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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 order 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 linear mechanical systems, preserving the underlying second-order structure. Furthermore, we 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 inference problem. We illustrate the proposed methodologies using three numerical examples. [ABSTRACT FROM AUTHOR]