PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Nonlinear homogeneous dynamical system of fully cracked concrete beam

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Purpose: Purpose of this paper is the theoretical formulation of elasto-dynamics behaviour of fully cracked concrete beams for two-degree of freedom (DOF) dynamical system. Such modelled system is demonstrated by a new class of two-DOF conservative, fully-nonlinear systems known as nonlinear homogeneous dynamical (NHD) systems. Design/methodology/approach: The theoretical formulation of Two-DOF dynamical system has been developed by using the fundamental concept of structural analysis. Further, the behaviour of such class of conservative dynamical system has been concluded by using MATLAB. Findings: Findings can be distinguished into two aspects. First, when subjected to service loads, reinforced concrete structures possess tension cracks. Due to load variation with time leads the breathing action (opening-closing-reopening) of existing cracks and the behaviour of such structures are nonlinearly-elastic. Second, such class of fully nonlinear dynamical system possess dependence of stiffness coefficients on nodal displacements. Research limitations/implications: The mechanism behind such class of fully nonlinear dynamical system is not yet fully explored. Practical implications: Practical implications are related to the structural response of fully cracked concrete beam to different earthquake excitation, especially to understand the response of such nonlinear homogeneous elasto-dynamical system with two-DOF concrete beam. Originality/value: Elasto-dynamics of fully cracked concrete beams.
Rocznik
Strony
5--19
Opis fizyczny
Bibliogr. 68 poz., rys., tab., wykr.
Twórcy
autor
  • Department of Civil Engineering, National Institute of Technology, Hamirpur, H.P India
autor
  • Department of Civil Engineering, National Institute of Technology, Hamirpur, H.P India
Bibliografia
  • [1] Y. L. MO, Dynamic behavior of concrete structures, Elsevier, Amsterdam, 1994. DOI: https://doi.org/10.1016/C2009-0-09176-4
  • [2] A.K. Chopra, Dynamics of structures: theory and applications to earthquake engineering, Prentice Hall Englewood Cliffs, New Jersey, 1995.
  • [3] G.G. Penelis, A.J. Kappos, Earthquake-resistant concrete structures, CRC press, Florida, 1997.
  • [4] L. Davenne, F. Ragueneau, J. Mazars, A. Ibrahimbegovic, Efficient approaches to finite element analysis in earthquake engineering, Computers & Structures 81/12 (2003) 1223-1239. DOI: https://doi.org/10.1016/S0045-7949(03)00038-5
  • [5] T. Paulay, M.J.N. Priestley, Seismic design of reinforced concrete and masonry buildings, John Wiley & Sons, New York, 1992.
  • [6] IS 1893 (Part 1): 2002, Indian standard code of practice - criteria for earthquake resistant design of structures, New Delhi, 2002.
  • [7] F. Stangenberg, Nonlinear dynamic analysis of reinforced concrete structures, Nuclear Engineering and Design 29/1 (1974) 71-88. DOI: https://doi.org/10.1016/0029-5493(74)90099-5
  • [8] R.W. Clough, J. Penzien, Dynamics of structures, Computers & Structures, Inc., Berkeley, 1995.
  • [9] IS 456: 2000, Indian standard plain and reinforced concrete - code of practice, New Delhi, 2000.
  • [10] J. Lemaitre, Coupled elasto-plasticity and damage constitutive equations, Computer Methods in Applied Mechanics and Engineering 51/1-3 (1985) 31-49. DOI: https://doi.org/10.1016/0045-7825(85)90026-X
  • [11] B.M. Luccioni, D.E. López, R.F. Danesi, Bond-slip in reinforced concrete elements, Journal of Structural Engineering 131/11 (2005) 1690-1698. DOI: https://doi.org/10.1061/(ASCE)0733-9445(2005)131:11(1690)
  • [12] G.S. Benipal, Rational mechanics of reinforced concrete beams, I.I.Sc-Bangalore, Bangalore, 1994.
