大跨度结构随机脉动风场的快速模拟方法

针对传统谐波合成法计算量巨大、内存耗费多的缺点,研究了空间各点的分解功率谱密度函数曲线随频率变化的特点。在此基础上,提出采用三次均匀B样条插值方法来拟合分解谱密度函数曲线,引入矩阵Cholesky分解的优化递归算法来加速矩阵分解速度,同时利用FFT技术来减少谐波项合成所需要的时间。经过上述的改进,可以大大提高双索引频率下谐波合成法的计算效率。最后利用两个算例表明,这种方法可以高效、准确地模拟出适合大跨度结构的随机脉动风场。

A FAST SIMULATION METHOD OF STOCHASTIC WIND FIELD FOR LONG-SPAN STRUCTURES

In order to reduce the calculating amount and memory consumption of the traditional wave superposition method, the characteristics for the curves of the factorized power spectral density functions changing with frequencies are studied in detail. Then, the cubic uniform B-spline interpolation method is utilized to fit the factorized spectrum function curves. Furthermore, an optical recursive algorithm for Cholesky factorizations is applied to improve the efficiency of the matrix factorizations with double-indexing frequencies. At last, the FFT technique is used to decrease the time consumption of the wave superposition. After that, two examples using these methods are employed to indicate that the fast simulation method is suitable for simulating the stochastic wind field of long-span structures effectively and accurately.