Nonlinear dynamics and stability of a homogeneous model of tall buildings under resonant action

Document Type : Special Issue Paper


Department of Civil, Construction-Architectural and Environmental Engineering, University of L'Aquila, Italy


A homogeneous model of beam-like structure, roughly portraying  the mechanical behavior of a tall building, is considered to address nonlinear dynamic response in case of external resonant excitation. A  symmetric layout of the building is considered, so as to allow the existence of an in-plane response, whose features are evaluated by means of the Multiple Scale Method and accounting for internal resonance, necessarily occurring in the model. Furthermore, to take into account the three-dimensional nature of the problem, stability of the in-plane response to out-of-plane disturbances is addressed, solving the associated parametrically excited linear system.


Main Subjects

[1] Noor, A., Continuum modeling for repetitive lattice structures, Applied Mechanics Reviews, 1988, 41(7), 285–296.
[2] Tollenaere, H., Caillerie, D., Continuous modeling of lattice structures by homogenization, Advances in Engineering Software, 1998, 29(7), 699 – 705.
[3] Boutin, C., dell’Isola, F., Giorgio, I., Placidi, L., Linear pantographic sheets: Asymptotic micro-macro models identification, Mathematics and Mechanics of Complex Systems, 2017, 5, 127–162.
[4] dell’Isola, F., Eremeyev, V., Porubov, A., eds., Advances in mechanics of microstructured media and structures, vol. 87, Springer, Cham, 2018.
[5] DiCarlo, A., Rizzi, N., Tatone, A., Continuum modelling of a beam-like latticed truss: Identification of the constitutive functions for the contact and inertial actions, Meccanica, 1990, 25, 168–174.
[6] McCallen, D., Romstad, K., A continuum model for the nonlinear analysis of beam-like lattice structures, Computers & Structures, 1988, 29(2), 177– 197.
[7] Chajes, M., Zhang, L., Kirby, J., Dynamic analysis of tall building using reduced-order continuum model, Journal of Structural Engineering, 1996, 122(11), 1284–1291.
[8] Chajes, M., Finch, W., Kirby, J., Dynamic analysis of a ten-story reinforced concrete building using a continuum model, Computers & Structures, 1996, 58, 487–498.
[9] Cluni, F., Gioffrè, M., Gusella, V., Dynamic response of tall buildings to wind loads by reduced order equivalent shear-beam models, Journal of Wind Engineering and Industrial Aerodynamics, 2013, 123, 339 – 348.
[10] Luongo, A., Zulli, D., Parametric, external and self-excitation of a tower under turbulent wind flow, Journal of Sound and Vibration, 2011, 330(13), 3057–3069.
[11] Zulli, D., Luongo, A., Bifurcation and stability of a two-tower system under wind-induced parametric, external and self-excitation, Journal of Sound and Vibration, 2012, 331(2), 365–383.
[12] Zulli, D., Di Egidio, A., Galloping of internally resonant towers subjected to turbulent wind, Continuum Mechanics and Thermodynamics, 2015, 27(4), 835–849.
[13] Di Nino, S., Luongo, A., Nonlinear aeroelastic behavior of a base-isolated beam under steady wind flow, International Journal of Non-Linear Mechanics, 2019, 119, 103340.
[14] Piccardo, G., Tubino, F., Luongo, A., Equivalent Timoshenko linear beam model for the static and dynamic analysis of tower buildings, Applied Mathematical Modelling, 2019, 71, 77–95.
[15] Piccardo, G., Tubino, F., Luongo, A., A shear–shear torsional beam model for nonlinear aeroelastic analysis of tower buildings, Zeitschrift für Angewandte Mathematik und Physik, 2015, 66(4), 1895–1913.
[16] Piccardo, G., Tubino, F., Luongo, A., Equivalent nonlinear beam model for the 3-D analysis of shear-type buildings: Application to aeroelastic instability, International Journal of Non-Linear Mechanics, 2016, 80, 52 – 65.
[17] Luongo, A., Zulli, D., Mathematical Models of Beams and Cables, Iste-Wiley, 2013.
[18] D’Annibale, F., Ferretti, M., Luongo, A., Shear-shear-torsional homogeneous beam models for nonlinear periodic beam-like structures, Engineering Structures, 2019, 184, 115–133.
[19] Ferretti, M., D’Annibale, F., Luongo, A., Modeling beam-like planar structures by a one-dimensional continuum: an analytical-numerical method, Journal of Applied and Computational Mechanics, 2020.
[20] Ferretti, M., D’Annibale, F., Luongo, A., Buckling of tower-buildings on elastic foundation under compressive tip-forces and self-weight, Continuum Mechanics and Thermodynamics, 2020.
[21] Ferretti, M., Flexural torsional buckling of uniformly compressed beam-like structures, Continuum Mechanics and Thermodynamics, 2018, 30(5), 977–993.
[22] Luongo, A., D’Annibale, F., Ferretti, M., Shear and flexural factors for homogenized beam models of planar frames, Engineering Structures, 2020, submitted.
[23] Luongo, A., Zulli, D., Free and forced linear dynamics of a homogeneous model for beam-like structures, Meccanica, 2020, 55, 907–925.
[24] Nayfeh, A., Mook, D., Nonlinear oscillations, John Wiley, New York, 1979.
[25] Doedel, E., Oldeman, B., AUTO-07P: Continuation and Bifurcation Software for Ordinary Differential Equation, 2019.