  • [13] A.D. Dimarogonas, Vibration of cracked structures: A state of the art review, Engineering Fracture Mechanics 55/5 (1996) 831-857. DOI: https://doi.org/10.1016/0013-7944(94)00175-8
  • [14] S.M. Cheng, X.J. Xu, W. Wallace, A.S.J. Swamidas, Vibrational response of a beam with a breathing crack, Journal of Sound and Vibration 225/1 (1999) 201-208. DOI: https://doi.org/10.1006/jsvi.1999.2275
  • [15] M. Kisa, J. Brandon, The effects of closure of cracks on the dynamics of a cracked cantilever beam, Journal of Sound and Vibration 238/1 (2000) 1-18. DOI: https://doi.org/10.1006/jsvi.2000.3099
  • [16] T.G. Chondros, A.D. Dimarogonas, J. Yao, Vibration of a beam with a breathing crack, Journal of Sound and Vibration 239/1 (2001) 57-67. DOI: https://doi.org/10.1006/jsvi.2000.3156
  • [17] N.V. Hung, V.U.V. Hung, T.B. Viet, The effect of crack width on the service life of reinforced concrete structures, IOP Conference series: Earth & Environmental Science 143 (2018) 012044. DOI: https://doi.org/10.1088/1755-1315/143/1/012044
  • [18] G.S. Benipal, A study on the non-linear elastic behavior of reinforced concrete structural elements under normal loading, Indian Institute of Technology, Delhi, 1993.
  • [19] Y.C. Chu, M.H.H. Shen, Analysis of forced bilinear oscillators and the application to cracked beam dynamics, American Institute of Aeronautics and Astronautics Journal 30/10 (1992) 2512-2519. DOI: https://doi.org/10.2514/3.11254
  • [20] J.A. Inaudi, G. Leitmann, J.M. Kelly, Single degree of freedom nonlinear homogeneous systems, Journal of Engineering Mechanics 120/7 (1994) 1543-1562. DOI: https://doi.org/10.1061/(ASCE)0733-9399(1994)120:7(1543)
  • [21] J.M.T. Thompson, A.R. Bokaian, R. Ghaffari, Sub-harmonic and chaotic motions of a bilinear oscillator, IMA Journal of Applied Mathematics 31/3 (1983) 207-234. DOI: https://doi.org/10.1093/imamat/31.3.207
  • [22] U.K. Pandey, G.S. Benipal, Bilinear dynamics of SDOF concrete structures under sinusoidal loading, Advances in Structural Engineering 9/3 (2006) 393-407. DOI: https://doi.org/10.1260%2F136943306777641869
  • [23] U.K. Pandey, Nonlinear elasto-dynamics of cracked concrete beams, PhD Thesis, Indian Institute of Technology, Delhi, 2008.
  • [24] U.K. Pandey, G.S. Benipal, Bilinear elastodynamical models of cracked concrete beams, Structural Engineeing and Mechanics 39/4 (2011) 465-498. DOI: https://doi.org/10.12989/sem.2011.39.4.465
  • [25] U.K. Pandey, G.S. Benipal, Response of SDOF bilinear elasto-dynamical models of cracked concrete beams for El centro earthquake, IES Journal Part A: Civil & Structural Engineeing 6/3 (2013) 222-238. DOI: https://doi.org/10.12989/sem.2011.39.4.465
  • [26] T.K. Caughey, Sinusoidal excitation of a system with bilinear hysteresis, Journal of Applied Mechanics ASME 27/4 (1960) 640-643. DOI: https://doi.org/10.1115/1.3644075
  • [27] X. Jian, L. Qishao, H. Kelei, Non linear normal modes and their superposition in a two degrees of freedom asymmetric system with cubic nonlinearities, Applied Mathematics and Mechanics 19/12 (1998) 1167-1177. DOI: https://doi.org/10.1007/BF02456638
  • [28] T. Pirbodaghi and S. Hoseini, Nonlinear free vibration of a symmetrically conservative two-mass system with cubic nonlinearity, Journal of Computational and Nonlinear Dynamics 5/1 (2010) 011006. DOI: https://doi.org/10.1115/1.4000315
  • [29] M. Qaisi, A.W. Kilani, Power-series solution for a strongly non-linear two-degree-of-freedom system, Journal of Sound and Vibration 233/3 (2000) 489-494. DOI: https://doi.org/10.1006/jsvi.1999.2833
  • [30] M.A. Savi, P.M.C.L. Pacheco, Chaos in a two degree of freedom duffing oscillator, Journal of the Brazilian Society of Mechanical Sciences 24/2 (2002) 115-121. DOI: https://doi.org/10.1590/S0100-73862002000200006
  • [31] A.F. Vakakis, R.H. Rand, Normal modes and global dynamics of a two-degree-of-freedom non-linear system-I. Low energies, International Journal of Non-Linear Mechanics 27/5 (1992) 861-874. DOI: https://doi.org/10.1016/0020-7462(92)90040-E
  • [32] A.F. Vakakis, R.H. Rand, Normal modes and global dynamics of a two-degree-of-freedom non-linear system-II High energies, International Journal of Non-Linear Mechanics 27/5 (1992) 875-888. DOI: https://doi.org/10.1016/0020-7462(92)90041-5
  • [33] M. Falconi, E.A. Lacomba, C. Vidal, On the dynamics of mechanical systems with homogeneous polynomial potentials of degree 4, Bulletin of the Brazilian Mathematical Society, New Series 38/2 (2007) 301-333. DOI: https://doi.org/10.1007/s00574-007-0048-z
  • [34] A. Kozmin, Y. Mikhlin, C. Pierre, Transient in a two-DOF nonlinear system, Nonlinear Dynamics 51 (2008) 141-154. DOI: https://doi.org/10.1007/s11071-007-9198-1
  • [35] Z. Szabó, A. Lukács, Numerical stability analysis of a forced two-DOF oscillator with bilinear damping, Journal of Computational and Nonlinear Dynamics 2/3 (2007) 211-217. DOI: https://doi.org/10.1115/1.2727487
  • [36] A. Tondl, T. Ruijgrok, F. Verhulst, R. Nabergoj, Autoparametric resonance in mechanical systems, Cambridge University Press, Cambridge, 2015.
