{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T11:04:44Z","timestamp":1790075084749,"version":"4.0.1"},"reference-count":38,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2026,9,19]],"date-time":"2026-09-19T00:00:00Z","timestamp":1789776000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100011033","name":"Spanish State Research Agency","doi-asserted-by":"publisher","award":["PID2023-147535OB-I00"],"award-info":[{"award-number":["PID2023-147535OB-I00"]}],"id":[{"id":"10.13039\/501100011033","id-type":"DOI","asserted-by":"publisher"}]},{"award":["PID2023-147535OB-I00"],"award-info":[{"award-number":["PID2023-147535OB-I00"]}],"id":[{"id":"https:\/\/ror.org\/003x0zc53","id-type":"ROR","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006382","name":"University of Oviedo","doi-asserted-by":"publisher","award":["PRPUO-PUB-ASV-2025-PUENTE-05"],"award-info":[{"award-number":["PRPUO-PUB-ASV-2025-PUENTE-05"]}],"id":[{"id":"10.13039\/501100006382","id-type":"DOI","asserted-by":"publisher"}]},{"award":["PRPUO-PUB-ASV-2025-PUENTE-05"],"award-info":[{"award-number":["PRPUO-PUB-ASV-2025-PUENTE-05"]}],"id":[{"id":"https:\/\/ror.org\/006gksa02","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Monolithic and laminated glass elements are increasingly used in structural applications, where their response to impact loading must be assessed to ensure safety. For soft impacts, simplified simulations based only on the initial impact velocity may be inaccurate because the transient coupling between the impactor and the glass depends on the impactor stiffness and mass. This study investigates the dynamic response of monolithic and laminated glass beams under soft impact loading using accelerometers, an instrumented impact hammer, strain gauges, operational modal analysis, and simplified finite element models. The influence of three impactor heads and three hammer masses is examined. Two approaches are assessed: a modal simulation driven by the measured impact-force history and a sensor-based method that reconstructs stresses from measured structural responses and experimentally identified mode shapes. Comparisons with experimental measurements yield approximate absolute-peak errors of 2.1% for the monolithic-beam acceleration and 1.5% for the laminated-beam stress, normalised by the maximum absolute measured response in each case, with corresponding Pearson correlation coefficients of 0.972 and 0.943. The results show that accounting for the measured impact-force history and combining response measurements at discrete locations with modal information can provide efficient estimates of dynamic response and stress without explicitly modelling the impactor-glass contact.<\/jats:p>","DOI":"10.3390\/s26185929","type":"journal-article","created":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T10:21:48Z","timestamp":1790072508000},"page":"5929","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Sensor-Based Dynamic Response and Stress Estimation in Monolithic and Laminated Glass Beams Under Soft Impact Loading"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4870-7710","authenticated-orcid":false,"given":"Natalia","family":"Garc\u00eda-Fern\u00e1ndez","sequence":"first","affiliation":[{"name":"Department of Construction and Manufacturing Engineering, University of Oviedo, Campus de Gij\u00f3n, Zona Oeste, Edificio 7, 33203 Gij\u00f3n, Spain"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"software","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7915-9513","authenticated-orcid":false,"given":"F.","family":"Pelayo","sequence":"additional","affiliation":[{"name":"Department of Construction and Manufacturing Engineering, University of Oviedo, Campus de Gij\u00f3n, Zona Oeste, Edificio 7, 33203 Gij\u00f3n, Spain"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"}]},{"given":"Manuel","family":"Aenlle","sequence":"additional","affiliation":[{"name":"Department of Construction and Manufacturing Engineering, University of Oviedo, Campus de Gij\u00f3n, Zona Oeste, Edificio 7, 33203 Gij\u00f3n, Spain"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0733-8851","authenticated-orcid":false,"given":"Mario","family":"L\u00f3pez-Gallego","sequence":"additional","affiliation":[{"name":"Department of Construction and Manufacturing Engineering, University of Oviedo, Campus de Gij\u00f3n, Zona Oeste, Edificio 7, 33203 Gij\u00f3n, Spain"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"}]},{"given":"Mar\u00eda Jes\u00fas","family":"Lamela-Rey","sequence":"additional","affiliation":[{"name":"Department of Construction and Manufacturing Engineering, University of Oviedo, Campus de Gij\u00f3n, Zona Oeste, Edificio 7, 33203 Gij\u00f3n, Spain"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"methodology","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,19]]},"reference":[{"key":"ref_1","unstructured":"Ferry, J.D. (1980). Viscoelastic Properties of Polymers, John Wiley & Sons. [3rd ed.]