Wang Xianhui, Li Fanglin, Liu Yujian, Chen Huitao, Yu Jiangong. THERMOELASTIC WAVE PROPAGATION IN PLATES: AN IMPROVED LEGENDRE POLYNOMIAL APPROACH[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1277-1285. DOI: 10.6052/0459-1879-20-124
Citation:
Wang Xianhui, Li Fanglin, Liu Yujian, Chen Huitao, Yu Jiangong. THERMOELASTIC WAVE PROPAGATION IN PLATES: AN IMPROVED LEGENDRE POLYNOMIAL APPROACH[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1277-1285. DOI: 10.6052/0459-1879-20-124
Wang Xianhui, Li Fanglin, Liu Yujian, Chen Huitao, Yu Jiangong. THERMOELASTIC WAVE PROPAGATION IN PLATES: AN IMPROVED LEGENDRE POLYNOMIAL APPROACH[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1277-1285. DOI: 10.6052/0459-1879-20-124
Citation:
Wang Xianhui, Li Fanglin, Liu Yujian, Chen Huitao, Yu Jiangong. THERMOELASTIC WAVE PROPAGATION IN PLATES: AN IMPROVED LEGENDRE POLYNOMIAL APPROACH[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1277-1285. DOI: 10.6052/0459-1879-20-124
In recent years, the research of thermoelastic coupled wave has greatly promoted the development of high temperature online detection and laser ultrasonic technology. For its small attenuation, long propagation distance and wide signal coverage, ultrasonic guided wave has become one of the rapid development directions in the field of nondestructive testing. However, the development of guided wave high temperature on-line detection and laser ultrasonic guided wave technology is slow. The key lies in the difficulty in solving the coupled thermoelastic wave equation and the difficulty in studying the propagation and attenuation characteristics. As an effective method, Legendre polynomial approach has been widely used to solve the problem of guided wave propagation since 1999. But there are two shortcomings in this method, which limit its further development and application. Two defects are: (1) Due to the Legendre polynomial and its derivative in integral kernel function, the integrals in the solution process leads to low calculation efficiency; (2) Only the thermoelastic guided wave propagation with isothermal boundary conditions can be treated. In order to solve these two defects, an improved Legendre polynomial method is proposed to solve the fractional thermoelastic guided waves in plates. The analytical integral instead of numerical integration in the available conventional Legendre polynomial approach, which greatly improves the calculation efficiency. A new treatment of the adiabatic boundary condition for the Legendre polynomial is developed by introducing the temperature gradient expansion based on the rectangular window function. Compared with the available data shows the validity of the improved method. Comparison with the CPU time between two approaches indicates the higher efficiency of the presented approach. Finally, the phase velocity dispersion curves, attenuation curves, the stress, displacement and temperature distributions for a plate with different fractional orders are analysed. The fractional order has weak influence on the elastic mode velocity, but it has considerable influence on the elastic mode attenuation.
( Ding Juncai, Wu Bin, He Cunfu. The phase shift of SH0~guided wave propagating in bonding structure. Chinese Journal of Theoretical and Applied Mechanics, 2017,49(1):202-211 (in Chinese))
( Zhang Lele, Liu Xianglin, Liu Jinxi. Propagation characteristics of SH guided waves in a piezoelectric nanoplate. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(2):503-511 (in Chinese))
( He Cunfu, Zheng Mingfang, Lü Yan. Development, applications and challenges in ultrasonic guided waves testing technology. Chinese Journal of Scientific Instrument, 2016,37(8):1713-1735 (in Chinese))
[4]
Lefebvre JE, Zhang V, Gazalet J, et al. Legendre polynomial approach for modeling free-ultrasonic waves in multilayered plates. Journal of Applied Physics, 1999,85(7):3419-3427
[5]
Yu JG, Lefebvre JE, Guo YQ. Free-ultrasonic waves in multilayered piezoelectric plates: An improvement of the Legendre polynomial approach for multilayered structures with very dissimilar materials. Composites Part B Engineering, 2013,51:260-269
[6]
