Structural Engineering and Mechanics

  • 제75권2호
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  • Pages.239-246
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  • 2020
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Analytical approach on nonlinear vibration of dry cask storage systems

  • Bayat, M. (Department of Civil and Environmental Engineering, University of South Carolina) ;
  • Soltangharaei, V. (Department of Civil and Environmental Engineering, University of South Carolina) ;
  • Ziehl, P. (Department of Civil and Environmental Engineering, University of South Carolina)
  • 투고 : 2019.03.06
  • 심사 : 2020.02.21
  • 발행 : 2020.07.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, a novel analytical method, Max-Min Approach (MMA), has been presented and applied to consider the nonlinear vibration of dry cask storage systems. The nonlinear governing equation of the structure has been developed using the shell theory. The MMA results are compared with numerical solutions derived by Runge-Kutta's Method (RKM). The results indicate a satisfying agreement between MMA and numerical solutions. Parametric studies have been conducted on the nonlinear frequency of dry casks. The phase-plan of the problem is also presented and discussed. The proposed approach can potentially ca be extended to highly nonlinear problems.

키워드

과제정보

This research is based upon work supported by Electric Power Research Institute (EPRI) under the project number 1-108781.

참고문헌

  1. Andrianov, I. V., Awrejcewicz, J. and Manevitch, L. I. (2013), Asymptotical Mechanics of Thin-Walled Structures, Springer Science and Business Media, Germany.
  2. Arefi, M. (2018), "Nonlocal free vibration analysis of a doubly curved piezoelectric nano shell", Steel Compos. Struct., 27(4), 479-493. https://doi.org/10.12989/scs.2018.27.4.479.
  3. Avazpour, L. (2018), "Fractional Ostrowski type inequalities for functions whose derivatives are prequasiinvex", J. Inequal. Spec. Funct., 9, 15-29.
  4. Avazpoura, L., Allahviranloob, T. and Islamc, S. (2016), "Uncertain Hermite-Hadamard inequality for functions with (s,m)-Godunova-Levin derivatives via fractional integral", J. Nonlinear Sci. Appl., 9(5), 3333-3347. http://dx.doi.org/10.22436/jnsa.009.05.119
  5. Bayat, M., Bayat, M., Kia, M., Ahmadi, H. R. and Pakar, I. (2018), "Nonlinear frequency analysis of beams resting on elastic foundation using max-min approach", Geomech. Eng., 16(4), 355-361. http://dx.doi.org/10.12989/gae.2018.16.4.355
  6. Bayat, M., Pakar, I. and Cao, M. S. (2017), "Energy based approach for solving conservative nonlinear systems", Earthq. Struct., 13(2), 131-136. https://doi.org/10.12989/eas.2017.13.2.131.
  7. Bildik, N. and Konuralp, A. (2006), "The use of variational iteration method, differential transform method and Adomian decomposition method for solving different types of nonlinear partial differential equations", J. Nonlinear Sci. Numeric. Simulation, 7(1), 65-70. https://doi.org/10.1515/IJNSNS.2006.7.1.65.
  8. Braghin, F., Mehdipour, I., Lecis, N. O. R. A. and Galassi, C. (2016), "Periodic substructure for multi-frequency energy harvesting with single piezoelectric patch", Proceedings of Active and Passive Smart Structures and Integrated Systems 2016, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, 2016, Las Vegas, Nevada, USA, April. https://doi.org/10.1117/12.2219547.
  9. Chin, C.-M., Nayfeh, A.H. (1996), "Bifurcation and chaos in externally excited circular cylindrical shells", J. Appl. Mech., 63(6),565-574. https://doi.org/10.1115/1.2823335.
