In-plane and out-of-plane free vibration analysis of thin-walled box beams based on one-dimensional higher-order beam theory

References

• Y.K. Gere, and J.M. Lin, Coupled vibrations of thin-walled beams of open cross section, Trans. ASME J. Appl. Mech., vol. 25, no. 3, pp. 373–378, 1958. DOI: 10.1115/1.4011830.
   Google Scholar
• J.R. Banerjee, Coupled bending-torsional dynamic stiffness matrix for beam elements, Int. J. Numer. Meth. Eng., vol. 28, no. 6, pp. 1283–1298, 1989. DOI: 10.1002/nme.1620280605.
   Web of Science ®Google Scholar
• J.R. Banerjee, Explicit frequency equation and mode shapes of a cantilever beam coupled in bending and torsion, J. Sound Vib., vol. 224, no. 2, pp. 267–281, 1999. DOI: 10.1006/jsvi.1999.2194.
   Web of Science ®Google Scholar
• L.T. Stavridis and G.T. Michaltsos, Eigenfrequency analysis of thin-walled girders curved in plan, J. Sound Vib., vol. 227, no. 2, pp. 383–396, 1999. DOI: 10.1006/jsvi.1999.2350.
   Web of Science ®Google Scholar
• E. Carrera, A study of transverse normal stress effect on vibration of multilayered plates and shells, J. Sound Vib., vol. 225, no. 5, pp. 803–829, 1999. DOI: 10.1006/jsvi.1999.2271.
   Web of Science ®Google Scholar
• E. Carrera, A. Pagani, and J.R. Banerjee, Linearized buckling analysis of isotropic and composite beam-columns by Carrera Unified Formulation and dynamic stiffness method, Mech. Adv. Mater. Struct., vol. 23, no. 9, pp. 1092–1103, 2016. DOI: 10.1080/15376494.2015.1121524.
   Web of Science ®Google Scholar
• F.A. Fazzolari and E. Carrera, Advanced variable kinematics Ritz and Galerkin formulations for accurate buckling and vibration analysis of anisotropic laminated composite plates, Compos. Struct., vol. 94, no. 1, pp. 50–67, 2011. DOI: 10.1016/j.compstruct.2011.07.018.
   Web of Science ®Google Scholar
• A. Pagani, E. Carrera, and R. Augello, Evaluation of geometrically nonlinear effects due to large cross-sectional deformations of compact and shell-like structures, Mech. Adv. Mater. Struct., vol. 27, no. 14, pp. 1269–1277, 2020. DOI: 10.1080/15376494.2018.1507063.
   Web of Science ®Google Scholar
• A. Pagani, E. Carrera, and A.J.M. Ferreira, Higher-order theories and radial basis functions applied to free vibration analysis of thin-walled beams, Mech. Adv. Mater. Struct., vol. 23, no. 9, pp. 1080–1091, 2016. DOI: 10.1080/15376494.2015.1121555.
   Web of Science ®Google Scholar
• P.O. Friberg, Coupled vibrations of beams—an exact dynamic element stiffness matrix, Int. J. Numer. Meth. Eng., vol. 19, no. 4, pp. 479–493, 1983. DOI: 10.1002/nme.1620190403.
   Web of Science ®Google Scholar
• J.N. Heyliger and P.R. Reddy, A higher order beam finite element for bending and vibration problems, J. Sound Vib., vol. 126, no. 2, pp. 309–326, 1988. DOI: 10.1016/0022-460X(88)90244-1.
   Web of Science ®Google Scholar
• J.R. Banerjee, Development of an exact dynamic stiffness matrix for free vibration analysis of a twisted Timoshenko beam, J. Sound Vib., vol. 270, nos. 1–2, pp. 379–401, 2004. DOI: 10.1016/S0022-460X(03)00633-3.
   Web of Science ®Google Scholar
• K. Moon-Young, K. Nam, and Y. Hee-Taek, Exact dynamic and static stiffness matrices of shear deformable thin-walled beam-columns, J. Sound Vib., vol. 267, no. 1, pp. 29–55, 2003. DOI: 10.1016/S0022-460X(02)01410-4.
