Enhanced order reduction of forced nonlinear systems using new ritz vectors

Enhanced modal-based order reduction of forced structural dynamic systems with isolated nonlinearity has been performed using the iterated LELSM (Local equivalent linear stiffness method) modes and new type of Ritz vectors. The iterated LELSM modes have been found via iteration of the modes of the mass normalized local equivalent linear stiffness matrix of the nonlinear systems. The optimal basis vector of principal orthogonal modes (POMs) is found for such system via simulation and used for POD-based order reduction for comparison. Two new Ritz vectors are defined as a static load vectors where one of them gives a static displacement to the mass connected to the periodic forcing load and the other gives a static displacement to the mass connected to the nonlinear element. It is found that the use of these vectors, which are augmented to the iterated LELSM modes in the order reduction modal matrix, reduces the number of modes used in order reduction and considerably enhances the accuracy of order reduction. The combination of the new Ritz vectors with the iterated LELSM modes in the order reduction matrix yields more accurate reduced models than POD-based order reduction of forced and nonlinear systems. Hence, the LELSM modal-based order reduction is essentially enhanced over POD-based and linear-based order reductions by using these new Ritz vectors. In addition, the main advantage of using the iterated LELSM modes for order reduction is that, unlike POMs, they do not require a priori simulation and thus they can be combined with new Ritz vectors and applied directly to the system.