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首页> 外文期刊>Journal of thermal stresses >D'ALEMBERT'S SOLUTION IN THERMOELASTICITY-IMPACT OF A ROD AGAINST A HEATED BARRIER: PART I.A CASE OF UNCOUPLED STRAIN AND TEMPERATURE FIELDS
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D'ALEMBERT'S SOLUTION IN THERMOELASTICITY-IMPACT OF A ROD AGAINST A HEATED BARRIER: PART I.A CASE OF UNCOUPLED STRAIN AND TEMPERATURE FIELDS

机译：D'ALEMBERT在杆对热障的热弹性影响中的解决方案：第一部分：应变和温度场不耦合的情况

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The problem of impact of a thermoelastic rod against a heated rigid harrier is considered, in so doing lateral surfaces and free end of the rod are heat insulated, while there is either free heat exchange between the rod and the rigid obstacle within contacting end or ideal thermal contact, as a particular case. The rod's thermoelastic behavior is described by the Green-Naghdi theory of thermoelasticity. D'Alembert's method, which is based on the analytical solution of equations of the hyperbolic type describing the dynamic behavior of the thermoelastic rod, is used as the method of solution. This solution involves four arbitrary functions which are determined from the initial and boundary conditions and are piecewise constant functions. The procedure developed enables one to analyze the influence of thermoelastic parameters on the values to be found, as well as to investigate numerically the longitudinal coordinate dependence of the desired functions at each fixed instant of the time beginning from the moment of the rod's collision with the barrier up to the moment of its rebound. The case of uncoupled stress and temperature fields is examined in the first part of the paper, while the case of coupling thermoelasticity is considered in detail in the companion paper. It has been shown that the possibility for generating the reflected thermal wave from the incident elastic wave at the free rod's end is unavailable in the case of the uncoupled strain and temperature fields, and that the rod's rebound may occur either at the moment of arrival at the contact place of the reflected elastic wave from the incident thermal wave or at the time when the reflected elastic wave from the incident elastic wave reaches the contact point.
机译：考虑到热弹性杆撞击加热的刚性架的问题，这样做的目的是使杆的侧面和自由端隔热，而在杆和接触端内的刚性障碍物之间存在自由的热交换，或者在理想状态下热接触，在特定情况下。杆的热弹性行为由Green-Naghdi热弹性理论描述。求解方法是基于描述双曲线类型方程的热解的D'Alembert方法，该双曲线类型的方程描述了热弹性杆的动态行为。此解决方案涉及四个任意函数，这些函数是根据初始条件和边界条件确定的，它们是分段常数函数。开发的程序使人们能够分析热弹性参数对要找到的值的影响，并在从杆与杆碰撞的时刻开始的每个固定时刻，数值研究所需功能的纵向坐标依赖性。直至反弹的障碍。在本文的第一部分中研究了应力场与温度场不耦合的情况，而伴随热弹性的情况则在随附的论文中进行了详细讨论。已经表明，在应变场和温度场未耦合的情况下，无法从自由杆端的入射弹性波产生反射热波的可能性，并且杆的回弹可能会在到达时产生。来自入射热波的反射弹性波的接触位置，或者来自入射弹性波的反射弹性波到达接触点的时间。

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