郑州大学学报（理学版）

本文讨论了带有材料点的弦振动的古典问题,证明了若时间间隔没有限制,且 n(材料点数目)或是素数或是2的一些自然数次幂时,则带有材料点的弦振动问题的解和连续弦的振动问题的解没有一致近似的性质.另外,当 t→∞时,带有材料点系统的振动和连续介质的振动有很大区别,n 越大,区别越大(若 n 是素数或 n=2^N).

The classical problem of the beaded string vibrations is discussed.It is proved that if the time interval is not limited,and n(number of beads)is either prime or some natural power of 2,then the solution of the problem of the beaded string vibrations and that of the con- tinuous string does not have the property of the uniform proximity.Moreover,vibrations of the system of material points and vibrations of continuous medium ave very different as t→∞.This difference is stronger,as n is larger (if n is prime or n=2^N).