  Suppressing vibrations in mechanical systems, usually described by
second-order dynamical models, is a challenging task in mechanical engineering
in terms of computational resources even nowadays. One remedy is
structure-preserving model order reduction to construct easy-to-evaluate
surrogates for the original dynamical system having the same structure. In our
work, we present an overview of recently developed structure-preserving model
reduction methods for second-order systems. These methods are based on modal
and balanced truncation in different variants, as well as on rational
interpolation. Numerical examples are used to illustrate the effectiveness of
all described methods.
