Periodic solutions for highly nonlinear oscillation systems

• Autorzy: Ghadimi M. , Barari A. , Kaliji H. D. , Domairry G.
• Języki publikacji: EN

Abstrakty

EN

In this paper, Frequency-Amplitude Formulation is used to analyze the periodic behavior of tapered beam as well as two complex nonlinear systems. Many engineering structures, such as offshore foundations, oil platform supports, tower structures and moving arms, are modeled as tapered beams. The results obtained are compared with Variational Iteration Method (VIM) and other analytical methods as well as time marching solution. The results given show the effectiveness and accuracy of the proposed techniques.

Słowa kluczowe

EN

nonlinear vibration; frequency-amplitude formulation; periodic solution; approximate frequency; variational iteration method

PL

drganie belki; rozwiązanie okresowe; wariacyjna metoda iteracji

• Wydawca: Springer ; Wrocław University of Science and Technology
• Czasopismo: Archives of Civil and Mechanical Engineering
• Rocznik: 2012
• Tom: Vol. 12, no. 3
• Strony: 389--395
• Opis fizyczny: Bibliogr. 30 poz., tab., wykr.

Twórcy

autor

Ghadimi M.

• Department of Mechanical Engineering, Islamic Azad University, Semnan Branch, Semnan, Iran

autor

Barari A.

• Department of Civil Engineering, Aalborg University, Sohngardsholmsvej 57, 9000 Aalborg, Aalborg, Denmark

autor

Kaliji H. D.

• Department of Mechanical Engineering, Islamic Azad University, Semnan Branch, Semnan, Iran

autor

Domairry G.

• Department of Mechanical Engineering, Babol University of Technology, Babol, Iran

