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Equation of motion governing the dynamics of vertically collapsing buildings / Celso P. Pesce in Journal of engineering mechanics, Vol. 138 N° 12 (Décembre 2012) 

Public ISBD [article]  in Journal of engineering mechanics > Vol. 138 N° 12 (Décembre 2012) . - pp.1420–1431. Titre : Equation of motion governing the dynamics of vertically collapsing buildings Type de document : texte imprimé Auteurs : Celso P. Pesce, Auteur ; Leonardo Casetta, Auteur ; Flavia M. dos Santos, Auteur Année de publication : 2013 Article en page(s) : pp.1420–1431. Note générale : Mécanique appliquée Langues : Anglais (eng) Mots-clés : Collapsing  buildings  Proper  equation  of  motion  Extended  Lagrange’s  equation  Variable  mass  systems  WTC  Rayleigh-like  dissipation  function Résumé : The present paper aims at contributing to a discussion, opened by several authors, on the proper equation of motion that governs the vertical collapse of buildings. The most striking and tragic example is that of the World Trade Center Twin Towers, in New York City, about 10 years ago. This is a very complex problem and, besides dynamics, the analysis involves several areas of knowledge in mechanics, such as structural engineering, materials sciences, and thermodynamics, among others. Therefore, the goal of this work is far from claiming to deal with the problem in its completeness, leaving aside discussions about the modeling of the resistive load to collapse, for example. However, the following analysis, restricted to the study of motion, shows that the problem in question holds great similarity to the classic falling-chain problem, very much addressed in a number of different versions as the pioneering one, by von Buquoy or the one by Cayley. Following previous works, a simple single-degree-of-freedom model was readdressed and conceptually discussed. The form of Lagrange’s equation, which leads to a proper equation of motion for the collapsing building, is a general and extended dissipative form, which is proper for systems with mass varying explicitly with position. The additional dissipative generalized force term, which was present in the extended form of the Lagrange equation, was shown to be derivable from a Rayleigh-like energy function. ISSN : 0733-9399 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29EM.1943-7889.0000453 [article] Equation of motion governing the dynamics of vertically collapsing buildings [texte imprimé] / Celso P. Pesce, Auteur ; Leonardo Casetta, Auteur ; Flavia M. dos Santos, Auteur . - 2013 . - pp.1420–1431. Mécanique appliquée Langues : Anglais (eng) in Journal of engineering mechanics > Vol. 138 N° 12 (Décembre 2012) . - pp.1420–1431. Mots-clés : Collapsing  buildings  Proper  equation  of  motion  Extended  Lagrange’s  equation  Variable  mass  systems  WTC  Rayleigh-like  dissipation  function Résumé : The present paper aims at contributing to a discussion, opened by several authors, on the proper equation of motion that governs the vertical collapse of buildings. The most striking and tragic example is that of the World Trade Center Twin Towers, in New York City, about 10 years ago. This is a very complex problem and, besides dynamics, the analysis involves several areas of knowledge in mechanics, such as structural engineering, materials sciences, and thermodynamics, among others. Therefore, the goal of this work is far from claiming to deal with the problem in its completeness, leaving aside discussions about the modeling of the resistive load to collapse, for example. However, the following analysis, restricted to the study of motion, shows that the problem in question holds great similarity to the classic falling-chain problem, very much addressed in a number of different versions as the pioneering one, by von Buquoy or the one by Cayley. Following previous works, a simple single-degree-of-freedom model was readdressed and conceptually discussed. The form of Lagrange’s equation, which leads to a proper equation of motion for the collapsing building, is a general and extended dissipative form, which is proper for systems with mass varying explicitly with position. The additional dissipative generalized force term, which was present in the extended form of the Lagrange equation, was shown to be derivable from a Rayleigh-like energy function. ISSN : 0733-9399 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29EM.1943-7889.0000453