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首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >Three dimensional transient Green's functions in a thermoelastic transversely isotropic half-space
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Three dimensional transient Green's functions in a thermoelastic transversely isotropic half-space

机译:三维瞬态绿色在热弹性横向各向同性半空间中的功能

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摘要

A transversely isotropic thermoelastic half-space in both mechanical and thermal points of view is considered as the domain of the initial boundary value problem involved in this paper. The governing partial differential equations of thermoelasticity in a cylindrical coordinate system are uncoupled with the aid of a complete set of displacement-potential and temperature-potential functions, which with the help of Fourier series decomposition and Hankel-Laplace integral transforms, are reduced to ordinary differential equations in terms of depth. Then, the general solutions due to an arbitrary patch-load and surface heat flux are investigated for the case of a point load varying with time as Heaviside step function and a point heat flux varying with time as Dirac delta function in order to compute the related Green's functions. The governing equations for the potential functions are in such a way that different longitudinal and transverse waves are recognized and the transport properties can be discovered from the governing equations. Some numerical illustrations are also presented to depict the dependency of response on the thermal properties as well as the anisotropy of the medium.
机译:机械和热观点的横向各向同性热弹性半空间被认为是本文中涉及的初始边界值问题的域。圆柱坐标系中热弹性的控制局部微分方程借助于一组完整的位移 - 电位和温度 - 电位功能来耦合,这在傅立叶串联分解和Hankel-Laplace积分变换的帮助下,减少到普通在深度方面的微分方程。然后,针对随着时间的时间和点热通量随时间变化而随着DIRAC DELTA函数而变化的时间变化的点负载而变化的点负载,作为狄拉克倍增功能变化的点载荷和表面热通量的一般溶液。为了计算相关的绿色的功能。潜在功能的控制方程处于识别不同的纵向和横波,可以从控制方程发现传输特性。还提出了一些数值图以描绘对响应对热性质以及介质各向异性的依赖性。

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