Thermoelastic guided wave in fractional order functionally graded plates: An analytical integration Legendre polynomial approach

Wang, Xianhui; Li, Fanglin; Zhang, Xiaoming; Yu, Jiangong; Qiao, Hui

doi:10.1016/j.compstruct.2020.112997

Cited by 10 publications

(3 citation statements)

References 26 publications

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“…Then the analytical expression is deduced based on the orthogonality of Legendre polynomial for each type and used to improve the computational efficiency. The efficiency of the analytical integration on time‐consuming problems has been verified in references 27,28 . In reference, 27 the analytical expressions are developed for functionally graded structures based on the series expansion form of Legendre polynomial.…”

Section: Introductionmentioning

confidence: 99%

“…The efficiency of the analytical integration on time-consuming problems has been verified in references. 27,28 In reference, 27 the analytical expressions are developed for functionally graded structures based on the series expansion form of Legendre polynomial. In reference, 28 the analytical expressions are developed for uniform hollow cylinder mainly based on the iterative calculations.…”

Section: Introductionmentioning

confidence: 99%

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An analytical integration Legendre polynomial series approach for Lamb waves in fractional order thermoelastic multilayered plates

Wang

Zhang

et al. 2022

Math Methods in App Sciences

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The Legendre polynomial series approach (LPSA) has been widely used to solve guided wave propagation in various structures since 1999. The LPSA directly introduces the boundary conditions into the control equations through the rectangular window function. However, in the solving process, the Legendre polynomial series, the rectangular window function, and their derivatives are introduced into the integral kernel functions, which results in a lot of CPU time on the abundant numerical integration calculations. To overcome this defect, an analytical integration Legendre polynomial series approach (AILPSA) is presented and is used to solve the Lamb waves in fractional order thermoelastic multilayered plates. Coupled wave equations and heat conduction equation are solved by the AILPSA and the LPSA, respectively. Comparison between two approaches indicates the computational efficiency of the AILPSA is improved by more than 90%. In addition, a backward error estimation is given in the convergency analysis to make up for the deficiency of the numerical experiments. Finally, the influence of fractional order on the thermoelastic Lamb wave is discussed.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An analytical integration Legendre polynomial series approach for Lamb waves in fractional order thermoelastic multilayered plates

Wang

Zhang

et al. 2022

Math Methods in App Sciences

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“…This motivates the authors to extend the Legendre orthogonal polynomial method (LOPM) to investigate the dispersion relations of Lamb and SH waves in FG micro/nano-plates. Since LOPM does not need to solve the FG structure hierarchically, it has been widely utilized to study guide wave propagation in various FG macro-structures [29][30][31]. Considering the couple stress effect, Liu et al [32] developed LOPM to calculate the reflection and transmission coefficients of FG micro-plates immersed in liquid.…”

Section: Introductionmentioning

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

Zhang

et al. 2021

Arch Appl Mech

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Thermoelastic guided wave in fractional order functionally graded plates: An analytical integration Legendre polynomial approach

Cited by 10 publications

References 26 publications

An analytical integration Legendre polynomial series approach for Lamb waves in fractional order thermoelastic multilayered plates

An analytical integration Legendre polynomial series approach for Lamb waves in fractional order thermoelastic multilayered plates

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

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

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