ДИНАМИЧЕСКИЙ РАСЧЁТ ФЕРМЫ ПОКРЫТИЯ ПРИ СВОБОДНЫХ КОНСТРУКТИВНО НЕЛИНЕЙНЫХ КОЛЕБАНИЯХ
Аннотация
Приведена математическая модель построения полной механической энергии дискретной статически нагруженной диссипативной системы в процессе свободных колебаний в форме метода временного анализа, основанного на исследовании характеристического матричного квадратного уравнения. Также даны выражения для определения кинематических (перемещений, скоростей, ускорений) и силовых (восстанавливающих, диссипативных, инерционных сил) параметров реакции конструкции. Показаны особенности поведения динамических параметров реакции при переходе упругой конструктивно нелинейной системы в новое состояние. Предложены критерии для оценки несущей способности конструкции при нелинейной работе. Использование математической модели иллюстрируется на примере расчёта плоской стальной статически неопределимой фермы покрытия в процессе свободных колебаний, вызванных внезапным отказом одного из несущих элементов. Выключение элемента вызвано потерей прочности вследствие химического растрескивания при коррозионном воздействии.
Ключевые слова
Полный текст:
PDFЛитература
Klaf R., Penzien D.Zh. Dinamika sooruzheniy [Structural Dynamics]. Moscow, Stroyizdat Publ., 1979. 320 p.
Erkhov M.I. Teoriya ideal'no plasticheskikh tel i konstruktsiy [The Theory of Ideal Plastic Bodies and Structures]. Moscow, Nauka Publ., 1978. 352 p.
Potapov A.N. [Time Analysis of Elastic-plastic Finite Dissipative Systems UnderNonstationary Effects] Bulletin of the South Ural State University. Ser. Construction Engineering and Architecture, 2005, iss. 3,
no. 13(53), pp. 57–62 (in Russ.).
Bezdelev V.V. [Numerical Simulation of the Dynamic Stress-strain State of Buildings under Seismic Actions in Order to Optimize Parameters of Damping Devices]. International Journal for Computational Civil and Structural Engineering, 2008, vol. 4, no. 2. pp. 24–25 (in Russ.).
Klyueva N.V., Azhzeurov O.V., Shuvalov K.A. [On the Issue of Development of Experimental Studies of Deformation and Fracture of Spatial Design Systems under Beyond Design Impacts]. Journal «Proceedings of the South-West State University», 2013, no. 1(46), pp. 111–116 (in Russ.).
Eremeev P.G. [Prevention Avalanche (Progressive) Collapse of Supporting Structures of Unique Large-span Structures during Emergency Loads]. Structural Mechanics and Analysis of Constructions, 2006, no. 2,
pp. 65–72 (in Russ.).
Shlychkov S.V., Ivanov S.P., Kuzovkov S.G., Loskutov Yu.V. [Calculation of Geometrically Nonlinear Structures Using Finite Element Method]. Bulletin of the higher educational institutions. Technical science. Machine Building and Engineering, 2008, iss. 4, pp. 145–152 (in Russ.).
Simon E.V. [Calculation of Geometrically Nonlinear Rod Systems in Mixed Form]. Internet-Vestnik VolgGASU. Polythematic Series, 2012, iss. 3 (23). http://vestnik.vgasu.ru/attachments/Simon-2012_3(23). (accessed 07.02.2016).
Sventikov A.A. [Geometrically Nonlinear Calculation of the Hanging Rod Designs. Part 2: The Matrix Calculation of Suspension Systems]. Journal «Construction and Architecture», 1970, vol. 1, no. 1, pp. 18–27
(in Russ.).
Perel'mutrer A.V. Besedy o stroitel'noy mekhanike [Conversations about the Structural Mechanics]. Moscow, SCAD Soft Publ., Izdatel'stvo ASV Publ., 2014. 250 p.
Potapov, A.N. Dinamicheskiy analiz diskretnykh dissipativnykh sistem pri nestatsionarnykh vozdeystviyakh: monografiya [Dynamical Analysis of Discreet Dissipative Systems under Nonstationary Loadings]. Chelyabinsk, South Ural St. Univ. Publ., 2003. 167 p.
