference statements)

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“…So, the above boundary conditions could be automatically incorporated into the following constitutive equations. The approach to deal with the boubdary conditions has been demonstrated [28] in detail. Accordingly, the generalized constitutive equations a functionally graded 2D hexagonal quasi‐crystal plate can be expressed as follows [29]:

\begin{matrix} left T_{11} = ((), C_{11}^{false(l false)} ε_{11} + C_{12}^{false(l false)} ε_{22} + C_{13}^{false(l false)} ε_{33} + R_{1}^{false(l false)} w_{11} + R_{2}^{false(l false)} w_{22}) π (z) \\ left T_{22} = ((), C_{12}^{false(l false)} ε_{11} + C_{11}^{false(l false)} ε_{22} + C_{13}^{false(l false)} ε_{33} + R_{2}^{false(l false)} w_{11} + R_{1}^{false(l false)} w_{22}) π (z) \\ left T_{33} = ((), C_{13}^{false(l false)} ε_{11} + C_{13}^{false(l false)} ε_{22} + C_{33}^{false(l false)} ε_{33} + R_{3}^{false(l false)} w_{11} + R_{3}^{false(l false)} w_{22}) π (z) \\ left T_{23} = (() 2 C_{44}^{(l)} ε_{23} + R_{4}^{(l)} w_{23}) π (z) \\ left T_{13} = ((), 2 C_{44}^{false(l false)} ε_{13} + R_{...}) \end{matrix}

…”

Section: Mathematics and Formulationsmentioning

confidence: 99%

Guided wave characteristics in the functionally graded two‐dimensional hexagonal quasi‐crystal plate

Zhang

et al. 2019

Z Angew Math Mech

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Due to the limit of preparation technology, defects, such as cracks and inclusions, are inevitable in the functionally graded quasi‐crystal material. For the purpose of the guided wave non‐destructive testing on the functionally graded (FG) two‐dimensional(2‐D) hexagonal quasi‐crystal(QC) plates, Lamb and SH wave characteristics in the context of the Bak's model are investigated by means of the Legendre polynomial method. The convergence of the polynomial method applied on the FG 2‐D hexagonal QC plate is analyzed. Some new wave characteristics resulted from the phonon‐phason coupling effect are revealed. There are three Lamb‐like modes without cut‐off frequencies for the x‐y and y‐z QC plates, but four Lamb‐like modes without cut‐off frequencies for the x‐z QC plate. For phonon modes, phonon displacements and stresses are bigger than phason displacements and stresses. However, they are just opposite for phason modes. It can be utilized to distinguish phonon modes and phason modes.

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\begin{matrix} left T_{11} = ((), C_{11}^{false(l false)} ε_{11} + C_{12}^{false(l false)} ε_{22} + C_{13}^{false(l false)} ε_{33} + R_{1}^{false(l false)} w_{11} + R_{2}^{false(l false)} w_{22}) π (z) \\ left T_{22} = ((), C_{12}^{false(l false)} ε_{11} + C_{11}^{false(l false)} ε_{22} + C_{13}^{false(l false)} ε_{33} + R_{2}^{false(l false)} w_{11} + R_{1}^{false(l false)} w_{22}) π (z) \\ left T_{33} = ((), C_{13}^{false(l false)} ε_{11} + C_{13}^{false(l false)} ε_{22} + C_{33}^{false(l false)} ε_{33} + R_{3}^{false(l false)} w_{11} + R_{3}^{false(l false)} w_{22}) π (z) \\ left T_{23} = (() 2 C_{44}^{(l)} ε_{23} + R_{4}^{(l)} w_{23}) π (z) \\ left T_{13} = ((), 2 C_{44}^{false(l false)} ε_{13} + R_{...}) \end{matrix}

…”

Section: Mathematics and Formulationsmentioning

confidence: 99%

Guided wave characteristics in the functionally graded two‐dimensional hexagonal quasi‐crystal plate

Zhang

et al. 2019

Z Angew Math Mech

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“…The theoretical bases for how position-dependent physical constants fulfil this role has been detailed in Ref. [34].…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Dispersion characteristics of guided waves in functionally graded anisotropic micro/nano-plates based on the modified couple stress theory

Liu

Xü

et al. 2021

Thin-Walled Structures

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In this paper, the acoustic wave motion characteristics of Lamb and SH waves in functionally graded (FG) anisotropic micro/nano-plates are studied based on the modified couple stress theory. A higher efficient computational approach, the extended Legendre orthogonal polynomial method (LOPM) is utilized to deduce solving process. This polynomial method does not need to solve the FG micro/nano-plates hierarchically, which provides a more realistic analysis model for FG micro/nano-plates and has high computational efficiency. Simultaneously, the solutions based on the global matrix method (GMM) are also deduced to verify the correctness of the polynomial method. Furthermore, the effects of size and material gradient are studied in detail. Numerical results show that the size effect causes wrinkles in Lamb wave dispersion curves, and the material gradient characteristic changes the amplitude and range of wrinkles. For SH waves, the length scale parameter L x increases the cut-off frequency but does not change the overall trend of the dispersion curve; on the contrary, L z does not change the cut-off frequency but causes the dispersion curve to show an upward trend.

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“…Then, the abovementioned boundary conditions can be automatically incorporated in the constitutive equations. Lefebvre et al 36 expounded the theoretical bases for mechanical and electrical boundary conditions and explained how position-dependent physical constants could fulfill this role.…”

Section: Mathematics and Formulation Of The Problemmentioning

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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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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Mapped orthogonal functions method applied to acoustic waves-based devices

Cited by 40 publications

References 49 publications

Guided wave characteristics in the functionally graded two‐dimensional hexagonal quasi‐crystal plate

Guided wave characteristics in the functionally graded two‐dimensional hexagonal quasi‐crystal plate

Dispersion characteristics of guided waves in functionally graded anisotropic micro/nano-plates based on the modified couple stress theory

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

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