Двусторонняя аналитическая оценка первой частоты плоской фермы

Автор: Воробьев Олег

Журнал: Строительство уникальных зданий и сооружений @unistroy

Статья в выпуске: 7 (92), 2020 года.

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Объект исследования - статически детерминированная консольная ферма. Трасса состоит из прямоугольных панелей с направленными вниз диагональными балками. Ферма имеет две опоры, одна из которых неподвижно-шарнирная, а другая роликовая. Массы располагаются в узлах верхней и нижней поясов. Силы в стержнях и реакции на опорах определяются методом совместной изоляции. Вертикальное смещение узлов выводится из метода Максвелла-Мора с предпосылкой линейной упругости. Зависимость вертикального смещения, оценок Дункерли и Рэлея частоты первичной фермы от количества панелей выводится из индуктивного анализа набора конкретных ферм с увеличивающимся количеством панелей. Рекуррентные уравнения, отвечающие определенным коэффициентам, выводятся с использованием специальных функций системы компьютерной алгебры Maple. Полученные решения являются полиномиальными с количеством панелей в качестве переменных. Коэффициент Рэлея рассчитывается с предположением, что первая мода вибрации равна прогибу фермы под действием равномерно распределенной нагрузки. Построены графики зависимости полученных оценок от масс узлов, количества панелей, жесткости и размеров фермы.

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Ферма, аналитическое решение, частота, метод Дункерли, фактор Рэлея, клен, символьная индукция

