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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\u2019 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.<\/jats:p>","DOI":"10.1007\/s10444-024-10118-7","type":"journal-article","created":{"date-parts":[[2024,4,11]],"date-time":"2024-04-11T08:02:40Z","timestamp":1712822560000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Structured barycentric forms for interpolation-based data-driven reduced modeling of second-order systems"],"prefix":"10.1007","volume":"50","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3580-4116","authenticated-orcid":false,"given":"Ion Victor","family":"Gosea","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4564-5999","authenticated-orcid":false,"given":"Serkan","family":"Gugercin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1667-4862","authenticated-orcid":false,"given":"Steffen W. 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