{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T13:43:00Z","timestamp":1769694180360,"version":"3.49.0"},"reference-count":32,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2021,7,2]],"date-time":"2021-07-02T00:00:00Z","timestamp":1625184000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Polymers"],"abstract":"<jats:p>The use of glass fibre reinforced polymer (GFRP) composites in civil engineering structures has seen considerable growth in recent years due to their high strength, low self-weight, and corrosion resistance, namely when compared to traditional materials, such as steel and reinforced concrete. To enable the structural use of GFRP composite materials in civil engineering applications, especially in footbridges, it is necessary to gather knowledge on their structural behaviour, particularly under dynamic loads, and to evaluate the ability of current design tools to predict their response. In fact, excessive vibration has a major influence on the in-service performance (comfort) of slender structures as well on their service life. The use of composite materials that combine high damping capacity with relatively high stiffness and low mass can provide functional and economic benefits, especially for footbridges. This paper aims to investigate the dynamic behaviour of GFRP free-supported beams to evaluate their modal characteristics (frequency, damping, and modal shape). To assess the benefits of using a structure made of pultruded GFRP rather than a conventional material\u2014steel, a comparative analysis between the dynamic characteristics of GFRP and steel beams is performed. To specifically address material damping and to minimize the interference of the boundary conditions, the beams are tested in a free condition, resting on a low-density foam base. The results show that the damping capacity of GFRP is much higher than that of steel, as the measured damping factor of GFRP is five times higher than that of steel for the same boundary conditions and similar geometry. Furthermore, the fact that the frequencies of the tested specimens resemble for the two different materials highlights the perceived damping qualities of the polymer-based composite material. Finally, an energy method for evaluating the influence of the scale factor on material damping is applied, which made it possible to infer that the damping varies as a function of frequency but is not explicitly affected by the length of the specimens.<\/jats:p>","DOI":"10.3390\/polym13132201","type":"journal-article","created":{"date-parts":[[2021,7,2]],"date-time":"2021-07-02T10:06:34Z","timestamp":1625220394000},"page":"2201","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Comparative Study of Damping on Pultruded GFRP and Steel Beams"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2708-334X","authenticated-orcid":false,"given":"Vitor","family":"Dacol","sequence":"first","affiliation":[{"name":"CONSTRUCT (ViBEST), Faculty of Engineering (FEUP), Universidade do Porto, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1188-5978","authenticated-orcid":false,"given":"Elsa","family":"Caetano","sequence":"additional","affiliation":[{"name":"CONSTRUCT (ViBEST), Faculty of Engineering (FEUP), Universidade do Porto, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5485-136X","authenticated-orcid":false,"given":"Jo\u00e3o Ramoa","family":"Correia","sequence":"additional","affiliation":[{"name":"CERIS, DECivil, IST, Universidade de Lisboa, 1049-001 Lisbon, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"7061","DOI":"10.1016\/j.matpr.2017.11.370","article-title":"Study of damping in composite beams","volume":"5","author":"Kulkarni","year":"2018","journal-title":"Mater. Today Proc."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/j.compstruct.2007.10.024","article-title":"El Damping analysis of composite materials and structures","volume":"85","author":"Berthelot","year":"2008","journal-title":"Compos. Struct."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"6177","DOI":"10.1016\/j.jsv.2013.06.016","article-title":"Finite element analysis and experimental study on dynamic properties of a composite beam with viscoelastic damping","volume":"332","author":"Wang","year":"2013","journal-title":"J. Sound Vib."},{"key":"ref_4","first-page":"76","article-title":"Viscoelastic Damping Technologies-Part I: Modeling and Finite Element Implementation","volume":"1","author":"Vasques","year":"2010","journal-title":"J. Adv. Res. Mech. Eng."},{"key":"ref_5","unstructured":"Nashif, A.D., Jones, D.I.G., and Henderson, J.P. (1985). Vibration Damping, Wiley & Sons Ltd."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/S0263-8223(98)00073-7","article-title":"Recent research on enhancement of damping in polymer composites","volume":"44","author":"Finegan","year":"1999","journal-title":"Compos. Struct."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"402","DOI":"10.1177\/002199837300700401","article-title":"Effect of fiber orientation and laminate geometry on the dynamic properties of CFRP","volume":"7","author":"Adams","year":"1973","journal-title":"J. Compos. Mater."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2969","DOI":"10.1016\/j.compstruct.2011.05.005","article-title":"Development of a pedestrian bridge with GFRP profiles and fiber reinforced self-compacting concrete deck","volume":"93","author":"Mendes","year":"2011","journal-title":"Compos. Struct."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1016\/j.proeng.2016.08.665","article-title":"FRP Composites and their Using in the Construction of Bridges","volume":"161","author":"Sonnenschein","year":"2016","journal-title":"Procedia Eng."