Короткий адрес: https://readera.org/143172555

IDR: 143172555   |   DOI: 10.18720/CUBS.92.4

Список литературы Двусторонняя аналитическая оценка первой частоты плоской фермы

  • Kirsanov, M., Serdjuks, D., Buka-Vaivade, K. Analytical Dependence of Deflection of the Lattice Truss on the Number of Panels. Lecture Notes in Civil Engineering. 2020. 70. Pp. 25-35. DOI: 10.1007/978-3-030-42351-3_3
  • Kirsanov, M., Tinkov, D. Analytical calculation of the deflection of the lattice truss. MATEC Web of Conferences. 2018. 193. Pp. 1-7. DOI: 10.1051/matecconf/201819303015
  • Kirsanov, M., Komerzan, E., Sviridenko, O. Inductive analysis of the deflection of a beam truss allowing kinematic variation. MATEC Web of Conferences. 2018. 239. DOI: 10.1051/matecconf/201823901012
  • Kirsanov, M., Tinkov, D., Boiko, O. Analytical calculation of the combined suspension truss. MATEC Web of Conferences. 2019. 265. Pp. 05025. DOI: 10.1051/matecconf/201926505025
  • Kirsanov, M. One feature of the constructive solutions of the lattice girder. International Journal for Computational Civil and Structural Engineering. 2018. 14(4). Pp. 90-97. 10.22337/2587- 9618-2018-14-4-90-97. DOI: 10.22337/2587-9618-2018-14-4-90-97
  • Kirsanov, M. Analysis of the deflection of a truss with a decorative lattice. Construction Science and Education. 2019. (1). Pp. 1-10.
  • DOI: 10.22227/2305-5502.2019.1.1
  • Kirsanov, M. Calculating model of a frame type planar truss having an arbitrary number of panels. Vestnik MGSU. 2018. (10). Pp. 1184-1192.
  • DOI: 10.22227/1997-0935.2018.10.1184-1192
  • Kirsanov, M., Serdjuks, D., Buka-Vaivade, K. Analytical Expression of the Dependence of the Multi-lattice Truss Deflection on the Number of Panels. Construction of Unique Buildings and Structures. 2020. 90(9003).
  • DOI: 10.18720/CUBS.90.3
  • Buka-Vaivade, K., Kirsanov, M., Serdjuks, D. Calculation of deformations of a cantilever-frame planar truss model with an arbitrary number of panels. Vestnik MGSU. 2020. (4). Pp. 510-517.
  • DOI: 10.22227/1997-0935.2020.4.510-517
  • Kirsanov, M., Ovsyannikova, V. Analytical calculation of girder deflection in the maple system. Structural Mechanics and Analysis of Constructions. 2020. (3). Pp. 15-19. 10.37538/0039- 2383.2020.3.15.19.
  • DOI: 10.37538/0039-2383.2020.3.15.19
  • Kirsanov, M., Komerzan, E., Sviridenko, O. Analytical calculation of the deflection of an externally statically indeterminate lattice truss. MATEC Web of Conferences. 2019. 265. Pp. 05027.
  • DOI: 10.1051/matecconf/201926505027
  • Kirsanov, M. Lower estimate of the fundamental frequency of natural oscillations of a truss with an arbitrary number of panels. Vestnik MGSU. 2019. (7). Pp. 844-851. 10.22227/1997- 0935.2019.7.844-851.
  • DOI: 10.22227/1997-0935.2019.7.844-851
  • Kirsanov, M., Tinkov, D. Analytical solution of the frequency of the load oscillation at an arbitrary girder node in the system Maple. Construction Science and Education. 2019. (4). Pp. 3-3.
  • DOI: 10.22227/2305-5502.2018.4.3
  • Kirsanov, M., Tinkov, D. Analysis of the frequencies of load oscillations, depending on its position in the nodes of planar truss. Building and reconstruction. 2020. 87(1). Pp. 14-19. 10.33979/2073-7416-2020-87-1-14-19. URL: https:// href='contents.asp?titleid=7849' title='Клиническая лабораторная диагностика'>elibrary.ru/item.asp?id=42532000.
  • DOI: 10.33979/2073-7416-2020-87-1-14-19.URL
  • Kirsanov, M.N., Tinkov, D. V. Formulas for calculating the frequency spectrum of natural oscillations of a beam truss with an arbitrary number of panels. Постулат. 2019. 3(564). Pp. 1- 19.
  • DOI: 10.4324/9781315853178
  • Kirsanov, M., Tinkov, D. Analytical expressions of the frequencies of small oscillations of a girder with an arbitrary number of panels. Structural mechanics and structures. 2019. 1(20). Pp. 14-20.
  • Kirsanov, M.N., Tinkov, D. V. Analysis of the natural frequencies of oscillations of a planar truss with an arbitrary number of panels. Vestnik MGSU. 2019. 14(3). Pp. 284-292. 10.22227/1997-0935.2019.3.284-292. URL: http://vestnikmgsu.ru/ru/component/sjarchive/issue/article.display/2019/3/284-292.
  • DOI: 10.22227/1997-0935.2019.3.284-292.URL
  • Mazurek, A. Geometrical aspects of optimum truss like structures for three-force problem. Structural and Multidisciplinary Optimization. 2012. 45(1). Pp. 21-32. 10.1007/s00158-011- 0679-y.
  • DOI: 10.1007/s00158-011-0679-y
  • Mazurek, A., Baker, W.F., Tort, C. Geometrical aspects of optimum truss like structures. Structural and Multidisciplinary Optimization. 2011. 43(2). Pp. 231-242.
  • DOI: 10.1007/s00158-010-0559-x
