Prediction of resonantly forced vibrations for suspended footbridges

References

• Abdel-Ghafar, A., and L. Rubin. 1983a. Nonlinear free vibration of suspension bridges: Theory. Journal of Engineering Mechanics ASCE 109:313–29. doi: 10.1061/(ASCE)0733-9399(1983)109:1(313).
   Google Scholar
• Abdel-Ghafar, A., and L. Rubin. 1983b. Nonlinear free vibration of suspension bridges: Application. Journal of Engineering Mechanics ASCE 109:330–45. doi: 10.1061/(ASCE)0733-9399(1983)109:1(330).
   Web of Science ®Google Scholar
• Brownjohn, J. M. W. 1994. Observations on non-linear dynamic characteristics of suspension bridges. Earthquake Engineering & Structural Dynamics 23(12):1351–67. doi: 10.1002/eqe.4290231206.
   Web of Science ®Google Scholar
• Bruno, L., F. Venuti, and V. Nascé. 2012. Pedestrian-induced torsional vibrations of suspended footbridges: Proposal and evaluation of vibration countermeasures. Engineering Structure 36:228–38. doi: 10.1016/j.engstruct.2011.12.012.
   Web of Science ®Google Scholar
• Bruno, L., F. Venuti, and A. Scotti. 2011. Limit of hanger linearity in suspension footbridge dynamics: A new section model. Journal of Sound and Vibration 330(26):6387–406. doi: 10.1016/j.jsv.2011.07.042.
   Web of Science ®Google Scholar
• Capsoni, A., R. Ardito, and A. Guerrieri. 2017. Stability of dynamic response of suspension bridges. Journal of Sound and Vibration 393:285–307. doi: 10.1016/j.jsv.2017.01.009.
   Web of Science ®Google Scholar
• Chen, Z., H. Cao, H. Zhu, J. Hu, and S. Li. 2014. A simplified structural mechanics model for cable-truss footbridges and its implications for preliminary design. Engineering Structures 68:121–33. doi: 10.1016/j.engstruct.2014.02.015.
   Web of Science ®Google Scholar
• Clough, R., and J. Penzien. 1993. Dynamics of structures (2nd ed.). New York: McGraw-Hill Book Co.
   Google Scholar
• Diaferio, M. 2000. Modelli non lineari di strutture elastiche sospese. PhD dissertation, University of Firenze (in Italian).
   Google Scholar
• Diaferio, M., and V. Sepe. 2004. Smoothed slack cable models for large amplitude oscillations of suspension bridges. Mechanics Based Design of Structures and Machines 32(3):363–400. doi: 10.1081/SME-200028000.
   Web of Science ®Google Scholar
• Diaferio, M., and V. Sepe. 2014. Nonlinear oscillations of suspended bridges and footbridges: A regularization technique for non-smooth hangers behavior. Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 (pp.1183–1188), Porto, Portugal, June 30–July 2.
   Google Scholar
• Drygala, I., J. Dulinska, and K. Kondrat. 2018. Dynamic performance of a suspended reinforced concrete footbridge under pedestrian movements. IOP Conference Series: Materials Science and Engineering 307:012060. doi: 10.1088/1757-899X/307/1/012060.
   Google Scholar
• Glover, A. C., P. Lazer, and J. McKenna. 1989. Existence and stability of large scale nonlinear oscillations in suspension bridges. ZAMP Zeitschrift fur Angewandte Mathematik Und Physik 40(2):172–200. doi: 10.1007/BF00944997.
   Google Scholar
• Grigorjeva, T., and Z. Kamaitis. 2015. Numerical analysis of the effects of the bending stiffness of the cable and the mass of structural members on free vibrations of suspension bridges. Journal of Civil Engineering and Management 21(7):948–57.
   Web of Science ®Google Scholar
• Jacover, D., and P. J. McKenna. 1994. Nonlinear torsional flexings in a periodically forced suspended beam. Journal of Computational and Applied Mathematics 52(1–3):241–65.
   Web of Science ®Google Scholar
• Lai, E., C. Gentile, and M. G. Mulas. 2017. Experimental and numerical serviceability assessment of a steel suspension footbridge. Journal of Constructional Steel Research 132 :16–28. doi: 10.1016/j.jcsr.2017.01.005.
   Web of Science ®Google Scholar
• Lazer, A. C., and P. J. McKenna. 1990. Large-amplitude periodic oscillations in suspension bridges: Some new connections with nonlinear analysis. SIAM Review 32(4):537–48. doi: 10.1137/1032120.
   Web of Science ®Google Scholar
• Lepidi, M., and V. Gattulli. 2016. Non-linear interactions in the flexible multi-body dynamics of cable-supported bridge cross-sections. International Journal of Non-Linear Mechanics 80:14–28. doi: 10.1016/j.ijnonlinmec.2015.09.009.