   Web of Science ®Google Scholar
• M. Ohga, H. Takao, and T. Hara, Natural frequencies and mode shapes of thin-walled members, Comput. Struct., vol. 55, no. 6, pp. 971–978, 1995. DOI: 10.1016/0045-7949(94)00517-7.
   Web of Science ®Google Scholar
• C.N. Chen, Dynamic equilibrium equations of non-prismatic beams defined on an arbitrarily selected co-ordinate system, J. Sound Vib., vol. 230, no. 2, pp. 241–260, 2000. DOI: 10.1006/jsvi.1999.2618.
   Web of Science ®Google Scholar
• V.H. Cort Inez, M.T. Piovan, and S. Machado, DQM for vibration analysis of composite thin-walled curved beams, J. Sound Vib., vol. 246, no. 3, pp. 551–555, 2001. DOI: 10.1006/jsvi.2001.3600.
   Web of Science ®Google Scholar
• A. Prokić and D. Lukic, Dynamic analysis of thin-walled closed-section beams, J. Sound Vib., vol. 302, nos. 4–5, pp. 962–980, 2007. DOI: 10.1016/j.jsv.2007.01.007.
   Web of Science ®Google Scholar
• N. Kim, Dynamic stiffness matrix of composite box beams, Steel Compos. Struct., vol. 9, no. 5, pp. 473–497, 2009. DOI: 10.12989/scs.2009.9.5.473.
   Web of Science ®Google Scholar
• M.O. Kaya and O.O. Ozdemir, Flexural–torsional-coupled vibration analysis of axially loaded closed-section composite Timoshenko beam by using DTM, J. Sound Vib., vol. 306, nos. 3–5, pp. 495–506, 2007. DOI: 10.1016/j.jsv.2007.05.049.
   Web of Science ®Google Scholar
• T.P. Vo and J. Lee, Free vibration of thin-walled composite box beams, Compos. Struct., vol. 84, no. 1, pp. 11–20, 2008. DOI: 10.1016/j.compstruct.2007.06.001.
   Web of Science ®Google Scholar
• M. Filippi, A. Pagani, M. Petrolo, G. Colonna, and E. Carrera, Static and free vibration analysis of laminated beams by refined theory based on Chebyshev polynomials, Compos. Struct., vol. 132, pp. 1248–1259, 2015. DOI: 10.1016/j.compstruct.2015.07.014.
   Web of Science ®Google Scholar
• Wassim Jrad, Foudil Mohri, Guillaume Robin, El Mostafa Daya, and Jihad Al-Hajjar, Analytical and finite element solutions of free and forced vibration of unrestrained and braced thin-walled beams, J. Vib. Control., vol. 26, nos. 5–6, pp. 255–276, 2020. DOI: 10.1177/1077546319878901.
   Web of Science ®Google Scholar
• F. Mohri, L. Azrar, and M. Potier-Ferry, Vibration analysis of buckled thin-walled beams with open sections, J. Sound Vib., vol. 275, nos. 1–2, pp. 434–446, 2004. DOI: 10.1016/j.jsv.2003.10.028.
   Web of Science ®Google Scholar
• I. Kaleel, M. Petrolo, and E. Carrera, Elatoplastic analysis of compact and thin-walled structures using classical and refined beam finite element models, Mech. Adv. Mater. Struct., vol. 26, no. 3, pp. 274–286, 2019. DOI: 10.1080/15376494.2017.1378780.
   Web of Science ®Google Scholar
• Hugo Elizalde, Diego Cárdenas, Juan Carlos Jáuregui-Correa, Marcelo T. Piovan, and Oliver Probst, Vibrations of composite thin-walled beams with arbitrary curvature: a unified approach, Thin. Walled Struct., vol. 147, pp. 106473, 2020. DOI: 10.1016/j.tws.2019.106473.
   Web of Science ®Google Scholar
• M. Vukasovic and R. Pavazza, Flexural analysis of thin-walled laminated composite beams with arbitrary open sections and shear influence, Mech. Adv. Mater. Struct., vol. 29, no. 26, pp. 5041–5058, 2022. DOI: 10.1080/15376494.2021.1946222.
   Web of Science ®Google Scholar
• H.R. Ovesy and P.K. Masjedi, Investigation of the effects of constitutive equations on the free vibration behavior of single-celled thin-walled composite beams, Mech. Adv. Mater. Struct., vol. 21, no. 10, pp. 836–852, 2014. DOI: 10.1080/15376494.2012.725266.
