{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,23]],"date-time":"2025-09-23T12:56:31Z","timestamp":1758632191324,"version":"3.41.2"},"reference-count":24,"publisher":"Emerald","issue":"6","license":[{"start":{"date-parts":[[2021,10,14]],"date-time":"2021-10-14T00:00:00Z","timestamp":1634169600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["MMMS"],"published-print":{"date-parts":[[2021,10,26]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-subheading\">Purpose<\/jats:title><jats:p>The purpose of this paper is to present a study on the application of four damage factors to several single and multiple damage scenarios of aluminium beams. Each one of these damage factors is defined by the information given by modal curvatures of the beams.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Design\/methodology\/approach<\/jats:title><jats:p>The methodology consisted of a first experimental stage in which the modal rotations were measured with shearography and a subsequent numerical analysis in order to obtain the modal curvatures. To this end, three finite difference formulae were applied. The modal curvatures were then used to calculate the damage factors.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Findings<\/jats:title><jats:p>It was found that the profile of the damage factors varies according to the finite difference formula used. In view of the findings, the differences among the damage factors analysed are highlighted and some final recommendations to improve damage identifications via modal curvature-based are presented.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Originality\/value<\/jats:title><jats:p>To the best of the authors\u2019 knowledge, the application and comparison of several finite difference formulae and corresponding optimal sampling has not been carried out before. With the proposed approach, it is possible to identify multiple damages, which is still a great challenge. The post-processing of shearography measurements with a numerical method, which is inherently a multidisciplinary approach, is also a substantial improvement upon other type of approaches found in the literature.<\/jats:p><\/jats:sec>","DOI":"10.1108\/mmms-07-2021-0124","type":"journal-article","created":{"date-parts":[[2021,10,13]],"date-time":"2021-10-13T16:43:31Z","timestamp":1634143411000},"page":"1061-1080","source":"Crossref","is-referenced-by-count":2,"title":["Improvement on modal curvatures methods for multiple damage identification in beams"],"prefix":"10.1108","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1830-4179","authenticated-orcid":false,"given":"Daniele","family":"Cinque","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3662-6166","authenticated-orcid":false,"given":"Jose Viriato Araujo dos","family":"Santos","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8264-2792","authenticated-orcid":false,"given":"Stefano","family":"Gabriele","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2166-9788","authenticated-orcid":false,"given":"Sonia","family":"Marfia","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9344-8503","authenticated-orcid":false,"given":"Hern\u00e2ni","family":"Lopes","sequence":"additional","affiliation":[]}],"member":"140","published-online":{"date-parts":[[2021,10,14]]},"reference":[{"issue":"4","key":"key2021102507344384000_ref001","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1016\/S0030-4018(99)00116-9","article-title":"Simple and effective method for filtering speckle-interferometric phase fringe patterns","volume":"162","year":"1999","journal-title":"Optics Communications"},{"key":"key2021102507344384000_ref002","doi-asserted-by":"publisher","first-page":"1441","DOI":"10.1177\/1475921717744480","article-title":"Damage identification using modal strains identified from operational fiber-optic Bragg grating data","volume":"17","year":"2018","journal-title":"Structural Health Monitoring"},{"key":"key2021102507344384000_ref003","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1016\/j.ymss018.11.012","article-title":"Modal curvature-based damage localization in weakly damaged continuous beams","volume":"121","year":"2019","journal-title":"Mechanical Systems and Signal Processing"},{"issue":"3","key":"key2021102507344384000_ref004","doi-asserted-by":"publisher","first-page":"272","DOI":"10.1016\/j.compstruct.2006.06.034","article-title":"Damage localization in laminated composite plates using mode shapes measured by pulsed TV holography","volume":"76","year":"2006","journal-title":"Composite Structures"},{"key":"key2021102507344384000_ref005","doi-asserted-by":"publisher","DOI":"10.1088\/0957-0233\/21\/10\/102001","article-title":"Shearography technology and applications: a review","volume":"21","year":"2010","journal-title":"Measurement Science and Technology"},{"volume-title":"Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software","year":"1998","key":"key2021102507344384000_ref006"},{"volume-title":"Handbook of Holographic Interferometry: Optical and Digital Methods","year":"2005","key":"key2021102507344384000_ref007"},{"key":"key2021102507344384000_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/j.euromechsol.2021.104259","article-title":"Crack detection near the ends of a beam using wavelet transform and high resolution beam deflection measurement","volume":"88","year":"2021","journal-title":"European Journal of Mechanics \u2013 A\/Solids"},{"issue":"19-20","key":"key2021102507344384000_ref009","doi-asserted-by":"publisher","first-page":"1754","DOI":"10.1016\/j.compstruc.2011.03.014","article-title":"A numerical-experimental method for damage location based on rotation fields spatial differentiation","volume":"89","year":"2011","journal-title":"Computers and Structures"},{"issue":"5","key":"key2021102507344384000_ref010","doi-asserted-by":"publisher","first-page":"835","DOI":"10.3233\/SAV-2012-0692","article-title":"Interferometric techniques in structural damage identification","volume":"19","year":"2012","journal-title":"Shock and Vibration"},{"key":"key2021102507344384000_ref011","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/j.ymss016.02.039","article-title":"Damage identification in beams using speckle shearography and an optimal spatial sampling","volume":"79","year":"2016","journal-title":"Mechanical Systems and Signal Processing"},{"issue":"1","key":"key2021102507344384000_ref012","doi-asserted-by":"publisher","first-page":"548","DOI":"10.1016\/j.compstruct.2013.09.050","article-title":"A new technique to optimize the use of mode shape derivatives to localize damage in laminated composite plates","volume":"108","year":"2014","journal-title":"Composite Structures"},{"key":"key2021102507344384000_ref013","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1016\/j.compstruct.2015.08.011","article-title":"Application of higher order finite differences to damage localization in laminated composite plates","volume":"156","year":"2016","journal-title":"Composite Structures"},{"key":"key2021102507344384000_ref014","doi-asserted-by":"publisher","DOI":"10.1007\/s00366-021-01481-w","article-title":"Parameter tuning for wavelet transform-based damage index using mixture design","year":"2021","journal-title":"Engineering with Computers"},{"key":"key2021102507344384000_ref015","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1016\/0022-460X(91)90595-B","article-title":"Damage detection from Mode changes in curvature","volume":"145","year":"1991","journal-title":"Journal of Sound and Vibration"},{"issue":"4-5","key":"key2021102507344384000_ref016","doi-asserted-by":"publisher","first-page":"601","DOI":"10.3233\/SAV-2010-0551","article-title":"Identification of damage in a beam structure by using mode shape curvature squares","volume":"17","year":"2010","journal-title":"Shock and Vibration"},{"first-page":"193","article-title":"Vibrational Based Inspection of Civil Engineering Structures","year":"1993","key":"key2021102507344384000_ref017"},{"issue":"4-5","key":"key2021102507344384000_ref018","doi-asserted-by":"publisher","first-page":"783","DOI":"10.1016\/j.jsv.2004.08.021","article-title":"Optimal spatial sampling interval for damage detection by curvature or strain energy mode shapes","volume":"285","year":"2005","journal-title":"Journal of Sound and Vibration"},{"key":"key2021102507344384000_ref019","doi-asserted-by":"publisher","DOI":"10.1111\/str.12266","article-title":"Damage detection in beams from modal and wavelet analysis using a stationary roving mass and noise estimation","volume":"54","year":"2018","journal-title":"Strain"},{"issue":"8","key":"key2021102507344384000_ref020","doi-asserted-by":"publisher","first-page":"789","DOI":"10.3390\/app7080789","article-title":"Structural health monitoring (SHM) of civil structures","volume":"7","year":"2017","journal-title":"Applied Sciences"},{"issue":"2","key":"key2021102507344384000_ref021","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1006\/jsvi.1999.2295","article-title":"Damage detection in bridges using modal curvatures: application to a real damage scenario","volume":"226","year":"1999","journal-title":"Journal of Sound and Vibration"},{"key":"key2021102507344384000_ref022","doi-asserted-by":"publisher","DOI":"10.1088\/1361-665x\/ab6fe6","article-title":"Singular energy component for identification of initial delamination in CFRP laminates through piezoelectric actuation and non-contact measurement","volume":"29","year":"2020","journal-title":"Smart Materials and Structures"},{"key":"key2021102507344384000_ref024","doi-asserted-by":"publisher","first-page":"763","DOI":"10.1016\/j.ymss016.07.005","article-title":"Fourier spectral-based modal curvature analysis and its application to damage detection in beams","volume":"84","year":"2017","journal-title":"Mechanical Systems and Signal Processing"},{"volume-title":"Digital Shearography: New Developments and Applications","year":"2016","key":"key2021102507344384000_ref023"}],"container-title":["Multidiscipline Modeling in Materials and Structures"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/MMMS-07-2021-0124\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/MMMS-07-2021-0124\/full\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T21:43:10Z","timestamp":1753393390000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.emerald.com\/mmms\/article\/17\/6\/1061-1080\/298236"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,14]]},"references-count":24,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2021,10,14]]},"published-print":{"date-parts":[[2021,10,26]]}},"alternative-id":["10.1108\/MMMS-07-2021-0124"],"URL":"https:\/\/doi.org\/10.1108\/mmms-07-2021-0124","relation":{},"ISSN":["1573-6105"],"issn-type":[{"type":"print","value":"1573-6105"}],"subject":[],"published":{"date-parts":[[2021,10,14]]}}}