."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Lakes, R.S. (2009). Viscoelastic Materials, Cambridge University Press.","DOI":"10.1017\/CBO9780511626722"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.engstruct.2011.12.039","article-title":"Effective thickness of laminated glass beams: New expression via a variational approach","volume":"38","author":"Galuppi","year":"2012","journal-title":"Eng. Struct."},{"key":"ref_4","unstructured":"Bennison, S.J., Qin, M.H., and Davies, P.S. (2008). High-performance laminated glass for structurally efficient glazing. Innovative Light-Weight Structures and Sustainable Facades, The Hong Kong Polytechnic University."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1016\/j.compositesb.2014.07.018","article-title":"Dynamic effective thickness in laminated-glass beams and plates","volume":"67","author":"Pelayo","year":"2014","journal-title":"Compos. Part B Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"140183","DOI":"10.1016\/j.conbuildmat.2025.140183","article-title":"Thermomechanical high strain rate behavior of LG polymeric interlayer materials","volume":"464","author":"Elkilani","year":"2025","journal-title":"Constr. Build. Mater."},{"key":"ref_7","unstructured":"(2003). Glass in Building\u2014Pendulum Test\u2014Impact Test Method and Classification for Flat Glass (Standard No. UNE-EN 12600:2003)."},{"key":"ref_8","unstructured":"(2005). Laminated Glass (Standard No. JIS R 3205:2005)."},{"key":"ref_9","unstructured":"(2009). Safety Glazing Materials Used in Buildings\u2014Safety Performance Specifications and Methods of Test (Standard No. ANSI Z97.1-2009)."},{"key":"ref_10","unstructured":"Boeykens, G. (2014). Numerical Simulation of a Pendulum Impact Setup for Laminated Glass, Ghent University."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1016\/j.ijimpeng.2010.10.035","article-title":"Failure criterion for laminated glass under impact loading and its application in finite element simulation","volume":"38","author":"Pyttel","year":"2011","journal-title":"Int. J. Impact Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1465","DOI":"10.1016\/j.ijimpeng.2006.07.008","article-title":"A finite element model for impact simulation with laminated glass","volume":"34","author":"Timmel","year":"2007","journal-title":"Int. J. Impact Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.engstruct.2014.08.043","article-title":"A reduced model for the design of glass structures subjected to dynamic impulse load","volume":"80","author":"Persson","year":"2014","journal-title":"Eng. Struct."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"111315","DOI":"10.1016\/j.engstruct.2020.111315","article-title":"Royer-Carfagni, Engineered modelling of the soft-body impact test on glazed surfaces","volume":"226","author":"Viviani","year":"2021","journal-title":"Eng. Struct."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"113988","DOI":"10.1016\/j.engstruct.2022.113988","article-title":"Reduced order modeling of soft-body impact on glass panels","volume":"256","author":"Andersson","year":"2022","journal-title":"Eng. Struct."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/s40940-024-00266-z","article-title":"Experimental and numerical characterization of input forces in glass curtain walls under soft body impact","volume":"9","author":"Cella","year":"2024","journal-title":"Glass Struct. Eng."},{"key":"ref_17","first-page":"36","article-title":"Dynamic response of laminated glass subjected to soft-body impact in intact and post-fracture states","volume":"640","author":"Kosmal","year":"2025","journal-title":"Mater. Bud."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1007\/s40940-026-00321-x","article-title":"Experimental and numerical study of impact loading on multi-layered laminated safety glass","volume":"11","author":"HosseinKhani","year":"2026","journal-title":"Glass Struct. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Gupta, A.K., Lin, Y., Pesek, S., McDougal, N., Kent, R., and Dietsche, L. (2024). Predictive Analysis of Laminated Glass Performance Under Static and Dynamic Loading Conditions. Challenging Glass Conf. Proc., 9.","DOI":"10.47982\/cgc.9.626"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s40940-026-00317-7","article-title":"Neural networks for the pendulum test with twin-tire impactor on flat and cylindrically curved glass panels","volume":"11","author":"Timmers","year":"2026","journal-title":"Glass Struct. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1771","DOI":"10.1177\/10996362221084636","article-title":"Response of laminated glass elements subject to dynamic loadings using a monolithic model and a stress effective Young\u2019s modulus","volume":"24","year":"2022","journal-title":"J. Sandw. Struct. Mater."