Rokhlin S I, Wang L
The Ohio State University, Nondestructive Evaluation Program, Edison Joining Technology Center, Columbus 43221, USA.
J Acoust Soc Am. 2002 Sep;112(3 Pt 1):822-34. doi: 10.1121/1.1497365.
An efficient recursive algorithm, the stiffness matrix method, has been developed for wave propagation in multilayered generally anisotropic media. This algorithm has the computational efficiency and simplicity of the standard transfer matrix method and is unconditionally computationally stable for high frequency and layer thickness. In this algorithm, the stiffness (compliance) matrix is calculated for each layer and recursively applied to generate a stiffness (compliance) matrix for a layered system. Next, reflection and transmission coefficients are calculated for layered media bounded by liquid or solid semispaces. The results show that the method is stable for arbitrary number and thickness of layers and the computation time is proportional to the number of layers. It is shown both numerically and analytically that for a thick structure the solution approaches the solution for a semispace. This algorithm is easily adaptable to laminates with periodicity, such as multiangle lay-up composites. The repetition and symmetry of the unit cell are naturally incorporated in the recursive scheme. As an example the angle beam time domain pulse reflections from fluid-loaded multilayered composites have been computed and compared with experiment. Based on this method, characteristic equations for Lamb waves and Floquet waves in periodic media have also been determined.
针对多层一般各向异性介质中的波传播问题，开发了一种高效的递归算法——刚度矩阵法。该算法具有标准传递矩阵法的计算效率和简便性，并且在高频和层厚情况下无条件计算稳定。在该算法中，为每层计算刚度（柔度）矩阵，并递归应用以生成层状系统的刚度（柔度）矩阵。接下来，计算由液体或固体半空间界定的层状介质的反射系数和透射系数。结果表明，该方法对于任意层数和厚度都是稳定的，计算时间与层数成正比。数值和解析结果均表明，对于厚结构，解趋近于半空间的解。该算法易于适用于具有周期性的层合材料，如多角铺层复合材料。晶胞的重复性和对称性自然地包含在递归方案中。作为一个例子，计算了流体加载多层复合材料的角梁时域脉冲反射，并与实验进行了比较。基于该方法，还确定了周期介质中兰姆波和弗洛凯波的特征方程。
