On the Number of Modes Necessary for Accurate Response and Resulting Forces in Dynamic Analyses

Frequency domain analysis of model order reduction techniques

“…One class of techniques such as [2][3][4][5][6][7][8][9][10] uses a direct reduction of physical model coordinates by omitting some selected degrees-of-freedom (DOF), whose accuracy is very sensitive to the selection of active DOFs. The second class of methods [11,12] is the modal methods having better accuracy, yielding decoupled equations and giving a better insight into the problems; however, they have the following disadvantages: computation of the modes may be costly if too many modes are needed in the analyses and their results may be unacceptable due to the effects of truncated modes. In order to overcome this drawback, quasi-static compensation (QSC) method studied in [13][14][15][16][17][18] was developed.…”

A new modal correction method for linear structures subjected to deterministic and random loadings

“…In order to include in the analysis the additional flexibility arising from the neglected modes of vibration, the MAM (modal acceleration method) has been proposed [2,3]. The correction formula can be expressed as:…”

“…The most popular modal correction technique is the so-called mode acceleration method (MAM), in which the adjustment is simply given by the pseudo-static contribution of the higher modes of vibration [2,3]. This procedure has been also extended to cope with random loadings represented via KarhunenLoève decomposition [4].…”

Linear Stability Analysis of Multiparameter Dynamical Systems via a Numerical-Perturbation Approach

“…Indeed, it was found that an inaccurate choice of them would lead to erroneous results. Here, consistently with the procedure suggested in [12], the following shape functions were selected:…”