Order reduction of nonsmooth structural systems with multiple surfaces of discontinuity

A technique for order reduction of nonsmooth vibrating systems in structural form of arbitrary dimension with multiple surfaces of discontinuity is presented. By utilizing methods based on the bilinear frequency relation which approximates the nonlinear normal mode (NNM) frequencies and mode shapes, reduced order models are constructed which retain the form of the nonsmooth nonlinearity of the full model and more accurately represent the NNM dynamics in the full model than do reduced models obtained via linear transformations. The technique is applied to multi-degree-of-freedom systems with nonsmooth nonlinearities of deadzone and saturation type in which the full and reduced models are compared by direct numerical simulation. The advantages of the present technique include obtaining a reduced order model which uses a subset of the original physical coordinates and can easily accommodate large order systems and multiple nonsmooth nonlinearities with several surfaces of discontinuity. These characteristics make the method practical for use in large-scale structural dynamics applications in which the linear part of the model dominates the dynamics.