Elmaimouni L, Lefebvre JE, Zhang V, et al. A polynomial approach to the analysis of guided waves in anisotropic cylinders of infinite length. Wave Motion, 2005,42(2):177-189
[7]
Elmaimouni L, Lefebvre JE, Zhang V, et al. Guided waves in radially graded cylinders: A polynomial approach. NDT & E International, 2005,38(5):344-353
( Zhang Xiaoming, Li Zhi, Yu Jiangong. Dispersion characteristics of circumferential evanescent guided waves in orthotropic cylindrical curved plates. Journal of Beijing University of Technology, 2018,44(5):770-776 (in Chinese))
[9]
Yu JG, Wu B, Chen GQ. Wave characteristics in functionally graded piezoelectric hollow cylinders. Archive of Applied Mechanics, 2009,79(9):807-824
( Zhang Xiaoming, Gao Anru, Yu Jiangong, et al. Circumferential evanescent guided waves in functionally graded cylindrical curved plates. Chinese Journal of Solid Mechanics, 2018,39(5):462-471 (in Chinese))
[11]
Yu JG, Wu B, He CF. Guided thermoelastic waves in functionally graded plates with two relaxation times. International Journal of Engineering Science, 2010,48(12):1709-1720
[12]
Yu JG, Ding JC, Ma ZJ. On dispersion relations of waves in multilayered magneto-electro-elastic plates. Applied Mathematical Modelling, 2012,36(12):5780-5791
[13]
Zhang B, Yu JG, Zhang XM, et al. Complex guided waves in functionally graded piezoelectric cylindrical structures with sectorial cross-section. Applied Mathematical Modelling, 2018,63:288-302
[14]
Lord HW, Shulman YA. A generalized dynamical theory of thermoelasticity. Journal of the Mechanics and Physics of Solids, 1967,15(5):299-309
[15]
Green AE, Lindsay KA. Thermoelasticity. Journal of Elasticity, 1972,2:1-7
[16]
Green AE, Naghdi PM. On undamped heat waves in an elastic solid. Journal of Thermal Stresses, 1992,15:253-264
[17]
Heydarpour Y, Aghdam MM. Transient analysis of rotating functionally graded truncated conical shells based on the Lord--Shulman model. Thin-Walled Structures, 2016,104:168-184
[18]
Sarkar N, Lahiri A. The effect of gravity field on the plane waves in a fiber-reinforced two-temperature magneto-thermoelastic medium under Lord-Shulman theory. Journal of Thermal Stresses, 2013,36(7-9):895-914
[19]
Bagri A, Eslami MR. Generalized coupled thermoelasticity of disks based on the Lord--Shulman model. Journal of Thermal Stresses, 2004,27(8):691-704
( Xu Yeshou, Xu Zhaodong, Ge Teng, et al. Equivalent fractional order micro-structure standard linear solid model for viscoelastic materials. Chinese Journal of Theoretical and Applied Mechanics, 2017,49(5):1059-1069 (in Chinese))
[21]
Youssef HM. Theory of fractional order generalized thermoelasticity. Journal of Heat Transfer, 2010,132(6):1-7
Sherief HH, El-Sayed AMA, El-Latief AMA. Fractional order theory of thermoelasticity. International Journal of Solids and Structures, 2010,47(2):269-275
[24]
Tiwari R, Mukhopadhyay S. On harmonic plane wave propagation under fractional order thermoelasticity: An analysis of fractional order heat conduction equation. Mathematics and Mechanics of Solids, 2017, 10.1177/1081286515612528
[25]
Deswal S, Kalkal KK. Plane waves in a fractional order micropolar magneto-thermoelastic half-space. Wave Motion, 2014,51(1):100-113
[26]
Kumar R, Gupta V. Wave propagation at the boundary surface of an elastic and thermoelastic diffusion media with fractional order derivative. Applied Mathematical Modelling, 2015,39(5-6):1674-1688
[27]
Kumar R, Gupta V. Plane wave propagation and domain of influence in fractional order thermoelastic materials with three-phase-lag heat transfer. Mechanics of Advanced Materials and Structures, 2016,23(8):896-908
( Xu Guangying, Wang Jinbao, Xue Dawen. Investigations on the thermal behavior and associated thermal stresses of the fractional heat conduction for short pulse laser heating. Chinese Journal of Theoretical and Applied Mechanics, 2020,52(2):491-502 (in Chinese))
( Zhang Pei, He Tianhu. A generalized thermoelastic problem with nonlocal effect and memory-dependent derivative. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(3):508-516 (in Chinese))
[30]
Al-Qahtani H, Datta S. Thermoelastic waves in an anisotropic infinite plate. Journal of Applied Physics, 2004,96(7):3645-3658
[31]
Gradshteyn IS, Ryzhik IM, Jeffrey A. Table of Integrals, Series, and Products. Pittsburgh: Academic Press, 2007
DownLoad: