三相滞后对有球形空腔无限介质双温广义热弹性的影响

S·班尼克; M·卡诺尼亚

doi:10.3879/j.issn.1000-0887.2012.04.007

三相滞后对有球形空腔无限介质双温广义热弹性的影响

doi: 10.3879/j.issn.1000-0887.2012.04.007

加尔各答大学应用数学系,加尔各答700009,印度

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中图分类号: O343.6
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出版历程
- 收稿日期: 2010-12-20
- 修回日期: 2011-10-15
- 刊出日期: 2012-04-15

Effects of Three-Phase-Lag on Two Temperature Generalized Thermoelasticity for an Infinite Medium With a Spherical Cavity

Department of Applied Mathematics, University of Calcutta, Kolkata 700009, India

摘要

摘要: 就各向同性的无限弹性体，具有一个球形空腔时，从双温广义热弹性理论（2TT）角度，研究三相滞后热方程的热弹性相互作用问题．在三相滞后理论中，热传导方程是一个含时间四阶导数的、双曲型的偏微分方程．假设无限介质初始时静止，通过Laplace变换，将基本方程用向量矩阵微分方程的形式表示，然后通过状态空间法求解．将得到的通解应用于特殊问题：空腔边界上承受着热荷载（热冲击和坡型加热）和力学荷载．使用Fourier级数展开技术，实现Laplace变换的求逆．计算了铜类材料物理量的数值解．图形显示，两种模型：带能量耗散的双温Green-Naghdi理论（2TGNIII）和双温3相滞后模型（2T3相）明显不同．还对双温和坡型参数的影响进行了研究．
- 双温广义热弹性 /
- Green-Naghdi模型 /
- 三相滞后模型 /
- 球形空腔 /
- 状态空间法
Abstract: The thermoelastic interaction for the three-phase-lag heat equation in an isotropic infinite elastic body with a spherical cavity was studied in the context of two temperature generalized thermoelasticity theory (2TT). The heat conduction equation in the theory of three-phase-lag was a hyperbolic partial differential equation with a fourth order derivative with respect to time. The medium was assumed initially quiescent. By using the Laplace transformation, the fundamental equations had been expressed in the form of a vector-matrix differential equation, which was then solved by state space approach. The general solution obtained was applied to a specific problem, when the boundary of the cavity was subjected to thermal loading (thermal shock and ramp type heating) and the mechanical loading. The inversion of the Laplace transform was carried out by the Fourier series expansion techniques. The numerical values of the physical quantity were computed for copper like material. Significant dissimilarities between two models (two temperature Green-Naghdi theory with energy dissipation (2TGNIII) and two temperature three-phase-lag model (2T3phase)) were shown graphically. The effect of two temperature and the ramping parameters were also studied.
- two temperature generalized thermoelasticity /
- Green-Naghdi model /
- three-phase-lag model /
- spherical cavity /
- state-space approach

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