边缘有混合边界条件的半无限波导中波场的特性

IF 0.1
N. Gorodetskaya, I. Starovoit, T. Shcherbak
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引用次数: 0

摘要

本文研究了半无限弹性条形结构中瑞利-兰姆波第一次法向传播在条形结构边缘的反射所激发的波场,该条形结构部分为刚性夹持,部分为无应力条形结构。边值问题属于混合边值问题,其特征是在边界条件类型的变化点处存在应力的局部特征。为了解决这一边值问题,本文提出了一种叠加法,该方法考虑了由于未知系数的渐近性质而引起的应力特征。系数的渐近依赖关系是由特征的性质决定的,这是从静态问题的解中已知的。所得结果正确性的判据是控制了能量守恒定律的精度,在整个考虑的频率范围内,其误差不超过入射波能量的2%。本文对边界条件的精度进行了评价。结果表明,除了在一个特殊点($\epsilon$)周围外,沿半无限带的整个末端,边界条件都满足图形精度。在这种情况下,沿夹紧端在半无限带材附近的一个特殊应力点保持有限。区域$\epsilon$和有限应力的存在是由于这样一个事实,即计算考虑了描述波场的系列的$N$成员,并从该系列的$N+1$成员开始移动到未知系数的渐近值,其数量也被限制为$2N$。随着$N$值的增大,边界条件的精度增大,区域$\epsilon$减小,奇点附近应力的大小增大。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
PARTICULARS OF A WAVE FIELD IN A SEMI-INFINITE WAVEGUIDE WITH MIXED BOUNDARY CONDITIONS AT ITS EDGE
The work is devoted to the analysis of the wave field, which is excited by the reflection of the first normal propagation Rayleigh-Lamb wave from the edge of an elastic semi-infinite strip, part of which is rigidly clamped, and part is free from stresses. The boundary value problem belongs to the class of mixed boundary value problems, the characteristic feature of which is the presence of a local feature of stresses at the point of change of the type of boundary conditions. To solve this boundary value problem, the paper proposes a method of superposition, which allows to take into account the feature of stresses due to the asymptotic properties of the unknown coefficients. Asymptotic dependences for coefficients are determined by the nature of the feature, which is known from the solution of the static problem. The criterion for the correctness of the obtained results was the control of the accuracy of the law of conservation of energy, the error of which did not exceed 2% of the energy of the incident wave for the entire considered frequency range. The paper evaluates the accuracy of the boundary conditions. It is shown that the boundary conditions are fulfilled with graphical accuracy along the entire end of the semi-infinite strip, except around a special point ($\epsilon$). In this case, along the clamped end of the semi-infinite strip in the vicinity of a special point of stress remain limited. The presence of the region $\epsilon$ and the limited stresses are due to the fact that the calculations took into account the $N$ members of the series that describe the wave field, and starting from the $N+1$ member of the series moved to asymptotic values of unknown coefficients, the number of which was also limited to $2N$. As the value $N$ increased, the accuracy of the boundary conditions increased, the region $\epsilon$ decreased, and the magnitude of the stresses near the singular point increased.
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