Thermomechanical Responses of 3D Media Under Moving Heat Sources Based on Fractional-Order Strains
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摘要: 基于分数阶应变理论,研究了移动热源作用下三维弹性体的热机动态响应.将分数阶应变理论下的控制方程应用于三维半空间模型,通过Laplace积分变换、双重Fourier变换及其数值反变换对控制方程进行求解,得到了不同热源速度和不同分数阶参数下,无量纲温度、应力、应变和位移的分布规律.结果表明,分数阶应变参数对机械波影响显著而对热波影响有限,热源速度对热机械波影响显著.Abstract: Based on the theory of fractional-order strains, the thermomechanical dynamic responses of 3D elastomers under moving heat sources were studied. The governing equations under the theory of fractional-order strains were applied to the 3D semi-space model, and solved by means of the Laplace transform, the double Fourier transform and its numerical reverse transform. The distributions of non-dimensional temperatures, stresses, strains and displacements were obtained under different heating source velocities and different fractional-order parameters. The results show that, the fractional-order strain parameters have significant effects on mechanical waves but minor effects on heat waves, and the heat source velocity has significant effects on thermomechanical waves.
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Key words:
- 3D model /
- Laplace transform /
- Fourier transform /
- fractional-order strain /
- moving heat source
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[1] LORD H W, SHULMAN Y A. A generalized dynamical theory of thermoelasticity[J]. Journal of the Mechanics and Physics of Solids,1967,15(5): 299-309. [2] GREEN A E, LINDSAY K A. Thermoelasticity[J]. Journal of Elasticity,1972,2(1): 1-7. [3] GREEN A E, NAGHDI P M. On undamped heat waves in an elastic solid[J]. Journal of Thermal Stresses ,1992,15(2): 252-264. [4] MORSE R M, FESHBACH H. Methods of theoretical physics[J]. American Journal of Physics,1953,22(12): 5-12. [5] MUSII R S. Equations in stresses for two- and three-dimensional dynamic problems of thermoelasticity in spherical coordinates[J]. Materials Science,2003,39(1): 48-53. [6] PODNIL’CHUK IU N, KIRICHENKO A M. Thermoelastic deformation of a parabolic cylinder[J]. Vychislitel’naia i Prikladnaia Matematika,1989,67: 80-88. [7] EZZAT M A, YOUSSEF H M. Three-dimensional thermal shock problem of generalized thermoelastic half-space[J]. Applied Mathematical Modelling,2010,34(11): 3608-3622. [8] EZZAT M A, YOUSSEF H M. Two-temperature theory in three-dimensional problem for thermoelastic half space subjected to ramp type heating[J]. Mechanics of Composite Materials & Structures,2014,21(4): 293-304. [9] EZZAT M A, YOUSSEF H M. Three-dimensional thermo-viscoelastic material[J]. Mechanics of Advanced Materials and Structures,2016,23(1): 108-116. [10] YOUSSEF H M. Generalized thermoelastic infinite medium with cylindrical cavity subjected to moving heat source[J]. Mechanics Research Communications,2009,36(4): 487-496. [11] YOUSSEF H M. Two-temperature generalized thermoelastic innite medium with cylindrical cavity subjected to moving heat source[J]. Archive of Applied Mechanics,2010,80(11): 1213-1224. [12] YOUSSEF H M, AL-LEHAIBI E A N. The boundary value problem of a three-dimensional generalized thermoelastic half-space subjected to moving rectangular heat source[J]. Boundary Value Problems,2019,8: 1-15. [13] POVSTENKO Y Z. Fractional heat conduction equation and associated thermal stresses[J]. Journal of Thermal Stresses,2004,28(1): 83-102. [14] POVSTENKO Y Z. Fractional thermoelasticity[J]. Encyclopedia of Thermal Stresses,2015,219: 1778-1787. [15] MA Y B, LIU Z Q, HE T H. Two-dimensional electromagneto-thermoelastic coupled problem under fractional order theory of thermoelasticity[J]. Journal of Thermal Stresses,2018,41(5): 645-657. [16] MA Y B, HE T H. Investigation on a thermo-piezoelectric problem with temperature-dependent properties under fractional order theory of thermoelasticity[J]. Mechanics of Advanced Materials and Structures,2019,26(6): 552-558. [17] MA Y B, PENG W. Dynamic response of an infinite medium with a spherical cavity on temperature-dependent properties subjected to a thermal shock under fractional-order theory of thermoelasticity[J]. Journal of Thermal Stresses,2018,41(3): 302-312. [18] 马永斌, 何天虎. 基于分数阶热弹性理论的含有球型空腔无限大体的热冲击动态响应[J]. 工程力学, 2016,33(7): 31-38.(MA Yongbin, HE Tianhu. Thermal shock dynamic response of an infinite body with a spherical cavity under fractional order theory of thermoelasticty[J]. Engineering Mechanics,2016,33(7): 31-38.(in Chinese)) [19] MA Y B, CAO L C, HE T H. Variable properties thermopiezoelectric problem under fractional thermoelasticity[J]. Smart Structures and Systems,2018,21(2): 163-170. [20] YOUSSEF H M. Theory of generalized thermoelasticity with fractional order strain[J]. Journal of Vibration and Control,2015,22(18): 3840-3857. [21] YOUSSEF H M, AL-LEHAIBI E A N. State-space approach to three-dimensional generalized thermoelasticity with fractional order strain[J]. Mechanics of Advanced Materials and Structures,2019,26(10): 878-885. [22] XUE Z N, YU Y J, LI X Y, et al. Nonlocal thermoelastic analysis with fractional order strain in multilayered structures[J]. Journal of Thermal Stresses,2017,41(1): 80-97. [23] 包立平, 李文彦, 吴立群. 非Fourier温度场分布的奇摄动解[J]. 应用数学和力学, 2019,40(5): 68-77.(BAO Liping, LI Wenyan, WU Liqun. Singularly perturbed solutions of non-Fourier temperature field distribution in single-layer materials[J]. Applied Mathematics and Mechanics,2019,40(5): 68-77.(in Chinese)) [24] YOUSSEF H M. A two-temperature generalized thermoelastic medium subjected to a moving heat source and ramp-type heating: a state-space approach[J]. Journal of Mechanics of Materials and Structures,2010,4(9): 1637-1649. [25] TZOU D Y. Macro- to Microscale Heat Transfer: the Lagging Behavior [M]. Washington DC: John Wiley & Sons, 1996.
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