Numerical and experimental optimization of local visco-elastic damping layer placements for design of calm, smart and smooth structures

• Applicants: Professor Dr.-Ing. Boris Lohmann; Professor Dr. Daniel J. Rixen
• Subject Area: Mechanics ; Acoustics ; Engineering Design, Machine Elements, Product Development
• Term: from 2016 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 314987946

• Final Report Year: 2022

Final Report Abstract

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. In a book chapter, 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 report 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. Accurate simulation models to motivate design decisions in early product development phases is a challenge. Especially models containing viscoelastic materials or undergoing large deformations can lead to high computation times. It is desired to reduced these times to accelerate simulations in the concept phase. A promising method to achieve this goal is model reduction. We have shown different methods to reduce Finite element models of mechanical structures undergoing large deformations. The challenge here is to find reduction bases that are able to capture nonlinear effects and parametric dependencies. Furthermore a hyperreduction must be applied to accelerate evaluation of the nonlinear restoring force term. A cantilever beam case study illustrates the potential of the methods. Furthermore, we have introduced how viscoelasticity is modeled in Finite Element models. The equations of motion contain many internal states that can be considered as additional system states that can increase the system dimension drastically. Some reduction bases are proposed to reduce these models. A case study on a plate with an acoustic black hole illustrates the performance of the reduction bases. Further research is necessary to also apply the parametric methods from the geometric nonlinear reduced order models to the viscoelastic systems. Hyperreduction methods can also be a potential candidate to reduce the evaluation costs of internal states in viscoelastic models.

Publications

• „Modellordnungsreduktion für parametrische nichtlineare mechanische Systeme mittels erweiterter simulationsfreier Basen und Hyperreduktion“. In: Methoden und Anwendungen der Regelungstechnik. Erlangen-Münchener Workshops 2015 und 2016. Hrsg. von B. Lohmann und G. Roppenecker. Shaker Verlag, 2017, S. 67–86
  C. Lerch und C. Meyer
  
• „Simulation-Free Hyper-Reduction For Geometrically Nonlinear Structures Based On Stochastic Krylov Training Sets“. In: Proceedings of COMPDYN 2017, 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering. Hrsg. von M. F. M. Papadrakakis. European Community on Computational Methods in Applied Sciences (ECCOMAS), 2017
  C. H. Meyer, J. B. Rutzmoser und D. J. Rixen
  
• „Efficient basis updating for parametric nonlinear model order reduction“. In: PAMM 18.1 (2018)
  C. H. Meyer, C. Lerch, M. Karamooz Mahdiabadi und D. Rixen
  
• „Parametric Nonlinear Model Reduction for Structural Dynamics“. In: MATHMOD 2018 – 9th Vienna International Conference on Mathematical Modelling. Wien, Österreich, 2018
  C. Lerch und C. Meyer
  
• „Complex Modal Derivatives For Model Reduction Of Nonclassically Damped, Geometrically Nonlinear Structures“. In: 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2019), Crete, Greece. Hrsg. von M. Papadrakakis und M. Fragiadakis. Crete, 2019
  C. H. Meyer, F. M. Gruber und D. J. Rixen
  
• Simulation-Lean Training-Sets for Hyper-Reduction of Parametric Geometric Non-Linear Structures“. In: XI International Conference on Structural Dynamics. EASD, 2020
  C. H. Meyer und D. J. Rixen
  
• „2 Model order reduction in mechanical engineering“. In: Model Order Reduction - Volume 3: Applications. Hrsg. von P. B. et al. De Gruyter, 2020, S. 33–74
  B. Lohmann, T. Bechtold, P. Eberhard, J. Fehr, D. J. Rixen, M. C. Varona, C. Lerch, C. D. Yuan, E. B. Rudnyi, B. Fröhlich, P. Holzwarth, D. Grunert, C. H. Meyer und J. B. Rutzmoser