圆柱各向异性径向非均匀弹性固体的波阻抗矩阵
Wave impedance matrices for cylindrically anisotropic radially inhomogeneous elastic solids
摘要：
对于径向非均匀结构，利用时谐位移-牵引6-向量的Stroh类一阶微分方程组获得阻抗矩阵。特别注意的是新确定的固体圆柱体阻抗矩阵${\mathbf Z} (r)$适当的圆柱体材料在$r=0$，其极限值在这一点上，固体圆柱体阻抗矩阵${\mathbf Z}_0$。我们证明了${\mathbf Z}_0$是一个基本的材料性质，它只依赖于弹性模量和方位阶$n$，${\mathbf Z} (r)$是厄米的，而${\mathbf Z}_0$是负半定的。在单斜对称和更高材料对称下给出了${\mathbf Z}_0$的显式解，并详细讨论了$n=0$和1的特殊情况.提出了两种求解${\mathbf Z} (r)$的方法，一种是基于Frobenius级数解，另一种是利用以${\mathbf Z}_0$为初值的微分Riccati方程. %的代数Riccati方程的解决方案一致的方式。辐射阻抗矩阵的定义和示出是非厄米特。这些阻抗矩阵，使简洁和有效的公式的色散方程的波导，散射和相关的波问题的解决方案，在圆柱体。
英文摘要：
Impedance matrices are obtained for radially inhomogeneous structures using the Stroh-like system of six first order differential equations for the time harmonic displacement-traction 6-vector. Particular attention is paid to the newly identified solid-cylinder impedance matrix ${\mathbf Z} (r)$ appropriate to cylinders with material at $r=0$, and its limiting value at that point, the solid-cylinder impedance matrix ${\mathbf Z}_0$. We show that ${\mathbf Z}_0$ is a fundamental material property depending only on the elastic moduli and the azimuthal order $n$, that ${\mathbf Z} (r)$ is Hermitian and ${\mathbf Z}_0$ is negative semi-definite. Explicit solutions for ${\mathbf Z}_0$ are presented for monoclinic and higher material symmetry, and the special cases of $n=0$ and 1 are treated in detail. Two methods are proposed for finding ${\mathbf Z} (r)$, one based on the Frobenius series solution and the other using a differential Riccati equation with ${\mathbf Z}_0$ as initial value. %in a consistent manner as the solution of an algebraic Riccati equation. The radiation impedance matrix is defined and shown to be non-Hermitian. These impedance matrices enable concise and efficient formulations of dispersion equations for wave guides, and solutions of scattering and related wave problems in cylinders.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
