Wang L, Rokhlin S I
Nondestructive Evaluation Program, Edison Joining Technology Center, The Ohio State University, Columbus, OH 43221, USA.
Ultrasonics. 2001 Oct;39(6):413-24. doi: 10.1016/s0041-624x(01)00082-8.
The numerical instability problem in the standard transfer matrix method has been resolved by introducing the layer stiffness matrix and using an efficient recursive algorithm to calculate the global stiffness matrix for an arbitrary anisotropic layered structure. For general anisotropy the computational algorithm is formulated in matrix form. In the plane of symmetry of an orthotropic layer the layer stiffness matrix is represented analytically. It is shown that the elements of the stiffness matrix are as simple as those of the transfer matrix and only six of them are independent. Reflection and transmission coefficients for layered media bounded by liquid or solid semi-spaces are formulated as functions of the total stiffness matrix elements. It has been demonstrated that this algorithm is unconditionally stable and more efficient than the standard transfer matrix method. The stiffness matrix formulation is convenient in satisfying boundary conditions for different layered media cases and in obtaining modal solutions. Based on this method characteristic equations for Lamb and surface waves in multilayered orthotropic media have been obtained. Due to the stability of the stiffness matrix method, the solutions of the characteristic equations are numerically stable and efficient. Numerical examples are given.
通过引入层刚度矩阵并使用高效的递归算法来计算任意各向异性层状结构的整体刚度矩阵，解决了标准传递矩阵法中的数值不稳定性问题。对于一般各向异性，计算算法以矩阵形式表示。在正交各向异性层的对称平面内，层刚度矩阵以解析形式表示。结果表明，刚度矩阵的元素与传递矩阵的元素一样简单，且其中只有六个是独立的。由液体或固体半空间界定的层状介质的反射和透射系数被表示为整体刚度矩阵元素的函数。已经证明，该算法是无条件稳定的，并且比标准传递矩阵法更有效。刚度矩阵公式便于满足不同层状介质情况的边界条件并获得模态解。基于此方法，已获得多层正交各向异性介质中兰姆波和表面波的特征方程。由于刚度矩阵法的稳定性，特征方程的解在数值上是稳定且高效的。给出了数值示例。
