Application of parametric model reduction with matrix interpolation for simulation of moving loads in elastic multibody systems

The method of elastic multibody systems enables the analysis, simulation, and optimization of mechanical systems with consideration of elastic deformations and nonlinear rigid body motions. The combination of multibody systems with elastic bodies requires to reduce the elastic degrees of freedom by model order reduction. To gain satisfying reduction results, the boundary conditions and acting loads have to be considered in the model reduction process. In a rising number of industrial applications the boundary conditions or the position of acting loads on the elastic bodies are not known a-priori. The simulation, e.g., of cranes, turning processes or gear wheels requires the definition of elastic systems with moving loads. For a good approximation of mechanical systems with moving loads a large number of ansatz functions is required to consider the local deformations generated by the changing load. This approach leads to very large reduced systems and is not feasible if the possible contact area is large or is not known prior to the simulation. In this contribution, the moving load is described by a parameter dependent input matrix. The application of parametric model order reduction techniques based on matrix interpolation to generate interpolated reduced systems without regarding the original system for each parameter value is proposed. Two mechanical examples are examined to illustrate the problems and developed solutions in the application of these methods for the simulation of moving loads in elastic multibody systems.