Abstract
This paper deals with the dynamic behavior of reticulated beams made of the periodic repetition of symmetric unbraced frames. Such archetypical cells can present a high contrast between shear and compression deformability, conversely to “massive” media. This opens the possibility of enriched local kinematics involving phenomena of global rotation, inner deformation or inner resonance, according to studied configuration and frequency range. Firstly, the existence of these atypical behaviors is established theoretically through the homogenization method of periodic discrete media. Then, the results are adapted to buildings and confirmed with a numerical example.
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References
Basu, A.K., Nagpal, A.K., Bajaj, R.S., Guliani, A.K.: Dynamic characteristics of coupled shear walls. J. Struct. Div. 105(8), 1637–1652 (1979)
Boutin, C., Hans, S.: Homogenisation of periodic discrete medium: Application to dynamics of framed structures. Comput. Geotech. 30(4), 303–320 (2003)
Boutin, C., Hans, S., Ibraim, E., Roussillon, P.: In situ experiments and seismic analysis of existing buildings. Part II: Seismic integrity threshold. Earthq. Eng. Struct. Dyn. 34(12), 1531–1546 (2005)
Caillerie, D., Trompette, P., Verna, P.: Homogenisation of periodic trusses. In: IASS Symposium, 10 Years of Progress in Shell and Spatial Structures. Madrid (1989)
Chesnais, C.: Dynamique de milieux réticulés non contreventés. Application aux bâtiments. PhD thesis, ENTPE, Lyon (2010)
Chesnais, C., Hans, S., Boutin, C.: Wave propagation and diffraction in discrete structures: Effect of anisotropy and internal resonance. PAMM 7(1), 1090,401–1090,402 (2007)
Chesnais, C., Hans, S., Boutin, C.: Dynamics of reticulated structures. Evidence of atypical gyration modes. Int. J. Multiscale Comput. Eng. (accepted)
Cioranescu, D., Saint Jean Paulin., J: Homogenization of Reticulated Structures, Applied Mathematical Sciences, Vol. 136. Springer-Verlag, New York (1999)
Hans, S., Boutin, C.: Dynamics of discrete framed structures: A unified homogenized description. J. Mech. Mater. Struct. 3(9), 1709–1739 (2008)
Hans, S., Boutin, C., Ibrahim, E., Roussillon, P.: In situ experiments and seismic analysis of existing buildings. Part I: Experimental investigations. Earthq. Eng. Struct. Dyn. 34(12), 1513–1529 (2005)
Kerr, A.D., Accorsi, M.L.: Generalization of the equations for frame-type structures; a variational approach. Acta Mech. 56(1–2), 55–73 (1985)
Moreau, G., Caillerie, D.: Continuum modeling of lattice structures in large displacement applications to buckling analysis. Comput. Struct. 68(1–3), 181–189 (1998)
Ng, S.C., Kuang, J.S.: Triply coupled vibration of asymmetric wall-frame structures. J. Struct. Eng. 126(8), 982–987 (2000)
Noor, A.K.: Continuum modeling for repetitive lattice structures. Appl. Mech. Rev. 41(7), 285–296 (1988)
Potzta, G., Kollár, L.P.: Analysis of building structures by replacement sandwich beams. Int. J. Solids Struct. 40(3), 535–553 (2003)
Sanchez-Palencia, E.: Non-homogeneous media and vibration theory, Lecture notes in physics, vol. 127. Springer-Verlag, Berlin (1980)
Skattum, K.S.: Dynamic analysis of coupled shear walls and sandwich beams. Rep. EERL 71-06 PhD thesis, California Institute of Technology (1971)
Stafford Smith, B., Kuster, M., Hoenderkamp, J.C.D.: Generalized method for estimating drift in high-rise structures. J. Struct. Eng. 110(7), 1549–1562 (1984)
Tollenaere, H., Caillerie, D.: Continuous modeling of lattice structures by homogenization. Adv. Eng. Softw. 29(7–9), 699–705 (1998)
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Chesnais, C., Boutin, C., Hans, S. (2011). Structural Dynamics and Generalized Continua. In: Altenbach, H., Maugin, G., Erofeev, V. (eds) Mechanics of Generalized Continua. Advanced Structured Materials, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19219-7_3
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DOI: https://doi.org/10.1007/978-3-642-19219-7_3
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