结构动力数值分析的时频域转换算法研究

Research on numerical conversion algorithms of structure dynamic analysis in time and frequency domains

研究地震波激励信号及结构响应之间在时频域上的数值对照关系,对于结构动力分析方法的深入发展,及先进时域算法的频域考题验证均有重要意义.首先从理论上公式推导了复数域傅里叶频谱求解方法与实数域三角函数频谱求解方法之间的等价条件,从而在离散傅里叶变换之外,找到了一种可求解时程曲线针对任意频率点频谱的三角函数频谱算法.并针对阻尼体系的动力响应分析,进行了频域与时域算法在激励输入与结构响应领域的转换关系的解析推导,为结构动力响应求解提供了一种新思路.最后,以多质点的阻尼体系的动力响应分析为例数值验证了该方法的有效性.

The research on the numerical relations between signal of seismic wave input and output responses is significant for further study of the methods of structural dynamic analysis and the verification of advanced time domain algorithm in frequency domain. Firstly, the condition of equivalence between Fourier transform and trigonometric series is deduced in theory, then an algorithm of trigonometric function is introduced to obtain spectrum of arbitrary frequency excluding the methods of discrete Fourier transform. Considering the dynamic response of damp system, the analytical verification of relations between signal input and output responses in time and frequency domains is carried out. Finally, availability of the trigonometric function algorithm is proved through dynamic response analysis of multiple particles damp system.