论文标题
板中波传播问题的数值解
Numerical solution of the wave propagation problem in a plate
论文作者
论文摘要
在这项工作中，计算了薄板中超声波脉冲的传播，以求解模拟此问题的微分方程。为了求解这些方程式，有限差异用于离散时间变量，而使用有限元方法将空间变量离散。获得了与时间固定值相对应的问题的变异公式，并证明了解决方案的唯一性。所提出的方法导致具有相同稀疏，对称和正定矩阵的线性系统序列。免费软件FreeFem ++用于使用多项式三角元素计算近似解。数值实验表明，使用用于不同频率值的近似位移计算的速度与相位速度的分析分散曲线相当良好。
In this work, the propagation of an ultrasonic pulse in a thin plate is computed solving the differential equations modeling this problem. To solve these equations finite differences are used to discretize the temporal variable, while spacial variables are discretized using Finite Element method. The variational formulation of the problem corresponding to a fixed value of time is obtained and the existence an uniqueness of the solution is proved. The proposed approach leads to a sequence of linear systems with the same sparse, symmetric and positive defined matrix. The free software FreeFem++ is used to compute the approximated solution using polynomial triangular elements. Numerical experiments show that velocities computed using the approximated displacements for different frequency values are in good correspondence with analytical dispersion curves for the phase velocity.
