{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T17:26:17Z","timestamp":1754155577397,"version":"3.41.2"},"reference-count":24,"publisher":"Emerald","issue":"1","license":[{"start":{"date-parts":[[2022,10,31]],"date-time":"2022-10-31T00:00:00Z","timestamp":1667174400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJSI"],"published-print":{"date-parts":[[2023,2,8]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-subheading\">Purpose<\/jats:title><jats:p>Laminated composite materials are a staple of modern material development, with extremely strong fibers being combined with resins to form versatile and efficient engineering structures. However, the advancements in material development must be accompanied by equally advanced methods for damage detection, localization and quantification, as these materials develop inherently unique failure modes. This paper aims to further the study of the use of modal shapes and their spatial derivatives to localize damage in laminated composite rectangular plates. Exploring different damage scenarios and models, as well as different orders of mode shape derivatives of laminated plates.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Design\/methodology\/approach<\/jats:title><jats:p>ANSYS\u00ae Parametric Design Language (APDL) is used to perform finite element analysis of plates with several damage scenarios and damage mechanics models. MATLAB\u00ae is used to post-process these simulation results, namely by calculating the derivatives using finite differences, applying three distinct sets of damage indices, including one that is presently proposed. To mimic experimental conditions and test the resilience of the derivative orders, different noise levels are introduced into the results of the finite element analysis. A quality index is employed to quantitatively evaluate the solutions, mainly regarding the response to the introduced noise.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Findings<\/jats:title><jats:p>The results show that the applied damage localization methods have comparable results in terms of quality. These results also show that the quality of the damage localizations is higher when the damaged areas coincide with high displacement\/curvature areas of the mode shapes and that higher noise levels have a more noticeable negative impact when employing higher-order derivatives.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Originality\/value<\/jats:title><jats:p>Exploring different damage scenarios and models, as well as different orders of mode shape derivatives of laminated plates. The influence of a specific damage layer on the order of derivatives of modal response is evaluated, showing promising results concerning its identification.<\/jats:p><\/jats:sec>","DOI":"10.1108\/ijsi-04-2022-0057","type":"journal-article","created":{"date-parts":[[2022,10,26]],"date-time":"2022-10-26T22:34:27Z","timestamp":1666823667000},"page":"57-73","source":"Crossref","is-referenced-by-count":3,"title":["On the use of finite differences for\u00a0vibration-based damage localization in laminated composite plates"],"prefix":"10.1108","volume":"14","author":[{"given":"Tom\u00e1s","family":"Oliveira","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3662-6166","authenticated-orcid":false,"given":"Jos\u00e9 V.","family":"Ara\u00fajo dos Santos","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":[[2022,10,31]]},"reference":[{"key":"key2023020711135449300_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruct.2021.114863","article-title":"A methodology for sensor number and placement optimization for vibration-based damage detection of composite structures under model uncertainty","volume":"279","year":"2022","journal-title":"Composite Structures"},{"edition":"2nd ed.","volume-title":"Composite Materials for Aircraft Structures","year":"2004","key":"key2023020711135449300_ref002"},{"issue":"6","key":"key2023020711135449300_ref003","doi-asserted-by":"publisher","first-page":"1061","DOI":"10.1108\/MMMS-07-2021-0124","article-title":"Improvement on modal curvatures methods for multiple damage identification in beams","volume":"17","year":"2021","journal-title":"Multidiscipline Modeling in Materials and Structures"},{"issue":"3","key":"key2023020711135449300_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"},{"issue":"2","key":"key2023020711135449300_ref005","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1002\/stc.210","article-title":"Experimental validation of the higher-order derivative discontinuity method for damage identification","volume":"15","year":"2008","journal-title":"Structural Control and Health Monitoring"},{"key":"key2023020711135449300_ref006","unstructured":"Hale, J. (2008), \u201cBoeing 787 from the ground up\u201d, available at: https:\/\/www.boeing.com\/commercial\/aeromagazine\/articles\/qtr_4_06\/AERO_Q 406_article4.pdf (accessed 30 March 2022)."