   Web of Science ®Google Scholar
• Lopez-Garcia, O., A. Carnicero, V. Torres, and J. R. Jimenez-Octavio. 2008. The influence of cable slackening on the stiffness computation of railway overheads. International Journal of Mechanical Sciences 50(7):1213–23. doi: 10.1016/j.ijmecsci.2008.04.001.
   Web of Science ®Google Scholar
• McKenna, P. J. 2014. Oscillations in suspension bridges, vertical and torsional. Discrete and Continuous Dynamical Systems – Series S 7(4):785–91. doi: 10.3934/dcdss.2014.7.785.
   Web of Science ®Google Scholar
• McKenna, P. J., and K. S. Moore. 2000. Multiple periodic solutions to a suspension bridge ordinary differential equation. Nonlinear Differential Equations 5:183–99.
   Google Scholar
• McKenna, P. J., and W. Walter. 1987. Nonlinear oscillations in a suspension bridge. Archive for Rational Mechanics and Analysis 98(2):167–77. doi: 10.1007/BF00251232.
   Web of Science ®Google Scholar
• Mulas, M. G., E. Lai, and G. Lastrico. 2018. Coupled analysis of footbridge-pedestrian dynamic interaction. Engineering Structures 176:127–42. doi: 10.1016/j.engstruct.2018.08.055.
   Web of Science ®Google Scholar
• Naghavi Riabi, A. R., and A. Shooshtari. 2015. A numerical method to material and geometric nonlinear analysis of cable structures. Mechanics Based Design of Structures and Machines 43(4):407–23. doi: 10.1080/15397734.2015.1012295.
   Web of Science ®Google Scholar
• Nayfeh, A. H., and D. T. Mook. 1979. Nonlinear oscillations. New York: Wiley-Interscience.
   Google Scholar
• Peterson, I. 1990. Rock and roll bridge: A new analysis challenges the common explanation of a famous collapse. Science News 137(22):344–56. doi: 10.2307/3974221.
   Google Scholar
• Plaut, R. H., and F. M. Davis. 2007. Sudden lateral asymmetry and torsional oscillations of section models of suspension bridges. Journal of Sound and Vibration 307(3–5):894–905. doi: 10.1016/j.jsv.2007.07.036.
   Web of Science ®Google Scholar
• Pratiher, B., and S. K. Dwivedy. 2011. Nonlinear vibrations and frequency response analysis of a cantilever beam under periodically varying magnetic field. Mechanics Based Design of Structures and Machines 39(3):378–39.
   Web of Science ®Google Scholar
• Sepe, V., and G. Augusti. 2001. A deformable section model for the dynamics of suspension bridges. Part I: Model and linear response. Wind and Structures 4 (1):1–18. doi: 10.12989/was.2001.4.1.001.
   Web of Science ®Google Scholar
• Sepe, V., M. Diaferio, and G. Augusti. 2003. A deformable section model for the dynamics of suspension bridges. Part II: Nonlinear analysis and large amplitude oscillations. Wind and Structures 6(6):451–70. doi: 10.12989/was.2003.6.6.451.
   Web of Science ®Google Scholar
• Venuti, F., V. Racic, and A. Corbetta. 2017. Modelling framework of pedestrian-footbridge interaction in vertical direction. Procedia Engineering 199:2901–6. doi: 10.1016/j.proeng.2017.09.588.
   Google Scholar
• Wattanasakulpong, N., and A. Chaikittiratana. 2014. On the linear and nonlinear vibration responses of elastically end restrained beams using DTM. Mechanics Based Design of Structures and Machines 42(2):135–50. doi: 10.1080/15397734.2013.847778.
   Web of Science ®Google Scholar
• Yayli, M. Ö. 2013. Torsion of nonlocal bars with equilateral triangle cross sections. Journal of Computational and Theoretical Nanoscience 10(2):376–9. doi: 10.1166/jctn.2013.2707.
   Google Scholar
• Yayli, M. Ö. 2018a. On the torsional vibrations of restrained nanotubes embedded in an elastic medium. Journal of the Brazilian Society of Mechanical Sciences and Engineering 40(9):419.
   Web of Science ®Google Scholar
• Yayli, M. Ö. 2018b. Torsional vibrations of restrained nanotubes using modified couple stress theory. Microsystem Technologies 24(8):3425–35. doi: 10.1007/s00542-018-3735-3.
   Web of Science ®Google Scholar
• Yayli, M. Ö. 2018c. Torsional vibration analysis of nanorods with elastic torsional restraints using non-local elasticity theory. Micro & Nano Letters 13(5):595–9. doi: 10.1049/mnl.2017.0751.
   Web of Science ®Google Scholar