弹性方柱中波的传播规律Ⅳ·边界条件的作用

材料的物理属性、结构的空间表现和系统的边界状态是波导系统的3个组成要素。讨论了弹性波导系统的边界状态在整个系统的作用。发现边界条件的集合是与实数集等势的集合;边界条件方程与控制方程共同构成Hilbert函数空间中的线性微分表达式,并且其具备的线性性质使得结构经过仿射变换后,频谱之间具有仿射变换的规律。这些优异性质使得求解出仿射结构集合中某一结构的频谱,就能够完全得到该集合中所有结构的频谱和稳态响应。

Wave Propagation in Elastic Square Columns IV·Effect of Boundary Condition

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 system is 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 aff...