Maria Cruz Varona

Maria Cruz Varona, Nico Schneucker, Boris Lohmann

This paper transfers the concept of moment matching to nonlinear structural systems and further provides a simulation-free reduction scheme for such nonlinear second-order models. After first presenting the steady-state interpretation of linear moment matching, we then extend this reduction concept to the nonlinear second-order case based on Astolfi [2010]. Then, similar simplifications as in Cruz Varona et al. [2019] are proposed to achieve a simulation-free nonlinear moment matching algorithm. A discussion on the simplifications and their limitations is presented, as well as a numerical example which illustrates the efficiency of the algorithm.

Maria Cruz Varona, Boris Lohmann

In this paper we consider different model reduction techniques for systems with moving loads. Due to the time-dependency of the input and output matrices, the application of time-varying projection matrices for the reduction offers new degrees of freedom, which also come along with some challenges. This paper deals with both simple methods for the reduction of particular linear time-varying systems, as well as with a more advanced technique considering the emerging time derivatives.

Maria Cruz Varona, Raphael Gebhart

This paper focuses on the systems theory of bilinear dynamical systems using the Volterra series representation. The main contributions are threefold. First, we gain an input-output representation in the frequency domain, where the Laplace transform of the kernels can indeed be interpreted as transfer functions. Then, we derive the response of bilinear systems to a nascent delta function in time domain, i.e. the impulse response of bilinear systems. Finally, we study the relationships between this novel impulse response and the well-known Volterra kernels and adjust those to be compatible to the impulse response.