  • Prager, W. Nearly optimal design of trusses. Computers & Structures. 1978. 8(3-4). Pp. 451-454. 10.1016/0045-7949(78)90190-6. URL: https://linkinghub.elsevier.com/retrieve/pii/0045794978901906.
  • DOI: 10.1016/0045-7949(78)90190-6.URL
  • Prager, W. Optimal layout of trusses with finite numbers of joints†. Journal of the Mechanics and Physics of Solids. 1978. 26(4). Pp. 241-250. 10.1016/0022-5096(78)90019-4. URL: https://linkinghub.elsevier.com/retrieve/pii/0022509678900194.
  • DOI: 10.1016/0022-5096(78)90019-4.URL
  • Sokół, T., Lewiński, T. On the solution of the three forces problem and its application in optimal designing of a class of symmetric plane frameworks of least weight. Structural and Multidisciplinary Optimization. 2010. 42(6). Pp. 835-853.
  • DOI: 10.1007/s00158-010-0556-0
  • Zhu, R., Li, F., Shao, F., Zhang, D. Static and dynamic behaviour of a hybrid PFRP-aluminium space truss girder: Experimental and numerical study. Composite Structures. 2020. 243(March). Pp. 112226. 10.1016/j.compstruct.2020.112226. URL: 10.1016/j.compstruct.2020.112226.
  • DOI: 10.1016/j.compstruct.2020.112226.URL
  • Wang, D., Xu, W. Minimum Weight Optimal Design of Truss Structure with Frequency Response Function Constraint. Journal of Aerospace Engineering. 2020. 33(4). Pp. 1-12.
  • DOI: 10.1061/(ASCE)AS.1943-5525.0001149
  • Jalili, S., Talatahari, S. Optimum Design of Truss Structures Under Frequency Constraints using Hybrid CSS-MBLS Algorithm. KSCE Journal of Civil Engineering. 2018. 22(5). Pp. 1840-1853.
  • DOI: 10.1007/s12205-017-1407-y
  • Tejani, G.G., Savsani, V.J., Patel, V.K., Mirjalili, S. Truss optimization with natural frequency bounds using improved symbiotic organisms search. Knowledge-Based Systems. 2018. 143. Pp. 162-178. 10.1016/j.knosys.2017.12.012. URL: 10.1016/j.knosys.2017.12.012.
  • DOI: 10.1016/j.knosys.2017.12.012.URL
  • Millan-Paramo, C., Abdalla Filho, J.E. Size and Shape Optimization of Truss Structures with Natural Frequency Constraints Using Modified Simulated Annealing Algorithm. Arabian Journal for Science and Engineering. 2020. 45(5). Pp. 3511-3525. 10.1007/s13369-019-04138-5. URL: 10.1007/s13369-019-04138-5.
  • DOI: 10.1007/s13369-019-04138-5.URL
  • Jalili, S., Hosseinzadeh, Y. Combining Migration and Differential Evolution Strategies for Optimum Design of Truss Structures with Dynamic Constraints. Iranian Journal of Science and Technology. Transactions of Civil Engineering. 2019. 43(Gomes 2011). Pp. 289-312. 10.1007/s40996- 018-0165-5. URL: 10.1007/s40996-018-0165-5.
  • DOI: 10.1007/s40996-018-0165-5.URL
  • Farshchin, M., Camp, C. V., Maniat, M. Multi-class teaching-learning-based optimization for truss design with frequency constraints. Engineering Structures. 2016. 106. Pp. 355-369. 10.1016/j.engstruct.2015.10.039. URL: 10.1016/j.engstruct.2015.10.039.
  • DOI: 10.1016/j.engstruct.2015.10.039.URL
  • Mortazavi, A. Size and layout optimization of truss structures with dynamic constraints using the interactive fuzzy search algorithm. Engineering Optimization. 2020. Pp. 1-23. 10.1080/0305215X.2020.1726341. URL: 0305215X.2020.1726341.
  • DOI: 10.1080/0305215X.2020.1726341.URL
  • Padil, K.H., Bakhary, N., Abdulkareem, M., Li, J., Hao, H. Non-probabilistic method to consider uncertainties in frequency response function for vibration-based damage detection using Artificial Neural Network. Journal of Sound and Vibration. 2020. 467. Pp. 115069. 10.1016/j.jsv.2019.115069. URL: 10.1016/j.jsv.2019.115069.
  • DOI: 10.1016/j.jsv.2019.115069.URL
  • Grzywiński, M., Selejdak, J., Dede, T. Truss optimization with frequency constraints based on TLBO algorithm. AIP Conference Proceedings. 2020. 2239(May). URL: http://aip.scitation.org/doi/abs/.
  • DOI: 10.1063/5.0007818
  • Li, J., Zhang, R., Liu, J., Cao, L., Chen, Y.F. Determination of the natural frequencies of a prestressed cable RC truss floor system. Measurement: Journal of the International Measurement Confederation. 2018. 122(July). Pp. 582-590. 10.1016/j.measurement.2017.08.048. URL: 10.1016/j.measurement.2017.08.048.
  • DOI: 10.1016/j.measurement.2017.08.048.URL
  • Zhang, W.F., Li, Y., Liu, Y.C., Huang, B., Yan, W. Analytical solution and characteristics of vertical seismic displacement of truss cable structures. IOP Conference Series: Earth and Environmental Science. 2019. 218(1). Pp. 0-6.
  • DOI: 10.1088/1755-1315/218/1/012093
  • Suwała, G., Jankowski. Nonparametric identification of structural modifications in Laplace domain. Mechanical Systems and Signal Processing. 2017. 85(October 2015). Pp. 867-878.
  • DOI: 10.1016/j.ymssp.2016.09.018
