  Model-order reduction techniques allow the construction of low-dimensional
surrogate models that can accelerate engineering design processes. Often, these
techniques are intrusive, meaning that they require direct access to underlying
high-fidelity models. Accessing these models is laborious or may not even be
possible in some cases. Therefore, there is an interest in developing
non-intrusive model reduction techniques to construct low-dimensional models
directly from simulated or experimental data. In this work, we focus on a
recent data-driven methodology, namely operator inference, that aims at
inferring the reduced operators using only trajectories of high-fidelity
models. We present an extension of operator inference for mechanical systems,
preserving the second-order structure. We also study a particular case in which
complete information about the external forces is available. In this
formulation, the reduced operators having certain properties inspired by the
original system matrices are enforced by adding constraints to the optimization
problem. We illustrate the presented methodology using three numerical
examples.
