Wave propagation in thermoelastic inhomogeneous hollow cylinders by analytical integration orthogonal polynomial approach

Wang, Xianhui; Li, Fanglin; Zhang, Bo; Yu, Jiangong; Zhang, Xiaoming

doi:10.1016/j.apm.2021.06.008

Cited by 17 publications

(8 citation statements)

References 30 publications

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“…The open results [21,29] indicates that the integrals in Equation ( 13) can be obtained analytically to improve the computational efficiency,…”

Section: N-lpsamentioning

confidence: 99%

“…The dispersion relation of the SH waves in orthotropic plates has been obtained by analytical expression [21]. However, it is difficult to obtain the analytical expression of the dispersion relation in nonlocal nanoplates due to the constitutive relation in Equations ( 2) or (6).…”

Section: N-lpsamentioning

confidence: 99%

“…As an efficient numerical method, the Legendre polynomial series approach (LPSA) [19–25] has been widely applied to solve the wave propagation for the advantages of small‐scale characteristic matrix and low solving difficulty. Othmani et al.…”

Section: Introductionmentioning

confidence: 99%

“…As an efficient numerical method, the Legendre polynomial series approach (LPSA) [19][20][21][22][23][24][25] has been widely applied to solve the wave propagation for the advantages of small-scale characteristic matrix and low solving difficulty. Othmani et al [26] reviewed the LPSA, and further summarized the advantages of the LPSA for wave propagation in elastic, piezoelectric and magneto-electro-elastic composites.…”

Section: Introductionmentioning

confidence: 99%

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Formulation of SH wave characteristics in nonlocal nanoplates

Wang

Qiao

et al. 2022

Z Angew Math Mech

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The scale effect of mechanical properties is one of the most critical issues in application of the nanostructures. In order to study the scale effect on SH waves in nanoplates, a Legendre polynomial series method combined with the nonlocal theory (N-LPSA) is developed in this paper. The presented method enables the boundary condition achieved quickly by the derived iterative solution formula of the integral, which contains nonlocal factors and Legendre polynomials.Besides, the formula of escape frequency is deduced analytically to facilitate the study of wave propagation law. Numerical comparisons show the correctness of the N-LPSA. The results indicate that cut-off frequencies of some higher-order modes are higher than their escape frequencies. The anisotropy with the nonlocal effects can lead to the intersection of the modal curves, which does not appear in classical structures. Moreover, the fitting formulas of cut-off and crossing frequencies are developed to predict the compression and the intersection of the modal curves, respectively.

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“…The open results [21,29] indicates that the integrals in Equation ( 13) can be obtained analytically to improve the computational efficiency,…”

Section: N-lpsamentioning

confidence: 99%

Section: N-lpsamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Formulation of SH wave characteristics in nonlocal nanoplates

Wang

Qiao

et al. 2022

Z Angew Math Mech

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“…As an effective method to deal with FGM structures without the delamination, the Legendre polynomial method has been utilized to investigate guided waves propagating in various FGM crystal structures, such as plates (Lefebvre et al, 2001), cylinders (Wang et al, 2021), spherical plates (Yu and Ma, 2010), rectangular bars (Yu et al, 2015a), rings (Yu et al, 2015b), and cylindrical structures with sector cross-sections (Zhang et al, 2018). Therefore, it is extended to investigate the propagative and evanescent Lamb and SH waves in the FGPQC plates in the context of these two models, respectively.…”

Section: Introductionmentioning

confidence: 99%

Guided waves in a functionally graded 1-D hexagonal quasi-crystal plate with piezoelectric effect

Zhang

Zhou

et al. 2021

Journal of Intelligent Material Systems and Structures

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For the purpose of design and optimization for piezoelectric quasi-crystal transducers, guided waves in a functionally graded 1-D hexagonal piezoelectric quasi-crystal plate are investigated. In this paper, a model combined with the Bak’s and elastohydrodynamic models is utilized to derive governing equations of wave motion, and real, pure imaginary, and complex roots of governing equations are calculated by using the modified Legendre polynomial method. Subsequently, dispersion curves and displacements of phonon and phason modes are illustrated. Then, guided waves in functionally graded 1-D hexagonal piezoelectric quasi-crystal plates with different quasi-periodic directions are studied. And the phonon-phason coupling effect on Lamb and SH waves are analyzed. Accordingly, some interesting results are obtained: The phonon-phason coupling just affects Lamb waves in the x- and z-direction quasi-crystal plates, and SH waves in the y-direction quasi-crystal plate. Besides, frequencies of propagative phason modes decrease as phonon-phason coupling coefficients Ri increase. Furthermore, a variation in the polarization has a more significant influence on phonon modes, and a variation in the quasi-periodic direction has a more significant influence on phason modes.

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Generalized thermo-elastic waves propagating in bars with a rectangular cross-section

Zhang

et al. 2021

Arch Appl Mech

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Wave propagation in thermoelastic inhomogeneous hollow cylinders by analytical integration orthogonal polynomial approach

Cited by 17 publications

References 30 publications

Formulation of SH wave characteristics in nonlocal nanoplates

Formulation of SH wave characteristics in nonlocal nanoplates

Guided waves in a functionally graded 1-D hexagonal quasi-crystal plate with piezoelectric effect

Generalized thermo-elastic waves propagating in bars with a rectangular cross-section

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