A shear–shear torsional beam model for nonlinear aeroelastic analysis of tower buildings

In this paper, an equivalent one-dimensional beam model immersed in a three-dimensional space is proposed to study the aeroelastic behavior of tower buildings: linear and nonlinear dynamics are analyzed through a simple but realistic physical modeling of the structure and of the load. The beam is internally constrained, so that it is capable to experience shear strains and torsion only. The elasto-geometric and inertial characteristics of the beam are identified from a discrete model of three-dimensional frame, via a homogenization process. The model accounts for the torsional effect induced by the rotation of the floors around the tower axis; the macroscopic shear strain is produced by bending of the columns, accompanied by negligible rotation of the floors. Nonlinear aerodynamic forces are evaluated through the quasi-steady theory. The first aim is to investigate the effect of mechanical and aerodynamic coupling on the critical galloping conditions. Furthermore, the role of aerodynamic nonlinearities on the galloping post-critical behavior is analyzed through a perturbation solution which permits to obtain a reduced one-dimensional dynamical system, capable of capturing the essential dynamics of the problem.

[1]  Eduardo Miranda,et al.  Approximate Floor Acceleration Demands in Multistory Buildings. I: Formulation , 2005 .

[2]  Reza Rahgozar,et al.  A simple analytic method for computing the natural frequencies and mode shapes of tall buildings , 2012 .

[3]  Michael J. Chajes,et al.  ANALYSIS OF MULTIPLE-BAY FRAMES USING CONTINUUM MODEL , 1993 .

[4]  F. dell’Isola,et al.  Dynamics of solids with microperiodic nonconnected fluid inclusions , 1997 .

[5]  鈴木 増雄.  A. H. Nayfeh and D. T. Mook: Nonlinear Oscillations, John Wiley, New York and Chichester, 1979, xiv+704ページ, 23.5×16.5cm, 10,150円. , 1980 .

[6]  E. D. Langre,et al.  Fluid-Structure Interactions: Cross-Flow-Induced Instabilities , 2010 .

[7]  Tetsuro Tamura,et al.  The effect of turbulence on aerodynamic forces on a square cylinder with various corner shapes , 1999 .

[8]  Pierre Seppecher,et al.  Truss Modular Beams with Deformation Energy Depending on Higher Displacement Gradients , 2003 .

[9]  Vittorio Gusella,et al.  Dynamic response of tall buildings to wind loads by reduced order equivalent shear-beam models , 2013 .

[10]  G. Rosi,et al.  The effect of fluid streams in porous media on acoustic compression wave propagation, transmission, and reflection , 2013 .

[11]  Clive L. Dym,et al.  Estimating Fundamental Frequencies of Tall Buildings , 2007 .

[12]  Somsak Swaddiwudhipong,et al.  Approximate Analysis of Asymmetric Buildings , 1984 .

[13]  Liang Shu-guo,et al.  An evaluation of onset wind velocity for 2—D coupled galloping oscillations of tower buildings , 1993 .

[14]  Eddy Pramono,et al.  Dynamic Response of Tall Building to Wind Excitation , 1985 .

[15]  Angelo Luongo,et al.  Mathematical Models of Beams and Cables: Luongo/Mathematical Models of Beams and Cables , 2013 .

[16]  F. dell'Isola,et al.  A micro-structured continuum modelling compacting fluid-saturated grounds: the effects of pore-size scale parameter , 1998 .

[17]  Francesco dell’Isola,et al.  How contact interactions may depend on the shape of Cauchy cuts in Nth gradient continua: approach “à la D’Alembert” , 2012 .

[18]  A. Luongo,et al.  A Continuous Approach to the Aeroelastic Stability of Suspended Cables in 1 : 2 Internal Resonance , 2008 .

[19]  Victor A. Eremeyev,et al.  Deformation analysis of functionally graded beams by the direct approach , 2012 .

[20]  G. K. Nathan,et al.  Deterministic Model for Wind-Induced Oscillations of Buildings , 1989 .

[21]  Giuseppe Lacidogna,et al.  A global approach for three-dimensional analysis of tall buildings , 2009 .

[22]  Amiya K. Basu,et al.  Dynamic characteristics of coupled wall‐frame systems , 1982 .

[23]  Perturbation methods in torsion of thin hollow Saint-Venant cylinders , 1996 .

[24]  A Carcaterra,et al.  Energy equipartition and frequency distribution in complex attachments. , 2009, The Journal of the Acoustical Society of America.

[25]  Andrea Freda,et al.  Critical conditions of galloping for inclined square cylinders , 2011 .

[26]  Reza Rahgozar,et al.  An analytical model for dynamic response analysis of tubular tall buildings , 2014 .

[27]  Giuseppe Piccardo,et al.  Linear instability mechanisms for coupled translational galloping , 2005 .

[28]  Leopoldo Greco,et al.  An implicit G1 multi patch B-spline interpolation for Kirchhoff–Love space rod , 2014 .

[29]  Peretz P. Friedmann,et al.  Deterministic torsional building response to winds. , 1979 .

[30]  Angelo Luongo,et al.  Parametric, external and self-excitation of a tower under turbulent wind flow , 2011 .

[31]  Luisa Pagnini,et al.  Reliability analysis of wind-excited structures , 2010 .

[32]  Federica Tubino,et al.  Some research perspectives in galloping phenomena: critical conditions and post-critical behavior , 2015 .

[33]  Ugo Andreaus,et al.  At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical contribution of Gabrio Piola , 2013, 1310.5599.

[34]  Luisa-Carlotta Pagnini,et al.  Model reliability and propagation of frequency and damping uncertainties in the dynamic along-wind response of structures , 1996 .

[35]  Giuseppe Piccardo,et al.  On the effect of twist angle on nonlinear galloping of suspended cables , 2009 .

[36]  M. G. Faulkner,et al.  Variational theory for spatial rods , 1993 .

[37]  A. P. Jeary,et al.  EVALUATION OF 2D COUPLED GALLOPING OSCILLATIONS OF SLENDER STRUCTURES , 1998 .

[38]  Antonio Cazzani,et al.  Isogeometric analysis of plane-curved beams , 2016 .

[39]  Yasuharu Nakamura,et al.  TORSIONAL FLUTTER OF RECTANGULAR PRISMS , 1975 .

[40]  Clive L. Dym,et al.  Approximating Frequencies of Tall Buildings , 2013 .