Landsberga G. S. Elementarnyy uchebnik fiziki. Tom 1: Mekhanika. Teplota. Molekulyarnaya fizika [Elementary Physics. Volume 1: Mechanics. Heat. Molecular Physics]. Moscow, Fizmatlit Publ., 2000. 605 p.
Alfutov N.A. Osnovy rascheta na ustoychivost' uprugikh sistem [Fundamentals of Calculation on the Stability of Elastic Systems]. Moscow, Mashinostroenie Publ., 1978. 312 p.
Vasil'kov, G.V. Evolyutsionnaya teoriya zhiznennogo tsikla mekhanicheskikh sistem: Teoriya sooruzheniy [Evolutionary Theory of the Life Cycle of Mechanical Systems: Theory of Structures]. Moscow, URSS Publ., 2013. 320 p.
Potapov A.N., Ufimtsev E.M. [Time Analysis of the Structures with the Breaking Ties under the Pulse Load]. Integratsiya, partnerstvo i innovatsii v stroitel'noy nauke i obrazovanii: Sbornik trudov XXIV Mezhdunarodnoy nauchnoy konferentsii 19–21 oktyabrya 2011 [Proceedings of the XXIV International Conference “Integration, Partnership and Innovation in Construction Science and Education”, October 19–21, 2011]. Moscow, MGSU Publ., 2011. pp. 229–233 (in Russ.).
Potapov A.N. [Analysis of Vibrations of Structures with Breaked Ties]. Morskie intellektual'nye tekhnologii [Marine Intelligent Technologies]. 2011, no. 3, pp. 45–48 (in Russ.).
Ikrin V.A. Soprotivlenie materialov s elementami teorii uprugosti i plastichnosti: Uchebnik dlya vuzov po napravleniyu “Stroitel'stvo” [Strength of Materials with Elements of the Theory of Elasticity and Plasticity:
A Textbook for High Schools in the Direction of "Building"]. Moscow, Assotsiatsii stroitel'nykh vuzov Publ., 2005. 423 p.
GOST 8509-93. Ugolki stal'nye goryachekatanye ravnopolochnye. Sortament [Hot-rolled steel equal-leg angles. Dimensions]. Moscow, Standartinform Publ., 2005.
Bernshteyn M.F., Il'ichev V.A., Korenev B.G., Rabinovich I.M. Dinamicheskiy raschet zdaniy i sooruzheniy [Dynamic calculation of buildings and structures]. Moscow, Stroyizdat Publ., 1984. 303 p.
Potapov A.N., Ufimtsev E.M. [Oscillations of Systems with a Breaking Ties]. Teoriya i praktika rascheta zdaniy, sooruzheniy i elementov konstruktsiy. Analiticheskie i chislennye metody: Sbornik trudov mezhdunarodnoy nauchno-prakticheskoy konferentsii 29 iyunya 2011 [Proceedings of the international-term scientific and practical conference “Theory and practice of calculation of buildings, structures and structural elements. Analytical and numerical methods”, June 29, 2011]. Moscow, MGSU Publ., 2011, pp. 292–301 (in Russ.).
Ufimtsev E.M. [Time Analysis of Physically and Structurally Nonlinear Oscillations of Truss Structures in the Pulse Loading. Part 2: An Example of the Calculation of the Elastic Structurally Nonlinear Oscillations of the Roof Truss]. Stroitel'stvo. Ekologiya: teoriya, praktika, innovatsii: Sbornik dokladov I-y mezhdunarodnoy nauchno-prakticheskoy konferentsii 9 marta 2015 g. [Proceedings of the 1st International Scientific-Practical Conference “Building. Ecology: Theory, Practice, Innovation”, March 9, 2015]. Chelyabinsk, PIRS Publ., 2015,
pp. 106–108 (in Russ.).
D'yakonov V.P. MATLAB 7.*/R2006/R2007: Samouchitel' [MATLAB 7.*/R2006/R2007: Self-teacher]. Moscow, DMK Press Publ., 2008. 768 p.
Ссылки
- На текущий момент ссылки отсутствуют.