Experimental–Analytical Identification of Shear Elastic Modulus and Shear Correction Factor in Composite Wind Turbine Blades

Document Type : Research Paper

Authors
1 Centro de Investigación, Innovación y Desarrollo Tecnológico (CIIDETEC), Universidad del Valle de México (UVM), Campus Online, Av. Marina Nacional 500, Anáhuac I Secc, Miguel Hidalgo, Ciudad de México
2 División de Estudios de Posgrado, Universidad del Istmo, Ciudad Universitaria S/N Barrio Santa Cruz 4a. Sección, Sto. Domingo Tehuantepec, Oaxaca, 70760, México
3 Departamento de Metal Mecánica, Tecnológico Nacional de México/IT de Tuxtla Gutiérrez, Carretera Panamericana Km 1080, Tuxtla Gutiérrez C.P. 29050, México
4 Instituto de Investigación e Innovación en Energías Renovables, Universidad Autónoma de Ciencias y Artes de Chiapas, Libramiento norte poniente 1150, Lajas Maciel, Tuxtla Gutiérrez, Chis, 29039, México
5 Consejo de Ciencia y Tecnología del Estado de Querétaro (CONCYTEQ), Av. Prolongación Luis Pasteur 36, Centro, Santiago de Querétaro 76000, México
6 Programa Académico de Ingeniería Mecatrónica, Universidad Politécnica de Chiapas, Suchiapa 29150, México
7 Programa Académico de Ingeniería en Manufactura Avanzada, Universidad Politécnica de Chiapas, Suchiapa 29150, México
Abstract
Accurate estimation of the effective shear stiffness of composite wind turbine blades remains challenging because equivalent beam models require reliable shear properties for hollow anisotropic composite structures. This study proposes a hybrid experimental–analytical methodology that integrates experimental modal analysis, laminate-based sectional modeling, and thin-walled shear flow theory to identify the effective shear elastic modulus and determine the shear correction factor. Unlike conventional approaches based on prescribed material properties or simplified assumptions, the proposed framework directly links experimental dynamic response with equivalent structural parameters. The identified shear elastic modulus shows deviations below 1.1% across vibration modes. The methodology improves the accuracy of equivalent Timoshenko beam models for structural characterization, vibration analysis, and structural health monitoring of composite wind turbine blades.
Keywords
Subjects

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[1] Asef, M.R., Farrokhrouz, M., A Semi-Empirical Relation between Static and Dynamic Elastic Modulus, Journal of Petroleum Science and Engineering, 157, 2017, 359–363.
[2] Sahu, S.K., Das, P., Experimental and Numerical Studies on Vibration of Laminated Composite Beam with Transverse Multiple Cracks, Mechanical Systems and Signal Processing, 135, 2020, 106398.
[3] Ghoneam, S.M., Dynamic Analysis of Open Cracked Laminated Composite Beams, Composite Structures, 32, 1995, 3–11.
[4] Giaccu, G.F., Meloni, D., Concu, G., Valdes, M., Fragiacomo, M., Use of the Cantilever Beam Vibration Method for Determining the Elastic Properties of Maritime Pine Cross-Laminated Panels, Engineering Structures, 200, 2019, 109623.
[5] Guan, C., Zhang, H., Hunt, J.F., Yan, H., Determining Shear Modulus of Thin Wood Composite Materials Using a Cantilever Beam Vibration Method, Construction and Building Materials, 121, 2016, 285–289.
[6] Apsan, M.R., Mitu, A.M., Neagoe, C.A., Pop, N., Sireteanu, T., Non-Destructive Testing for Evaluation of Young’s Modulus by Using Free Vibration Response of Composite Materials, Applied Sciences, 15, 2025, 10189.
[7] Loh, T.B., Wu, Y., Goh, S.H., Kong, K.H., Goh, K.L., Chong, J.J., An Integrated Approach for the Determination of Young’s Modulus of a Cantilever Beam Using Finite Element Analysis and the Digital Image Correlation Technique, Electronics, 11, 2022, 2826.
[8] López-Puerto, A., Avilés, F., Gamboa, F., Oliva, A.I., A Vibrational Approach to Determine the Elastic Modulus of Individual Thin Films in Multilayers, Thin Solid Films, 565, 2014, 228–236.
[9] Lopez-Lopez, A., Robles-Ocampo, J.B., Lastres-Danguillecourt, O., Ibañez, G., Hernandez-Estrada, E., Sevilla-Camacho, P.Y., Novel Method for Determination the Dynamic Elastic Modulus of Composite Wind Turbine Blades, Engineering Structures, 312, 2024, 118254.
[10] Gruttmann, F., Wagner, W., Shear Correction Factors in Timoshenko’s Beam Theory for Arbitrary Shaped Cross-Sections, Computational Mechanics, 27, 2001, 199–207.
[11] Ding, Y.Y., Bai, L.H., Chen, W.F., Liu, Y.P., Chan, S.L., A Generalized Method for Shear Correction Factors of Arbitrary Thin-Walled Sections, Advanced Steel Construction, 19, 2023, 223–241.
[12] Freund, J., Karakoç, A., Shear and Torsion Correction Factors of Timoshenko Beam Model for Generic Cross Sections, Research on Engineering Structures and Materials, 2, 2016, 19–27.
[13] Dong, S.B., Alpdogan, C., Taciroglu, E., Much Ado about Shear Correction Factors in Timoshenko Beam Theory, International Journal of Solids and Structures, 47, 2010, 1651–1665.
[14] Kirad, A., Zebbiche, T., Boun-Jad, M., Numerical Computation of Shear Stress in a Complex Cross Section Subjected to a Shear Force and Application to Airfoils, Mechanics and Industry, 17, 2016, 511.
[15] Zefouni, O., Kirad, A.E.K., Determination of the Shear Correction Factors of Complex Plane Sections for the Bending of Beams and Application to Airfoils, Indian Journal of Physics, 96, 2022, 2457–2466.
[16] D’Ottavio, M., Polit, O., Classical, First Order, and Advanced Theories, Stability and Vibrations of Thin Walled Composite Structures, Woodhead Publishing, 2017, 91–140.
[17] Hutchinson, J.R., Shear Coefficients for Timoshenko Beam Theory, Journal of Applied Mechanics, 68, 2001, 87–92.
[18] Banerjee, J.R., Kennedy, D., Elishakoff, I., Further Insights into the Timoshenko–Ehrenfest Beam Theory, Journal of Vibration and Acoustics, 144, 2022, 041014.
[19] Lopez-Lopez, A., Sánchez-Albores, R.M., Sevilla-Camacho, P.Y., Torres-Ventura, H.H., Rodríguez-Resendíz, J., Robles-Ocampo, J.B., Nonlinear Dynamic Analysis of Composite Wind Turbine Blades Using Lamination and Equivalent Beam Theory, Journal of Applied and Computational Mechanics, 2026, DOI: 10.22055/jacm.2026.48947.5616.
[20] Wang, L., Liu, X., Guo, L., Renevier, N., Stables, M., A Mathematical Model for Calculating Cross-Sectional Properties of Modern Wind Turbine Composite Blades, Renewable Energy, 64, 2014, 52–60.
[21] Zheng, T., Ji, T., Equivalent Representations of Beams with Periodically Variable Cross-Sections, Engineering Structures, 33, 2011, 706–719.
[22] Mahmoud, M.A., Dynamic Spring Constants of Higher Resonance Modes of Uniform and Tapered Microcantilevers with Tip Masses, Micron, 129, 2020, 102795.

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Available Online from 08 September 2026