Ledet L S, Sorokin S V
Research group of Solid and Computational Mechanics, Aalborg University, Fibigerstraede 16, 9220, Aalborg, Denmark.
Philos Trans A Math Phys Eng Sci. 2019 Oct 21;377(2156):20190112. doi: 10.1098/rsta.2019.0112. Epub 2019 Sep 2.
The bi-orthogonality relation for eigenfunctions of self-adjoint operators is derived. Its composition is explained in view of the structure of a characteristic equation and of the energy flow components. Application of the bi-orthogonality relation for solving forcing problems is generalized and the connection between the bi-orthogonality relation and the virtual wave method is highlighted. Technicalities are illustrated in a non-trivial example of propagation of free/forced cylindrical waves in a thin elastic plate under heavy fluid loading. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 1)'.
推导了自伴算子本征函数的双正交关系。从特征方程的结构和能量流分量的角度解释了其构成。推广了双正交关系在求解强迫问题中的应用，并突出了双正交关系与虚拟波方法之间的联系。在重流体载荷下薄弹性板中自由/强迫柱面波传播的一个非平凡例子中说明了相关技术细节。本文是主题为“结构化介质中动态现象建模与局域化（第1部分）”的一部分。
