Parametrized model order reduction for second order systems with a low rank change in the system matrices

Recently, a parametric model order reduction scheme was developed that allows for low rank variability in the state matrices, but does not require an a priori sampling of the parameter space. In this work the methodology is extended to second order dynamic systems, allowing for an independent low rank variability in both the stiffness and damping matrix. This is achieved by augmenting the input and output vectors and shifting the parameter dependence to the throughput matrix of the state space model. A second order Arnoldi scheme is used to obtain the projection matrix required for calculating the reduced order model. The effectiveness of the method is shown by applying it on a finite element model of a plate, in which the aim is to find the precise location and severity of a crack. The potential crack locations are parametrized by a local stiffness variation.status: publishe