Hybrid (numerical-experimental) modeling of complex structures with linear and nonlinear components

Abstract

The present work investigates the performance of two systematic methodologies leading to hybrid modeling of complex mechanical systems. This is done by applying numerical methods in determining the equations of motion of some of the substructures of large order mechanical systems, while the dynamic characteristics of the remaining components are determined through the application of appropriate experimental procedures. In their simplest version, the models examined are assumed to possess linear characteristics. For such systems, it is possible to apply several hybrid methodologies. Here, the first of the methods selected is performed in the frequency domain, while the second method has its roots and foundation in time domain analysis. Originally, the accuracy and effectiveness of these methodologies is illustrated by numerical results obtained for two complex mechanical models, where the equations of motion of each substructure are first set up by applying the finite element method. Then, the equations of motion of the complete system are derived and their dimension is reduced substantially, so that the new model is sufficiently accurate up to a prespecified level of forcing frequencies. The formulation is developed in a general way, so that application of other methods, including experimental techniques, is equally valid. This is actually performed in the final part of this study, where experimental results are employed in conjunction with numerical results in order to predict the dynamic response of a mechanical structure possessing a linear substructure with high modal density, supported on four substructures with strongly nonlinear characteristics.