It is pointed out that the eigenvalues of these structures are the roots of a series of rational fraction polynomial equations. A theorem about the roots of these equations is proved in the paper.

本文指出了弱粘弹性材料结构的特征值是一组有理分式多项式方程的根，并给出了关于这些有理分式多项式方程根的一个定理。

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Through the corresponding between integral coefficient polynomial and rational number, this paper obtains factorization from factorization of polynomial by the way of sieve in true fraction series.

本文利用整系数多项式与正有理数的对应，将多项式因式分解通过对真分数序列筛选的办法求得因式。

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The paper available mapping of integral coefficient polynomial and rational number, obtain factorization from factorization of polynomial by the way of sieve in true fraction series.

通过研究多项式的系数来确定整系数多项式的有理根，进而得出整系数多项式的有理根的一个判定定理和根的存在定理。

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