Simulation-Free Model Reduction Approaches for Geometric-Nonlinear and Linear-Visco-Elastic Mechanical Systems

Virtual design studies for dynamics of advanced mechanical structures are often preferred over experimental studies. They allow a cheap evaluation of different designs. However, for systems undergoing large deformations or systems where viscoelastic effects cannot be neglected, these studies can mean long simulation times. A promising approach that can overcome this burden is model reduction. Model reduction reduces the computation costs by approximating high dimensional models by reduced order models with mathematical methods. For this reason, a research project was initiated within the Priority Program, whose goal is to develop reduction methods for such systems to enable faster design iterations. This article summarizes the results of this project: First, an overview over the equations of motion for geometric nonlinear systems is given. Then different reduction techniques for these system are summarized. A focus, here, is on simulation-free reduction techniques that avoid costly time simulations with the full order model and on parametric approaches that can consider design changes. This also includes geometric modifications that are handled by mesh morphing techniques which are able to maintain mesh topology making them perfectly suited to parametric reduction approaches. A case study illustrates the performance of the most promising approaches. Many literature references are given where the reader can find more information about the different approaches. The second part of the article deals with models containing viscoelastic materials. Here, a linear formulation for the equation of motion is considered. Different reduction bases are proposed to obtain a reduced order model. Their performance is illustrated with a plate model that contains an acoustic black hole with a viscoelastic constrained layer damper     «

Virtual design studies for dynamics of advanced mechanical structures are often preferred over experimental studies. They allow a cheap evaluation of different designs. However, for systems undergoing large deformations or systems where viscoelastic effects cannot be neglected, these studies can mean long simulation times. A promising approach that can overcome this burden is model reduction. Model reduction reduces the computation costs by approximating high dimensional models by reduced order...     »