Abstract
In this paper, a novel model for a single-storey irregular-plan building, subjected to earthquake and harmonic translational excitation, is presented to consider non-linear inertial coupling terms, which are ignored in conventional linear models. Furthermore, the effect of internal resonance is investigated. The governing equations of motion for a model of this type of structure are achieved in a non-inertial rotational system of reference, attached to the centre of mass of the rigid diaphragm of its floor. Non-linearities are caused by non-linear inertial coupled lateral and torsional responses. Using the method of multiple scales, the non-linear equations are reduced to approximate linear equations, and subsequently the dynamic stability of the steady-state responses near a two-to-one ratio of internal resonant conditions is studied. The difference between the responses of the proposed non-linear model and the conventional linear one is shown in time history and frequency domain analyses. By inspecting the effects of amplitude and frequency detuning parameters in the responses, some non-linear phenomena, such as saturation, hysteretic and jumping, are observed.
Similar content being viewed by others
References
Froude W.: Remarks on Mr. Scott Russell’s paper on rolling. Trans. Inst. Naval Arch. 4, 232–275 (1863)
Nayfeh A.H., Mook D.T., Marshall L.R.: Nonlinear coupling of pitch and roll modes in ship motion. J. Hydron. 7, 145–152 (1973)
Hatwal H., Mallik A.K., Ghosh A.: Non-linear vibrations of a harmonically excited autoparametric system. J. Sound Vib. 81, 153–164 (1982)
Miles J.: Resonantly forced motion of two quadratically coupled oscillators. Physica D 13, 247–260 (1984)
Lee W.K., Park H.D.: Chaotic dynamics of a harmonically excited spring-pendulum system with internal resonance. Non-linear Dyn. 14, 211–229 (1997)
Hsieh S.R., Shaw S.W.: The dynamic stability and nonlinear response of a flexible connecting rod: single-mode model. J. Sound Vib. 170, 25–49 (1994)
Mammandi A., Kargarnovin M.H., Younesian D.: Nonlinear dynamics of an inclined beam subjected to a moving load. Non-linear Dyn. 60, 277–293 (2010)
De Stefano M.D., Pintucchi B.: A review of research on seismic behavior of irregular building structures since 2002. Bull. Earthq. Eng. 6, 285–308 (2008)
Perus I., Fajfar P.: On the inelastic torsional response of single-storey structures under bi-axial excitation. Earthq. Eng. Struct. Dyn. 34, 931–941 (2005)
Marusic D., Fajfar P.: On the inelastic seismic response of asymmetric buildings under bi-axial excitation. Earthq. Eng. Struct. Dyn. 34, 943–963 (2005)
Myslimaj B., Tso W.K.: A design-oriented approach to strength distribution in single story asymmetric systems with elements having strength-dependent stiffness. Earthq. Spectra 21, 197–212 (2005)
Nayfeh A.H., Mook D.T.: Nonlinear Oscillations. Wiley-Interscience, New York (1979)
Amin Afshar, M.: Nonlinearities in asymmetric structures. Ph.D. Thesis, Iran University of Science and Technology (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Amini, F., Amin Afshar, M. Saturation in asymmetric structures under internal resonance. Acta Mech 221, 353–368 (2011). https://doi.org/10.1007/s00707-011-0511-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-011-0511-1