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1092","DOI":"10.1016\/j.engstruct.2013.06.018","article-title":"The effective-thickness concept in laminated-glass elements under static loading","volume":"56","author":"Pelayo","year":"2013","journal-title":"Eng. Struct."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Cao, D., Liu, X., Yang, Z., Huang, J., Xu, M., and Wan, D. (2025). The Validation and Discussion of a Comparative Method Based on Experiment to Determine the Effective Thickness of Composite Glass. Buildings, 15.","DOI":"10.3390\/buildings15142542"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1016\/j.bsecv.2024.05.001","article-title":"Characterization of the dynamic properties of an automotive laminated glass ceiling","volume":"63","author":"Achiaga","year":"2024","journal-title":"Bol. Soc. Esp. Ceram. Vidr."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1791","DOI":"10.1007\/s11340-015-0073-6","article-title":"Modal Analysis Based Stress Estimation for Structural Elements Subjected to Operational Dynamic Loadings","volume":"55","author":"Pelayo","year":"2015","journal-title":"Exp. Mech."},{"key":"ref_26","unstructured":"Garc\u00eda, I., Aenlle, M., and Pelayo, F. (2018, January 9\u201312). A time-domain effective Young\u2019s modulus to estimate stresses in laminated glass beams under dynamic loadings. Proceedings of the 4th International Conference on Mechanics of Composites (MECHCOMP 2018), Madrid, Spain."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.compositesb.2015.08.001","article-title":"An effective thickness to estimate stresses in laminated glass beams under dynamic loadings","volume":"82","author":"Aenlle","year":"2015","journal-title":"Compos. Part B Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"107505","DOI":"10.1016\/j.ymssp.2020.107505","article-title":"Full-field strain estimation of subsystems within time-varying and nonlinear systems using modal expansion","volume":"153","author":"Friis","year":"2021","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Ercan, T., and Papadimitriou, C. (2021). Optimal Sensor Placement for Reliable Virtual Sensing Using Modal Expansion and Information Theory. Sensors, 21.","DOI":"10.3390\/s21103400"},{"key":"ref_30","unstructured":"Clough, R.W., and Penzien, J. (1993). Dynamics of Structures, McGraw-Hill. [2nd ed.]."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1016\/j.measurement.2014.09.004","article-title":"Integrating time signals in frequency domain\u2014Comparison with time domain integration","volume":"58","author":"Brandt","year":"2014","journal-title":"Measurement"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/j.engstruct.2004.10.013","article-title":"The determination of bridge displacement using measured acceleration","volume":"27","author":"Park","year":"2005","journal-title":"Eng. Struct."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Friswell, M.I., and Mottershead, J.E. (1995). Finite Element Model Updating in Structural Dynamics, Springer.","DOI":"10.1007\/978-94-015-8508-8"},{"key":"ref_34","unstructured":"Heylen, W., Lammens, S., and Sas, P. (1997). Modal Analysis Theory and Testing, Katholieke Universiteit Leuven. [2nd ed.]."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Brincker, R., Zhang, L., and Andersen, P. (2000, January 7\u201310). Modal identification from ambient responses using frequency domain decomposition. Proceedings of the 18th International Modal Analysis Conference (IMAC-XVIII), San Antonio, TX, USA.","DOI":"10.1088\/0964-1726\/10\/3\/303"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Brincker, R., and Ventura, C.E. (2015). Introduction to Operational Modal Analysis, John Wiley & Sons, Ltd.","DOI":"10.1002\/9781118535141"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Shang, X.-Q., Huang, T.-L., He, Y.-B., and Chen, H.-P. (2024). Operational Modal Analysis of Civil Engineering Structures with Closely Spaced Modes Based on Improved Hilbert\u2013Huang Transform. Sensors, 24.","DOI":"10.3390\/s24237600"},{"key":"ref_38","unstructured":"Moebs, W., Ling, S.J., and Sanny, J. (2016). University Physics, OpenStax. Available online: https:\/\/openstax.org\/books\/university-physics-volume-1\/pages\/10-4-moment-of-inertia-and-rotational-kinetic-energy."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/18\/5929\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T10:24:57Z","timestamp":1790072697000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/18\/5929"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,19]]},"references-count":38,"journal-issue":{"issue":"18","published-online":{"date-parts":[[2026,9]]}},"alternative-id":["s26185929"],"URL":"https:\/\/doi.org\/10.3390\/s26185929","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,19]]}}}