},{"key":"ref_10","unstructured":"American Society of Civil Engineers (ASCE) (2010). Pre-Standard for Load & Resistance Factor Design (LRFD) of Pultruded Fiber Reinforced Polymer (FRP) Structures, American Society of Civil Engineers (ASCE)."},{"key":"ref_11","unstructured":"Ascione, L., Caron, J.F., Correia, J.C., De Corte, W., Godonou, P., Knippers, J., Moussiaux, E., Mottram, T., Oppe, M., and Silvestre, N. (2018). Prospect for New Guidance in the Design of FRP Structures: Updated Report, European Composites Industry Association (EuCIA). Available online: www.eucia.eu."},{"key":"ref_12","unstructured":"Italian National Research Council-CNR-DT 205\/2007 (2008). Guide for the Design and Construction of Structures Made of FRP Pultruded Elements, Advisory Committee on Technical Recommendations for Construction (CNR)."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"81","DOI":"10.7763\/IJET.2015.V7.771","article-title":"Dynamic Identification of All-FRP Pultruded Structures","volume":"7","author":"Boscato","year":"2015","journal-title":"Int. J. Eng. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1061\/(ASCE)1090-0268(2009)13:6(565)","article-title":"Free Vibrations of Pultruded FRP Elements: Mechanical Characterization, Analysis, and Applications","volume":"13","author":"Boscato","year":"2009","journal-title":"J. Compos. Constr."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"10013","DOI":"10.1051\/matecconf\/201926210013","article-title":"All-GFRP Footbridge under Human-Induced Excitation","volume":"262","author":"Stankiewicz","year":"2019","journal-title":"MATEC Web Conf."},{"key":"ref_16","unstructured":"SETRA (2006). Guide M\u00e9thodologique Passerelles Pi\u00e9tonnes (Technical Guide Footbridges: Assessment of Vibrational Behaviour of Footbridges under Pedestrian Loading), Service D\u2019\u00e9tudes Techniques des Routes et Autoroutes."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Silva, J.M.M., and Maia, N.M.M. (1999). Modal Analysis and Testing, Kluwer Academic Publishers.","DOI":"10.1007\/978-94-011-4503-9"},{"key":"ref_18","unstructured":"Caetano, E.D.S. (1992). Identifica\u00e7\u00e3o Experimental de Par\u00e2metros Din\u00e2micos em Sistemas Estruturais. [Master\u2019s Thesis, University of Porto]."},{"key":"ref_19","unstructured":"Rao, S.S. (2017). Mechanical Vibrations, Pearson Education Limited. [6th ed.]."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/0020-7403(75)90007-7","article-title":"Energy dissipation of a vibrating Timoshenko beam considering support and material damping","volume":"17","author":"MacBain","year":"1975","journal-title":"Int. J. Mech. Sci."},{"key":"ref_21","first-page":"179","article-title":"Estimation of modal damping for structures with localized dissipation","volume":"6","author":"Krifa","year":"2015","journal-title":"Conf. Proc. Soc. Exp. Mech. Ser."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/0141-6359(96)00051-7","article-title":"An integrated approach to structural damping","volume":"18","author":"Marsh","year":"1996","journal-title":"Precis. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"French, A.P. (2001). Vibrations and Waves, CRC Press LLC.","DOI":"10.1119\/1.4765679"},{"key":"ref_24","unstructured":"King, G.C. (2009). Vibrations and Waves, Wiley & Sons Ltd."},{"key":"ref_25","unstructured":"Nunes, F.F. (2016). Structural Behaviour of Frp Pultruded Beams and Columns. [Ph.D. Thesis, IST\u2014Civil Engineering, University of Lisboa]."},{"key":"ref_26","unstructured":"International Organization for Standardization (1997). ISO 527-1 Plastics\u2014Determination of Tensile Properties-Part 1: General Principles, Vernier."},{"key":"ref_27","unstructured":"(2002). ASTM D 695-02 Standard Test Method for Compressive Properties of Rigid Plastics, American Society for Testing and Materials."},{"key":"ref_28","unstructured":"International Organization for Standardization (2009). ISO\/DIS 527-5 Plastics\u2014Determination of Tensile Properties\u2014Part 5: Test Conditions for Unidirectional Fibre-Reinforced Plastic Composites, Vernier."},{"key":"ref_29","unstructured":"(2006). ASTM D2344 D2344M Standard Test Method for Short-Beam Strength of Polymer Matrix Composite Materials and Their Laminates, American Society for Testing and Materials."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Bauchau, O.A., and Craig, J.I. (2009). Structural Analysis. Solid Mechanics and Its Applications, Springer.","DOI":"10.1007\/978-90-481-2516-6"},{"key":"ref_31","unstructured":"Alsehnawi, R., Nakajima, A., Takeshima, R., and Sadeq, A.H. (2014, January 8\u201311). Vibration Amplitude-Dependent Natural Frequency and Damping Ratio of Repaired Pier Model. Proceedings of the EWSHM-7th European Workshop on Structural Health Monitoring, Nantes, France."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/0022-460X(72)90766-3","article-title":"An investigation of scaling laws for vibrating beams and plates with special attention to the effects of shear and rotatory inertia","volume":"20","author":"Kristiansen","year":"1972","journal-title":"J. Sound Vib."}],"container-title":["Polymers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4360\/13\/13\/2201\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:25:09Z","timestamp":1760163909000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4360\/13\/13\/2201"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,2]]},"references-count":32,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["polym13132201"],"URL":"https:\/\/doi.org\/10.3390\/polym13132201","relation":{},"ISSN":["2073-4360"],"issn-type":[{"value":"2073-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,7,2]]}}}