改善动柔度法之精度和效率的移频技术

Dynamic Flexibility Method with Local Shifting Frequency

作者曾提出过用于计算很多特证向量导数的动柔度法 ,这种方法对一般结构 ,即非密集根情况 ,不仅精度良好 ,而且计算上也是很有效的 ,然而遇到密集根时 ,因动柔度法的λ幂级数发散 ,导致精度急剧变坏 ,为此 ,提出了本阶移频动柔度法和混合移频动柔度法 ,这两种方法各自用于具有密集根的约束结构和自由结构的特征向量导数 ,或者是一般约束结构和一般自由结构的高阶特征向量导数计算将是最为理想的动柔度法。

The authors have proposed a Dynamic Flexibility(DF) method based on the power series expansion of dynamic flexibility in order to compute many eigenvector derivatives. The DF method is time consuming and possesses poor precision under the case that there is the motion of rigid body and concentrated roots (eigenvalues). When the rigid body motion exists,the coefficient matrix K of governing equation for the DF method is singular. In order to solve the present govering equation,one has to complement r independent equation associated with motion of rigid body so that the coefficient matrix K is changed to K+μMΦ RΦ T RM.Clearly, this matrix breaks down the band state characteristic of original matrix K, which results in the fall off of computation efficiency. In addition, when the concentrated roots occur, the power series in the DF method converges slowly so that the precision of DF method is changed to be poor. These questions can be solved by using various shifting frequency techniques . The authors have proposed some shifting frequency techniques, for example, the formal shifting frequency and system shifting frequency technique. This paper presents the more efficient local shifting frequency and mixed shifting frequency techniques. They can not only retain the band state characteristic of original stiffness matrix K,but also accelerate the convergence of the power series in the DF method. Numerical results show that these shifting frequency dynamic flexibility methods are efficient and possess the better precision.