Accelerated convergence of dynamic flexibility in series form

Procedure to reduce the effects of modal truncation in eigensolutionreanalysis

“…If one considers that the nodes concerned by the modification correspond to the displacement of the boundary occurring in the discrete model defined in Eq. (19), the prob- …”

“…(10), (11), and (14), not to the real system but to a modal model, Eq. (19), that takes the modal truncation into account in the form of a residual stiffness matrix K R .…”

Wave Propagation in Structures

“…On the other hand, if we include all the modes, then the computational cost is a big dis-incentive to do an accurate modeling of the joint region. We will accelerate the convergence with respect to the number of modes by using a suggestion made in References [78,119]. Noting that, without approximations, …”

A simple dynamic substructure method

“…In practice, the computation of K, ; ' K,, instead of the explicit inverse Ks;' is performed, and this may be accomplished by any equation solver which takes advantages of the sparsity of Kss. When substituting equation (7) into equation (3), one notes that even K, ; M,, K, ; ' is not required explicitly but rather (K,: ' K,m)T M,, K, ; ' Ksm. Therefore, the expansion of equation (7) does not introduce a large amount of computation because Ksi' K,,, and @ are needed anyway.…”

“…When substituting equation (7) into equation (3), one notes that even K, ; M,, K, ; ' is not required explicitly but rather (K,: ' K,m)T M,, K, ; ' Ksm. Therefore, the expansion of equation (7) does not introduce a large amount of computation because Ksi' K,,, and @ are needed anyway.…”