  An essential tool in data-driven modeling of dynamical systems from frequency
response measurements is the barycentric form of the underlying rational
transfer function. In this work, we propose structured barycentric forms for
modeling dynamical systems with second-order time derivatives using their
frequency domain input-output data. By imposing a set of interpolation
conditions, the systems' transfer functions are rewritten in different
barycentric forms using different parametrizations. Loewner-like algorithms are
developed for the explicit computation of second-order systems from data based
on the developed barycentric forms. Numerical experiments show the performance
of these new structured data driven modeling methods compared to other
interpolation-based data-driven modeling techniques from the literature.