Bibliografia

• [1] M. Babaelahi, D.D. Ganji, A.A. Joneidi, Analysis of velocity equation of steady flow of a viscous incompressible fluid in channel with porous walls, International Journal for Numerical Methods in Fluids 63 (9) (2010) 1048–1059.
• [2] A. Barari, H.D. Kaliji, M. Ghadimi, G. Domairry, Non-linear vibration of Euler-Bernoulli beams, Latin American Journal of Solids and Structures 8 (2) (2011) 139–148.
• [3] M. Bayat, A. Barari, M. Shahidi, Dynamic response of axially loaded Euler-Bernoulli beams, Mechanika 17 (2) (2011) 172–177.
• [4] D.P. Billington, The tower and the bridge-The new art of structural engineering, Princeton University Press, Princeton, New Jersey, 1985.
• [5] Shih-Shin Chen, Cha’o-Kuang Chen, Application of the differential transformation method to the free vibrations of strongly non-linear oscillators, nonlinear analysis, Real World Applications 10 (2009) 881–888.
• [6] F. Farrokhzad, P. Mowlaee, A. Barari, A.J. Choobbasti, H.D. Kaliji, Analytical investigation of beam deformation equation using perturbation, homotopy perturbation, variational iteration and optimal homotopy asymptotic methods, Carpathian Journal of Mathematics 27 (1) (2011) 51–63.
• [7] F. Fouladi, E. Hosseinzadeh, A. Barari, G. Domairry, Highly nonlinear temperature dependent fin analysis by variational iteration method, Journal of Heat and Transfer Research 41 (2) (2010) 155–165.
• [8] S.S. Ganji, A. Barari, D.D. Ganji, Approximate analyses of two mass-spring systems and buckling of a column, Computers and Mathematics with Applications 61 (4) (2011) 1088–1095.
• [9] E.W. Gaylord, Natural frequencies of two nonlinear systems compared with the pendulum, Journal of Applied Mechanics 26 (85) (1959) 145–146.
• [10] M. Ghadimi, H.D. Kaliji, A. Barari, Analytical solutions to nonlinear mechanical oscillation problems, Journal of Vibroengineering 13 (2) (2011) 133–143.
• [11] E. Ghasemi, S. Soleimani, A. Barari, H. Bararnia, G. Domairry, The influence of uniform suction/injection on heat transfer of MHD Hiemenz flow in porous media, Journal of Engineering Mechanics ASCE (2011) http://dx.doi.org/10.1061/(ASCE)EM.1943-7889.0000301.
• [12] A.R. Ghotbi, A. Barari, M. Omidvar, G. Domairry, Application of homotopy perturbation and variational iteration methods into SIR epidemic model, Journal of Mechanics in Medicine and Biology 11 (1) (2011) 149–161.
• [13] A.R. Ghotbi, M. Omidvar, A. Barari, Infiltration in unsaturated soils-An analytical approach, Computers and Geotechnics 38 (2011) 777–782.
• [14] M.N. Hamden, N.H. Shabaneh, On the large amplitude free vibrations of a restrained uniform beam carrying an intermediate lumped mass, Journal of Sound and Vibration 199 (1997) 711–736.
• [15] J.H. He, Comment on He’s frequency formulation for nonlinear oscillators, European Journal of Physics 29 (2008) 19–22.
• [16] J.H. He, An improved amplitude-frequency formulation for nonlinear oscillators, International Journal of Nonlinear Science and Numerical Simulation 9 (2) (2008) 211–212.
• [17] S.H. Hoseini, T. Pirbodaghi, M.T. Ahmadian, G.H. Farrahi, On the large amplitude free vibrations of tapered beams: an analytical approach, Mechanics Research Communications 36 (2009) 892–897.
• [18] E. Hosseinzadeh, A. Barari, F. Fouladi, G. Domairry, Numerical analysis of forth-order boundary value problems in fluid mechanics and mathematics, Thermal Science Journal 14 (4) (2010) 1101–1109.
• [19] L.B. Ibsen, A. Barari, A. Kimiaeifar, Analysis of strongly nonlinear oscillation systems using He’s max-min method and comparison with homotopy analysis method and energy balance methods, Sadhana 35 (4) (2010) 1–16.
• [20] A.A. Joneidi, D.D. Ganji, M. Babaelahi, Differential transformation method to determine fin efficiency of convective straight fins with temperature dependent thermal conductivity, International Communications in Heat and Mass Transfer 36 (7) (2009) 757–762.
• [21] H.D. Kaliji, A. Fereidoon, M. Ghadimi, M. Eftari, analytical solutions for investigating free vibration of cantilever beams, World Applied Sciences Journal 9 (2010) 44–48Special Issue for Applied Math 9 (2010) 44–48.
• [22] S. Karimpour, S.S. Ganji, A. Barari, L.B. Ibsen, G. Domairry, Nonlinear vibration of an elastically restrained tapered beam, Science China Physics Mechanics and Astronomy (2012), http://dx.doi.org/10.1007/s11433-012-4661-5.
• [23] G.Q. Li, J.J. Li, A tapered Timoshenko-Euler beam element for analysis of steel portal frames, Journal of Constructional Steel Research 58 (2002) 1531–1544.
• [24] I. Mehdipour, D.D. Ganji, M. Mozaffari, Application of the energy balance method to nonlinear vibrating equations, Current Applied Physics 10 (2010) 104–112.
• [25] M.O. Miansari, M.E. Miansari, A. Barari, G. Domairry, Analysis of Blasius equation for Flat-plate flow with infinite boundary value, International Journal for Computational Methods in Engineering Science and Mechanics 11 (2) (2010) 79–84.
• [26] H. Mirgolbabaei, A. Barari, L.B. Ibsen, M.G. Sfahani, Numerical solution of boundary layer flow and convection heat transfer over a flat plate, Archives of Civil and Mechanical Engineering 10 (2010) 41–51.
• [27] M. Omidvar, A. Barari, M. Momeni, D.D. Ganji, New class of solutions for water infiltration problems in unsaturated soils, International Journal of Geomechanics and Geoengineering 5 (2) (2010) 127–135.
• [28] M.G. Sfahani, S.S. Ganji, A. Barari, H. Mirgolbabae, G. Domairry, Analytical solutions to nonlinear conservative oscillator with fifth-order non-linearity, Journal of Earthquake Engineering and Engineering Vibration 9 (3) (2010) 367–374.
• [29] M.G. Sfahani, A. Barari, M. Omidvar, S.S. Ganji, G. Domairry, Dynamic response of inextensible beams by improved energy balance method, Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 225 (1) (2011) pp. 66–73.
• [30] J.D. Yau, Stability of tapered I-beams under torsional moments, Finite Elements in Analysis and Design 42 (2006) 914–927.