关键词: 边界条件集合, Hilbert函数空间, 线性微分表达式, 仿射变换, 仿射结构

Abstract: The physical property of the material, the space structure and the boundary condition are three important parts of the guided-wave system. The effect of the boundary condition in elastic guided-wave systemis discussed. The author finds that the cardinality of the boundary condition set equals the cardinality of the real number set; the boundary equation and the governing equation construct the linear differential expression in Hilbert space, and the spectrums have affine law between two structures which are affine transformation each other. So that if the spectrumand the steady-state response of one structure of the set about affine structures can be solved, the spectrum and the steady-state response of the whole set are obtained simultaneously.

Key words: boundary condition set, Hilbert space, linear differential expression, affine transformation, affine structure