{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,18]],"date-time":"2026-07-18T05:02:31Z","timestamp":1784350951660,"version":"3.55.0"},"reference-count":33,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2026,7,12]],"date-time":"2026-07-12T00:00:00Z","timestamp":1783814400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Key R&amp;D Program of China","award":["2023YFB2407300"],"award-info":[{"award-number":["2023YFB2407300"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Polymers"],"abstract":"<jats:p>This study addresses the inverse design of carbon fibre-reinforced polymer laminated plates with prescribed natural frequencies. The problem is difficult because stacking sequences are discrete, the design space is large, and multiple layups may produce nearly identical frequency spectra. This study does not seek to introduce a new tandem-network architecture. Rather, it adapts the established tandem inverse-design strategy to the discrete and non-unique vibration design of carbon fibre-reinforced polymer laminated plates. In the proposed framework, a trainable inverse network is coupled to a pre-trained forward frequency surrogate, allowing the inverse model to be optimised through frequency reconstruction instead of direct ply-angle supervision. A dataset of 50,000 symmetric CFRP laminates is generated using Classical Laminate Theory and a Rayleigh\u2013Ritz vibration solver, covering four boundary conditions and a range of plate geometries. The forward model achieves R2 values above 0.99 and mean absolute percentage errors below 3% for the first five natural frequencies. Compared with a genetic algorithm, the proposed inverse model provides stacking sequences about 7000 times faster while producing multiple feasible designs for each target. Permutation sensitivity analysis shows that plate geometry has the strongest influence on the frequency response, followed by boundary condition and ply orientation. Four engineering cases confirm the method\u2019s usefulness for vibration isolation, frequency-gap control, and multi-mode frequency prescription. The principal contribution is the integration of multi-boundary-condition vibration modelling, discrete stacking-sequence inverse design, response-based treatment of non-uniqueness, speed\/diversity benchmarking, and sensitivity-based physical interpretation within a single composite-laminate design framework.<\/jats:p>","DOI":"10.3390\/polym18141711","type":"journal-article","created":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T07:28:27Z","timestamp":1783927707000},"page":"1711","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Data-Driven Inverse Design of Carbon Fibre-Reinforced Polymer Laminated Plates via a Tandem Neural Network Framework"],"prefix":"10.3390","volume":"18","author":[{"given":"Mei","family":"Huang","sequence":"first","affiliation":[{"name":"Department of Nuclear Engineering and New Energy, The Engineering & Technical College of Chengdu University of Technology, Leshan 614000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lei","family":"Yuan","sequence":"additional","affiliation":[{"name":"Department of Nuclear Engineering and New Energy, The Engineering & Technical College of Chengdu University of Technology, Leshan 614000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Junjun","family":"Ran","sequence":"additional","affiliation":[{"name":"Department of Nuclear Engineering and New Energy, The Engineering & Technical College of Chengdu University of Technology, Leshan 614000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huili","family":"Liu","sequence":"additional","affiliation":[{"name":"Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Kunming 650093, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-4840-5562","authenticated-orcid":false,"given":"Yaoxin","family":"Huang","sequence":"additional","affiliation":[{"name":"Department of Mechanical, Materials and Manufacturing Engineering, University of Nottingham Ningbo China, Ningbo 315100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,7,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Reddy, J.N. 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