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本文系根据多自由度結构系統的动力反应基本理論,将黄文熙教授的拱坝、壳体和平板的結构分析方法推广应用于拱坝、壳体和平板的振动与动应力分析,用具有n个結点的格柵去代替实际結构,可以推得一組代表具有3n个自由度的結构系統的頻率方程組。結合本文所推得的在三向振动条件下的振型正交条件,可用迭代法或数字計算机解算这个3n元齐次代数方程組,从而确定系統的各个自振頻率和振型,然后在求出三向振动条件下的振型参与系数后,可按振型展开,求出系統在地震或其它干扰力作
Based on the dynamical reaction theory of multi-degree-of-freedom structural systems, this paper generalizes Professor Huang Wenxi’s structural analysis methods for arch dams, shells, and plates to be applied to the analysis of vibration and dynamic stress of arch dams, shells, and plates. Instead of the actual structure, the grid of nodes can be derived as a set of frequency equations representing a structural system with 3n degrees of freedom. Combining the orthogonal conditions of mode shapes under the triaxial vibration conditions derived in this paper, the 3n-element homogeneous algebraic equations can be solved by iterative method or digital computer to determine the system’s various natural frequencies and modes, and then After obtaining the vibration mode participation coefficient under the three-way vibration condition, the vibration mode can be expanded and the system can be used to determine the earthquake or other interference force.