  • [37] M.R. Sharma, A.K. Singh, G.S. Benipal, Parametric resonance in concrete beam-columns, Latin American Journal of Solids and Structures 11/1 (2014) 925-945. DOI: https://doi.org/10.1590/S1679-78252014000600002
  • [38] A.H. Nayfeh, L.D. Zavodney, The response of two-degree-of-freedom systems with quadratic non-linearities to a combination parametric resonance, Journal of Sound and Vibration 107/2 (1986) 329-350. DOI: https://doi.org/10.1016/0022-460X(86)90242-7
  • [39] W. Asrar, Two-degree-of-freedom systems with quadratic non-linearities subjected to parametric and self excitation, Journal of Sound and Vibration 150/3 (1991) 447-456. DOI: https://doi.org/10.1016/0022-460X(91)90897-S
  • [40] A. Manevich, L. Manevitch, The mechanics of nonlinear system with internal resonances, Imperial College Press, London, 2005.
  • [41] S. Voggu, S. Sasmal, Dynamic nonlinearities for identification of the breathing crack type damage in reinforced concrete bridges, Structural Health Monitoring 20/1 (2021) 339-359. DOI: https://doi.org/10.1177%2F1475921720930990
  • [42] S. Jerath, M.M. Shibani, Dynamic stiffness and vibration of reinforced concrete beams, American Concrete Institute Journal 82/2 (1985) 196-202.
  • [43] P.G. Kirmser, The effect of discontinuities on natural frequencies of beams, University of Kansas Science Bulletin, Manhattan, 1944.
  • [44] K.V.D. Abeele, J.D. Visscher, Damage assessment in reinforced concrete using spectral and temporal nonlinear vibration techniques, Cement and Concrete Research 30/9 (2000) 1453-1464. DOI: https://doi.org/10.1016/S0008-8846(00)00329-X
  • [45] W.L. Bayissa, N. Haritos, Experimental investigation into vibration characteristics of a cracked RC T-beam, Proceeding of the Conference of Australian Earthquake Engineeing Society, 2004, 1-6.
  • [46] J. Maeck, M.A. Wahab, B. Peeters, G.D. Roeck, J.D. Visscher, W.P.D. Wilde, J.M. Ndambi, J. Vantomme, Damage identification in reinforced concrete structures by dynamic stiffness determination, Engineeing Structures 22/10 (2000) 1339-1349. DOI: https://doi.org/10.1016/S0141-0296(99)00074-7
  • [47] W.I. Hamad, J.S. Owen, M.F.M. Hussein, Modelling the degradation of vibration characteristics of reinforced concrete beams due to flexural damage, Structural Control and Health Monitoring 22/6 (2015) 939-967. DOI: https://doi.org/10.1002/stc.1726
  • [48] A.K. Darpe, K. Gupta, A. Chawla, Transient response and breathing behaviour of a cracked Jeffcott rotor, Journal of Sound and Vibration 272/1-2 (2004) 207-243. DOI: https://doi.org/10.1016/S0022-460X(03)00327-4
  • [49] S. Orhan, Analysis of free and forced vibration of a cracked cantilever beam, NDT & E International 40/6 (2007) 443-450. DOI: https://doi.org/10.1016/j.ndteint.2007.01.010
  • [50] R. Ruotolo, C. Surace, P. Crespo, D. Storer, Harmonic analysis of the vibrations of a cantilevered beam with a closing crack, Computers & Structures 61/6 (1996) 1057-1074. DOI: https://doi.org/10.1016/0045-7949(96)00184-8
  • [51] E. Hamed, Y. Frostig, Free vibrations of cracked prestressed concrete beams, Engineering Structures 26/11 (2004) 1611-1621. DOI: https://doi.org/10.1016/j.engstruct.2004.06.004
  • [52] S.S. Law, X.Q. Zhu, Nonlinear characteristics of damaged concrete structures under vehicular load, Journal of Structural Engineering 131/8 (2005) 1277-1285. DOI: https://doi.org/10.1061/(ASCE)0733-9445(2005)131:8(1277)
  • [53] J.M. Ndambi, J. Vantomme, K. Harri, Damage assessment in reinforced concrete beams using eigenfrequencies and mode shape derivatives, Engineeing Structures 24/4 (2002) 501-515. DOI: https://doi.org/10.1016/S0141-0296(01)00117-1
  • [54] U.K. Pandey, G.S. Benipal, First order homogeneous dynamical systems 1: theoretical formulation, International Journal of Structural Engineering 8/3 (2017) 187-204. DOI: https://doi.org/10.1504/IJSTRUCTE.2017.086435
  • [55] U.K. Pandey, G.S. Benipal, First order homogeneous dynamical systems 2: Application to cracked concrete beams, International Journalof Structural Engineering 8/3 (2017) 205-226. DOI: https://doi.org/10.1504/IJSTRUCTE.2017.086436
  • [56] S. Timoshenko, Vibration problems in engineering, D Van Nostrand Company, New York, 1937.
