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R. Soc. Interface."],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:p>Flapping wing insects leverage the dynamics of their compliant flight systems to reduce the energetic costs of flying. However, the extent to which the wing hinge dynamics contribute to the overall system dynamics remains unknown. Therefore, we developed an approach to (i) quantify the passive dynamic properties of the wing hinge and (ii) identify the resonant frequency of the isolated wing\/wing hinge system. First, we measured the frequency response relating thorax deformation to wing stroke angle in sacrificed honeybees and army cutworm moths. Using these data, we developed a linear model of the flight system, which we then extended to incorporate nonlinear effects associated with large wing stroke angles. Our findings revealed that both species flap below the linear resonance of the wing hinge. At larger angles, nonlinear aerodynamic damping reduces the resonant frequency, causing both species to flap above wing hinge resonance. We discuss how wing\u2013thorax coupling and muscle dynamics may cause the resonant frequency of the entire flight system to deviate from that of the wing\/wing hinge system. Our estimates of wing hinge stiffness and damping provide quantitative parameters that can be incorporated into models of the insect flight system to enable more accurate predictions of resonance behaviour.<\/jats:p>","DOI":"10.1098\/rsif.2025.0074","type":"journal-article","created":{"date-parts":[[2025,9,16]],"date-time":"2025-09-16T23:06:01Z","timestamp":1758063961000},"update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Wing hinge dynamics influence stroke amplitudes in flapping wing insects: a frequency response approach"],"prefix":"10.1098","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4748-3033","authenticated-orcid":true,"given":"Cailin B.","family":"Casey","sequence":"first","affiliation":[{"name":"Department of Mechanical and Industrial Engineering, Montana State University","place":["Bozeman, USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7087-3945","authenticated-orcid":true,"given":"Braden","family":"Cote","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Industrial Engineering, Montana State University","place":["Bozeman, USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1406-7439","authenticated-orcid":true,"given":"Chelsea","family":"Heveran","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Industrial Engineering, Montana State University","place":["Bozeman, USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6305-0564","authenticated-orcid":true,"given":"Mark","family":"Jankauski","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Industrial Engineering, Montana State University","place":["Bozeman, USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"175","published-online":{"date-parts":[[2025,9,17]]},"reference":[{"key":"e_1_3_8_2_2","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.01484"},{"key":"e_1_3_8_3_2","doi-asserted-by":"publisher","DOI":"10.1038\/d41586-024-01508-4"},{"key":"e_1_3_8_4_2","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.115.1.293"},{"key":"e_1_3_8_5_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-022-16859-z"},{"key":"e_1_3_8_6_2","doi-asserted-by":"publisher","DOI":"10.1113\/jphysiol.1949.sp004326"},{"key":"e_1_3_8_7_2","doi-asserted-by":"publisher","DOI":"10.2142\/biophysics.7.21"},{"key":"e_1_3_8_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/s003600050152"},{"key":"e_1_3_8_9_2","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.131.1.373"},{"key":"e_1_3_8_10_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pbio.1001822"},{"key":"e_1_3_8_11_2","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2019.0543"},{"key":"e_1_3_8_12_2","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.128363"},{"key":"e_1_3_8_13_2","doi-asserted-by":"publisher","DOI":"10.1098\/rspb.2021.0352"},{"key":"e_1_3_8_14_2","doi-asserted-by":"publisher","DOI":"10.1242\/jeb.203.18.2713"},{"key":"e_1_3_8_15_2","doi-asserted-by":"publisher","DOI":"10.3390\/biomimetics7040207"},{"key":"e_1_3_8_16_2","doi-asserted-by":"publisher","DOI":"10.1098\/rsbl.2022.0063"},{"key":"e_1_3_8_17_2","doi-asserted-by":"publisher","DOI":"10.1088\/1748-3190\/ab835b"},{"key":"e_1_3_8_18_2","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2022.0080"},{"key":"e_1_3_8_19_2","doi-asserted-by":"publisher","DOI":"10.1098\/rsif.2020.0888"},{"key":"e_1_3_8_20_2","volume-title":"Principles of insect morphology","author":"Snodgrass RE","year":"2018","unstructured":"Snodgrass RE. 2018 Principles of insect morphology. 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