Structural Engineering and Mechanics

  • 제51권3호
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  • Pages.519-530
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  • 2014
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

An accurate novel method for solving nonlinear mechanical systems

  • Bayat, Mahdi (Department of Civil Engineering, College of Engineering, Mashhad Branch, Islamic Azad University) ;
  • Pakar, Iman (Young Researchers and Elites Club, Mashhad Branch, Islamic Azad University) ;
  • Bayat, Mahmoud (Department of Civil Engineering, College of Engineering, Mashhad Branch, Islamic Azad University)
  • 투고 : 2013.09.05
  • 심사 : 2014.06.20
  • 발행 : 2014.08.10
⟨ 이전 논문 다음 논문 ⟩

초록

This paper attempts to investigate the nonlinear dynamic analysis of strong nonlinear problems by proposing a new analytical method called Hamiltonian Approach (HA). Two different cases are studied to show the accuracy and efficiency of the method. This approach prepares us to obtain the nonlinear frequency of the nonlinear systems with the first order of the solution with a high accuracy. Finally, to verify the results we present some comparisons between the results of Hamiltonian approach and numerical solutions using Runge-Kutta's [RK] algorithm. This approach has a powerful concept and the high accuracy, so it can be apply to any conservative nonlinear problems without any limitations.

키워드

참고문헌

  1. Bayat, M. and Pakar, I. (2011a), "Nonlinear free vibration analysis of tapered beams by Hamiltonian approach", J. Vibroeng., 13(4), 654-661.
  2. Bayat, M. and Pakar, I. (2011b), "Application of He's energy balance method for nonlinear vibration of thin circular sector cylinder", Int. J. Phy. Sci., 6(23), 5564-5570.
  3. Bayat, M., Pakar, I. and Shahidi, M. (2011c), "Analysis of nonlinear vibration of coupled systems with cubic nonlinearity", Mechanika, 17(6), 620-629.
  4. Bayat, M., Pakar, I. and Domaiirry, G. (2012a), "Recent developments of Some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: A review", Lat. Am. J. Solid. Struct., 9(2),145-234.
  5. Bayat, M. and Pakar, I. (2012b), "Accurate analytical solution for nonlinear free vibration of beams", Struct. Eng. Mech., 43(3), 337-347. https://doi.org/10.12989/sem.2012.43.3.337
  6. Bayat, M., Pakar, I. and Bayat, M. (2013a), "Analytical solution for nonlinear vibration of an eccentrically reinforced cylindrical shell", Steel Compos. Struct., 14(5), 511-521. https://doi.org/10.12989/scs.2013.14.5.511
  7. Bayat, M. and Pakar, I. (2013b), "Nonlinear dynamics of two degree of freedom systems with linear and nonlinear stiffnesses", Earthq. Eng. Eng. Vib., 12(3), 411-420. https://doi.org/10.1007/s11803-013-0182-0
  8. Bayat, M. and Pakar, I. (2013c), "On the approximate analytical solution to non-linear oscillation systems", Shock Vib., 20(1), 43-52. https://doi.org/10.1155/2013/549213
  9. Bayat, M., Pakar, I. and Cveticanin, L. (2014a), "Nonlinear free vibration of systems with inertia and static type cubic nonlinearities: an analytical approach", Mech. Mach. Theor., 77, 50-58. https://doi.org/10.1016/j.mechmachtheory.2014.02.009
  10. Bayat, M., Pakar, I. and Cveticanin, L.(2014b), "Nonlinear vibration of stringer shell by means of extended Hamiltonian approach", Arch. Appl. Mech., 84(1), 43-50. https://doi.org/10.1007/s00419-013-0781-2
  11. Bayat, M., Bayat, M. and Pakar, I. (2014c), "Nonlinear vibration of an electrostatically actuated microbeam", Lat. Am. J. Solid. Struct., 11(3), 534-544. https://doi.org/10.1590/S1679-78252014000300009
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  20. Pakar, I., Bayat, M. and Bayat, M. (2012a), "On the approximate analytical solution for parametrically excited nonlinear oscillators", J. Vibroeng., 14(1), 423-429.
  21. Pakar, I. and Bayat, M. (2012b), "Analytical study on the non-linear vibration of Euler-Bernoulli beams", J. Vibroeng., 14(1), 216-224.
  22. Pakar, I. and Bayat, M. (2013a), "An analytical study of nonlinear vibrations of buckled Euler Bernoulli beams", Acta Physica Polonica A, 123(1), 48-52. https://doi.org/10.12693/APhysPolA.123.48
  23. Pakar, I. and Bayat, M. (2013b), "Vibration analysis of high nonlinear oscillators using accurate approximate methods", Struct. Eng. Mech., 46(1), 137-151. https://doi.org/10.12989/sem.2013.46.1.137
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피인용 문헌

  1. A novel approximate solution for nonlinear problems of vibratory systems vol.57, pp.6, 2016, https://doi.org/10.12989/sem.2016.57.6.1039
  2. Analytical study of nonlinear vibration of oscillators with damping vol.9, pp.1, 2015, https://doi.org/10.12989/eas.2015.9.1.221
  3. Study of complex nonlinear vibrations by means of accurate analytical approach vol.17, pp.5, 2014, https://doi.org/10.12989/scs.2014.17.5.721
  4. High conservative nonlinear vibration equations by means of energy balance method vol.11, pp.1, 2016, https://doi.org/10.12989/eas.2016.11.1.129