对称结构振型特性的一般性证明

对称结构大量的存在于实际工程中.对对称结构的力学分析通常都可采用相应的简化模型进行计算.在静力结构问题对称特性方面,已经进行了严格的证明并得出了完整的理论和结果.并已经被广泛应用.对对称结构动力分析中的若干性质虽也有些结论,但并不是普遍性的.这里利用数学物理方法,证明了对一般对称结构(包括由离散方法建立的对称力学模型),振型应该具有的一般性质.在对对称结构进行动力分析时利用对称结构本身的振型特性,可以大幅度简化计算.

Peculiarity in Symmetry Structure

There are many symmetry structures in engineering,and simplified model is used in mechanic analysis.In static symmetry structure,some result and theorem have been accepted,strictly proved and widely used.Although some results have been obtained for dynamic structure,they are not universal.By methods of mathematics and physics,some general results of symmetry structure model(including the mechanic model introduced by the numerical methods) are achieved,and compute process can be simplified greatly.