  • Zhou, X., Li, J., Liu, J., Frank Chen, Y. Dynamic Performance Characteristics of Pre-Stressed Cable RC Truss Floor System under Human-Induced Loads. International Journal of Structural Stability and Dynamics. 2017. 17(4). Pp. 1-20.
  • DOI: 10.1142/S0219455417500493
  • Zhou, X., Cao, L., Chen, Y.F., Liu, J., Li, J. Experimental and analytical studies on the vibration serviceability of pre-stressed cable RC truss floor systems. Journal of Sound and Vibration. 2016. 361. Pp. 130-147. 10.1016/j.jsv.2015.10.001. URL: 10.1016/j.jsv.2015.10.001.
  • DOI: 10.1016/j.jsv.2015.10.001.URL
  • Chen, Z., Chen, F., Zhou, L. Slow-fast dynamics in the truss core sandwich plate under excitations with high and low frequencies. Applied Mathematical Modelling. 2020. 88. Pp. 382-395. 10.1016/j.apm.2020.06.055. URL: 10.1016/j.apm.2020.06.055.
  • DOI: 10.1016/j.apm.2020.06.055.URL
  • Vorobyev, O. About methods of obtaining analytical solution for eigenfrequencies problem of trusses. Structural mechanics and structures. 2020. 1(24). Pp. 25-38.
  • Kim, M.J., Eun, H.C. Identification of damage-expected members of truss structures using frequency response function. Advances in Mechanical Engineering. 2017. 9(1). Pp. 1-10.
  • DOI: 10.1177/1687814016687911
  • Venglar, M., Sokol, M. Experimental modal analysis of diagonal members. Vibroengineering Procedia. 2019. 23. Pp. 110-114.
  • DOI: 10.21595/vp.2019.20671
  • Debnath, N., Dutta, A., Deb, S.K. Multi-modal Passive-vibration Control of Bridges under General Loading-condition. Procedia Engineering. 2016. 144. Pp. 264-273. 10.1016/j.proeng.2016.05.132. URL: 10.1016/j.proeng.2016.05.132.
  • DOI: 10.1016/j.proeng.2016.05.132.URL
  • Lin, R.M. Modelling, detection and identification of flexural crack damages in beams using frequency response functions. Meccanica. 2016. 51(9). Pp. 2027-2044. 10.1007/s11012- 015-0350-6.
  • DOI: 10.1007/s11012-015-0350-6
  • Siekierski, W. An analytical method to estimate the natural bending frequency of the spans of railway through truss bridges with steel-and-concrete composite decks. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit. 2016. 230(8). Pp. 1908-1918.
  • DOI: 10.1177/0954409715618691
  • Debnath, N., Deb, S.K., Dutta, A. Multi-modal vibration control of truss bridges with tuned mass dampers under general loading. JVC/Journal of Vibration and Control. 2016. 22(20). Pp. 4121- 4140.
  • DOI: 10.1177/1077546315571172
  • Çelebi, M., Ghahari, S.F., Haddadi, H., Taciroglu, E. Response study of the tallest California building inferred from the Mw7.1 Ridgecrest, California earthquake of 5 July 2019 and ambient motions. Earthquake Spectra. 2020. Pp. 875529302090683. 10.1177/8755293020906836. URL: http://journals.sagepub.com/doi/10.1177/8755293020906836.
  • DOI: 10.1177/8755293020906836.URL
  • Al-Azawi, T.K., Abdulmajeed, M.W., Hashoosh, A.A. Control of footstep vertical vibration for Vierendeel truss - supported steel footbridges. IOP Conference Series: Materials Science and Engineering. 2020. 737(1). 10.1088/1757-899X/737/1/012006. URL: https://iopscience.iop.org/article/10.1088/1757-899X/737/1/012006.
  • DOI: 10.1088/1757-899X/737/1/012006.URL
  • Li, B., Liu, Y., Tan, K.T. A novel meta-lattice sandwich structure for dynamic load mitigation. Journal of Sandwich Structures and Materials. 2019. 21(6). Pp. 1880-1905.
  • DOI: 10.1177/1099636217727144
  • Guo, Z., Liu, C., Li, F. Vibration analysis of sandwich plates with lattice truss core. Mechanics of Advanced Materials and Structures. 2019. 26(5). Pp. 424-429. 10.1080/15376494.2017.1400616. URL: 10.1080/15376494.2017.1400616.
  • DOI: 10.1080/15376494.2017.1400616.URL
  • An, X., Lai, C., Fan, H., Zhang, C. 3D acoustic metamaterial-based mechanical metalattice structures for low-frequency and broadband vibration attenuation. International Journal of Solids and Structures. 2020. 191-192. Pp. 293-306. 10.1016/j.ijsolstr.2020.01.020. URL: 10.1016/j.ijsolstr.2020.01.020.
  • DOI: 10.1016/j.ijsolstr.2020.01.020.URL
  • Stephen, N.G. On southwell's a novel dunkerley's method. Journal of Sound and Vibration. 1995. 181(1). Pp. 179-184. 10.1006/jsvi.1995.0133. URL: https://linkinghub.elsevier.com/retrieve/pii/S0022460X85701332.
  • DOI: 10.1006/jsvi.1995.0133.URL
  • Thomson, W.T. Theory of vibration with applications, fourth edition. Theory of Vibration with Applications, Fourth Edition. 2018. Pp. 1-546.
  • DOI: 10.1201/9780203718841
  • Aldrich, J. Doing least squares: Perspectives from Gauss and Yule. International Statistical Review. 1998. 66(1). Pp. 61-81. 10.1111/j.1751-5823.1998.tb00406.x. URL: http://doi.wiley.com/10.1111/j.1751-5823.1998.tb00406.x.
  • DOI: 10.1111/j.1751-5823.1998.tb00406.x.URL
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