一类二自由度系统振动的黄金分割率

摘要

As an important relation of the proportion in the history of mathematics,the golden section relation plays an important role in aesthetics,architecture,and even engineering.This paper studies the gold segmentation effect for a class of vibration system of two degrees of freedom.The free vibration characteristics,and the resonance mechanism of the forced vibration under harmonic loading are analyzed.It is shown that,the ratios of the structure circular frequency to the layer stiffness and mass,and that of the structural amplitudes at two points conform well with the golden section ratio.The structure shows the beauty of harmony in vibration.%作为数学史上一个重要的比例关系,黄金分割理论已在美学、建筑学甚至工程学中发挥了一定的作用.为了研究一类二自由度系统振动的黄金分割效应,首先介绍了黄金分割的基本理论,然后分别分析了该类二自由度体系的自由振动特征,以及简谐载荷作用下受迫振动的共振机制.结果表明,结构圆频率与层刚度和质量之比、两结构质点振幅之比都符合黄金分割率,结构在振动中具有和谐之美.