   Web of Science ®Google Scholar
• E. Zappino, T. Cavallo, and E. Carrera, Free vibration analysis of reinforced thin-walled plates and shells through various finite element models, Mech. Adv. Mater. Struct., vol. 23, no. 9, pp. 1005–1018, 2016. DOI: 10.1080/15376494.2015.1121562.
   Web of Science ®Google Scholar
• B.Y. Shi, J. Yang, and J. Wang, Forced vibration analysis of multi-degree-of-freedom nonlinear systems with the extended Galerkin method, Mech. Adv. Mater. Struct., vol. 30, no. 4, pp. 794–802, 2023. DOI: 10.1080/15376494.2021.2023922.
   Web of Science ®Google Scholar
• Aleksi Laakso, Jani Romanoff, Ari Niemelä, Heikki Remes, and Eero Avi, Free vibration by length-scale separation and inertia-induced interaction-application to large thin-walled structures, Mech. Adv. Mater. Struct., vol. 30, no. 6, pp. 1234–1248, 2023. DOI: 10.1080/15376494.2022.2029981.
   Google Scholar
• J.H. Kim and Y.Y. Kim, Thin walled closed box beam element for static and dynamic analysis, Int. J. Numer. Meth. Eng., vol. 45, no. 4, pp. 473–490, 1999. DOI: 10.1002/(SICI)1097-0207(19990610)45:4<473::AID-NME603>3.0.CO;2-B.
   Web of Science ®Google Scholar
• G.W. Jang and Y.Y. Kim, Theoretical analysis of coupled torsional, warping and distortional waves in a straight thin-walled box beam by higher-order beam theory, J. Sound Vib., vol. 330, no. 13, pp. 3024–3039, 2011. DOI: 10.1016/j.jsv.2011.01.014.
   Web of Science ®Google Scholar
• Xiangjie Yu, Bindi You, Cheng Wei, Haiyu Gu, and Zhaoxu Liu, Investigation on the improved absolute nodal coordinate formulation for variable cross-section beam with large aspect ratio, Mech. Adv. Mater. Struct., pp. 1–12, 2023. DOI: 10.1080/15376494.2023.2169795.
   Web of Science ®Google Scholar
• D. Hoffmeyer and J. Hogsberg, Damping of torsional vibrations in thin-walled beams by viscous bimoments, Mech. Adv. Mater. Struct., vol. 28, no. 3, pp. 308–320, 2021. DOI: 10.1080/15376494.2019.1567885.
   Web of Science ®Google Scholar
• D. Huang, T. Wang, and M. Shahawy, Vibration of thin-walled box-girder bridges excited by vehicles, J. Struct. Eng., vol. 121, no. 9, pp. 1330–1337, 1995. DOI: 10.1061/(ASCE)0733-9445(1995)121:9(1330).
   Web of Science ®Google Scholar
• E. Hamed and Y. Frostig, Free vibrations of multi-girder and multi-cell box bridges with transverse deformations effects, J. Sound Vib., vol. 279, nos. 3–5, pp. 699–722, 2005. DOI: 10.1016/j.jsv.2003.11.037.
   Web of Science ®Google Scholar
• D. Shin, S. Choi, G. Jang, and Y.Y. Kim, Higher-order beam theory for static and vibration analysis of composite thin-walled box beam, Compos. Struct., vol. 206, pp. 140–154, 2018. DOI: 10.1016/j.compstruct.2018.08.016.
   Web of Science ®Google Scholar
• M. Momeni and M.B. Dehkordi, Frequency analysis of sandwich beam with FG carbon nanotubes face sheets and flexible core using high-order element, Mech. Adv. Mater. Struct., vol. 26, no. 9, pp. 805–815, 2019. DOI: 10.1080/15376494.2017.1410918.
   Web of Science ®Google Scholar
• G. Ranzi and A. Luongo, A new approach for thin-walled member analysis in the frame work of GBT, Thin. Walled Struct., vol. 49, no. 11, pp. 1404–1414, 2011. DOI: 10.1016/j.tws.2011.06.008.
   Web of Science ®Google Scholar