受演变随机激励结构响应的增维精细时程积分法

Precise time-integration method with augmented matrix for structural responses to evolutionary random excitations

对受非均匀调制演变随机激励结构响应问题进行了研究.先用虚拟激励法将随机荷载化为确定性荷载,然后将非均匀调制演变随机模型用状态方程表示.借助于随机模型的状态方程表达式,可构造出增维精细时程积分格式,从而快速精确地求出结构的时变功率谱响应.同HPD-M格式相比,该方法不仅计算效率有所提高,而且由于避免了矩阵求逆,可直接处理具有刚体模态的结构.最后通过两个算例与HPD-M格式的计算效率进行比较,表明本方法具有显著的优越性.

The research on the responses of structures subjected to non-uniformly modulated evolutionary random excitations is performed. The random excitations are first transformed into pseudo excitations before the non-uniformly modulated evolutionary random models are expressed by state space equations. The precise time-integration scheme with augmented matrix is derived by using the state space expression of the random models and can quickly and precisely compute the time-dependent power spectral density of structural responses. Comparing with the HPD-M format, the present method is more efficient and can be used to deal with the structures with rigid-body modes since the inverse of a matrix is avoided. Two examples are given to show the advantages of this method over the HPD-M format when computing the time-dependent power spectral densities of the structural responses.