},{"key":"key2023020711135449300_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/j.measurement.2021.110388","article-title":"Using incomplete FRF measurements for damage detection of structures with closely-spaced eigenvalues","volume":"188","year":"2022","journal-title":"Measurement"},{"issue":"3","key":"key2023020711135449300_ref008","doi-asserted-by":"publisher","first-page":"101","DOI":"10.22115\/scce.2021.292279.1340","article-title":"Damage localization of RC beams via wavelet analysis of noise contaminated modal curvatures","volume":"5","year":"2021","journal-title":"Journal of Soft Computing in Civil Engineering"},{"key":"key2023020711135449300_ref009","doi-asserted-by":"publisher","first-page":"3055","DOI":"10.1016\/j.istruc.2021.09.059","article-title":"Wavelet-based damage localization and severity estimation of experimental RC beams subjected to gradual static bending tests","volume":"34","year":"2021","journal-title":"Structures"},{"volume-title":"Theory Reference for the Mechanical APDL and Mechanical Applications","year":"2009","key":"key2023020711135449300_ref010"},{"issue":"8","key":"key2023020711135449300_ref011","doi-asserted-by":"publisher","first-page":"763","DOI":"10.1016\/S0167-6636(02)00204-1","article-title":"On a damage mesomodel for laminates: micromechanics basis and improvement","volume":"35","year":"2003","journal-title":"Mechanics of Materials"},{"issue":"5","key":"key2023020711135449300_ref012","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":"key2023020711135449300_ref013","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/j.ymssp.2016.02.039","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"},{"key":"key2023020711135449300_ref014","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":"key2023020711135449300_ref015","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":"key2023020711135449300_ref016","first-page":"679","article-title":"Delamination identification on FRP composites using normalized modal curvature delamination","volume":"10","year":"2020","journal-title":"International Journal of Mechanical and Production Engineering Research and Development (IJMPERD)"},{"issue":"1","key":"key2023020711135449300_ref017","doi-asserted-by":"publisher","DOI":"10.1177\/1687814020987329","article-title":"Detection and localization of multiple small damages in beam","volume":"13","year":"2021","journal-title":"Advances in Mechanical Engineering"},{"issue":"2","key":"key2023020711135449300_ref018","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1016\/0022-460X(91)90595-B","article-title":"Damage detection from changes in curvature mode shapes","volume":"145","year":"1991","journal-title":"Journal of Sound and Vibration"},{"issue":"1","key":"key2023020711135449300_ref019","doi-asserted-by":"publisher","DOI":"10.1002\/stc.2856","article-title":"Application of cubic spline interpolation with optimal spatial sampling for damage identification","volume":"29","year":"2022","journal-title":"Structural Control and Health Monitoring"},{"first-page":"163","article-title":"Application of multilayer perceptron neural network for damage detection in rectangular laminated composite plates based on vibrational analysis","year":"2022","key":"key2023020711135449300_ref020"},{"issue":"4-5","key":"key2023020711135449300_ref021","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"},{"volume-title":"Fundamentals of Composites Manufacturing: Materials, Methods and Applications","year":"2008","key":"key2023020711135449300_ref022"},{"issue":"2","key":"key2023020711135449300_ref023","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"},{"issue":"2","key":"key2023020711135449300_ref024","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1006\/jsvi.1999.2624","article-title":"Vibration-based model-dependent damage (delamination) identification and health monitoring for composites structures","volume":"230","year":"2000","journal-title":"Journal of Sound and Vibration"}],"container-title":["International Journal of Structural Integrity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/IJSI-04-2022-0057\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/IJSI-04-2022-0057\/full\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T21:46:36Z","timestamp":1753393596000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.emerald.com\/ijsi\/article\/14\/1\/57-73\/160155"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,31]]},"references-count":24,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,10,31]]},"published-print":{"date-parts":[[2023,2,8]]}},"alternative-id":["10.1108\/IJSI-04-2022-0057"],"URL":"https:\/\/doi.org\/10.1108\/ijsi-04-2022-0057","relation":{},"ISSN":["1757-9864"],"issn-type":[{"type":"print","value":"1757-9864"}],"subject":[],"published":{"date-parts":[[2022,10,31]]}}}