  • [57] G.P. Tilly, Dynamic behaviour of concrete structures, The University of Michigan, Michigan, 1986.
  • [58] S.A. Neild, P.D. Mcfadden, M.S. Williams, A discrete model of a vibrating beam using a time-stepping approach, Journal of Sound and Vibration 239/1 (2001) 99-121. DOI: https://doi.org/10.1006/jsvi.2000.3158
  • [59] C. Dundar, I.F. Kara, Three dimensional analysis of reinforced concrete frames with cracked beam and column elements, Engineering Structures 29/9 (2007) 2262-2273. DOI: https://doi.org/10.1016/j.engstruct.2006.11.018
  • [60] C. Chan, M. Asce, Q. Wang, S.M. Asce, Nonlinear stiffness design optimization of tall reinforced concrete buildings under service loads, Journal of Structural Engineering 132/6 (2006) 978-990. DOI: https://doi.org/10.1061/(ASCE)0733-9445(2006)132:6(978)
  • [61] J. Hellesland, Mechanics and slenderness limits of sway-restricted, Journal of Structural Engineering 134/8 (2008) 1300-1309. DOI: https://doi.org/10.1061/(ASCE)0733-9445(2008)134:8(1300)
  • [62] M.R. Sharma, A.K. Singh, G.S. Benipal, Elastic stability of concrete beam-columns. Part I: static stability, International Journal of Structural Stability and Dynamics 17/1 (2017) 1750094. DOI: https://doi.org/10.1142/S0219455417500948
  • [63] M.R. Sharma, A.K. Singh, G.S. Benipal, Elastic Stability of Concrete Beam-Columns. Part II: Dynamic Stability, International Journal of Structural Stability and Dynamics 17/1 (2017) 1750095. DOI: https://doi.org/10.1142/S021945541750095X
  • [64] C. Zhang, G. Gholipour, A.A. Mousavi, Nonlinear dynamic behaviour of simply-supported RC beams subjected to combined impact-blast loading, Engineering Structures 181 (2019) 124-142. DOI: https://doi.org/10.1016/j.engstruct.2018.12.014
  • [65] G. Nanclares, D. Ambrosini, O. Curadelli, M. Domizio, Nonlinear dynamics anlaysis of a RC bridge subjected to seismic loading, Smart Structures and Systems 26/6 (2020) 765-779. DOI: http://dx.doi.org/10.12989/sss.2020.26.6.765
  • [66] R. Ramamrutham, R. Narayan, Theory of Structure, Dhanpat Rai Publishing Company, Delhi, 2003.
  • [67] R.R. Babu, G.S. Benipal, A.K. Singh, Constitutive model for bimodular elastic damage of concrete, Latin American Journal of Solids and Structures 7/2 (2010) 143-166. DOI: https://doi.org/10.1590/S1679-78252010000200003
  • [68] X.T.C. Man, P.Y. Robin, L.M. McClure, Z. Wang, R.D. Finch, B.H. Jansen, Slot depth resolution in vibration signature monitoring of beams using frequency shift, Journal of the Acoustical Society of America 95/4 (1994) 2029-2037. DOI: https://doi.org/10.1121/1.408666
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-9b268bd3-243b-46ad-ba36-11319ba622ae
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.