  10. Ebrahimi, F. and Fardshad, R. E. (2018), "Dynamic modeling of nonlocal compositionally graded temperature-dependent beams", Adv. Aircraft Spacecraft Sci., 5(1), 141. http://dx.doi.org/10.12989/aas.2018.5.1.141.
  11. Errico, F., Franco, F., Ichchou, M., De Rosa, S. and Petrone, G. (2019), "An investigation on the vibrations of laminated shells under aeroacoustic loads using a WFE approach", Adv. Aircraft Spacecraft Sci., 6(6),463-479. http://dx.doi.org/10.12989/aas.2019.6.6.463.
  12. Evkin, A. Y. and Kalamkarov, A. L. (2001), "Analysis of large deflection equilibrium states of composite shells of revolution. Part 1. General model and singular perturbation analysis", J. Solids Struct., 38(50-51), 8961-8974. https://doi.org/10.1016/S0020-7683(01)00184-6.
  13. Filippov, S. B. (1999), Theory of Conjugated and Reinforced Shells, St. Petersburg State University, St. Petersburg, Russia. (In Russian).
  14. Ganji, D.D. and Azimi, M. (2012), "Application of max min approach and amplitude frequency formulation to nonlinear oscillation systems", UPB Scientific Bulletin, 74(3), 131-140.
  15. Ganji, D.D., Esmaeilpour, M. and Soleimani, S. (2010), "Approximate solutions to Van der Pol damped nonlinear oscillators by means of He's energy balance method", J. Comput. Math., 87(9), 2014-2023. https://doi.org/10.1080/00207160802562564.
  16. Gao, J., Huang, P. and Yao, W. (2017), "Analytical and numerical study of temperature stress in the bi-modulus thick cylinder", Struct. Eng. Mech., 64(1), 81-92. http://dx.doi.org/10.12989/sem.2017.64.1.081.
  17. Garcia-Saldana, J. D. and Gasull, A. (2013), "A theoretical basis for the harmonic balance method", J. Diff. Equations, 254(1), 67-80. https://doi.org/10.1016/j.jde.2012.09.011.
  18. Genesio, R. and Tesi, A. (1992), "Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems", Automatica, 28(3), 531-548. https://doi.org/10.1016/0005-1098(92)90177-H
  19. Grigolyuk E. I., Kabanov V.V. (1987), Stability of Shells, Nauka, Moscow, Russia. (in Russian).
  20. Hashemiparast, S. and Avazpour, L. (2008), "Applying Quadrature Rules with Multiple Nodes to Solving Integral Equations", AIP Conference Proceedings, 1048, 257. https://doi.org/10.1063/1.2990906.
  21. He, J. H. (2003), "Homotopy perturbation method: a new nonlinear analytical technique", Appl. Math. Comput., 135(1), 73-79. https://doi.org/10.1016/S0096-3003(01)00312-5.
  22. He, J. H. (2004), "He Chengtian's inequality and its applications", Appl. Math. Comput., 151(3), 887-891. https://doi.org/10.1016/S0096-3003(03)00531-9
  23. He, J. H. (2008), "Max-min approach to nonlinear oscillators", J. Nonlinear Sci. Numeric. Simulation, 9(2), 207-210. https://doi.org/10.1515/IJNSNS.2008.9.2.207.
  24. He, J. H. (2010), "Hamiltonian approach to nonlinear oscillators", Phys. Lett. A, 374(23), 2312-2314. http://doi.org/10.1016/j.physleta.2010.03.064.
  25. Hieu, D. V. (2018), "Postbuckling and free nonlinear vibration of microbeams based on nonlinear elastic foundation", Math. Problems Eng., https://doi.org/10.1155/2018/1031237.
  26. Javanmard, M., Bayat, M. and Ardakani, A. (2013), "Nonlinear vibration of Euler-Bernoulli beams resting on linear elastic foundation", Steel Compos. Struct, 15(4), 439-449. https://doi.org/10.12989/scs.2013.15.4.439.
  27. Khan, K., Patel, B.P. and Nath, Y. (2015), "Free and forced vibration characteristics of bimodular composite laminated circular cylindrical shells", Compos. Struct., 126, 386-397. https://doi.org/10.1016/j.compstruct.2015.02.022.
  28. Koval, L.R. (1974), "Effect of longitudinal resonance the parametric stability of an axially excited cylindrical shell", The J. Acoustical Soc. America, 55(1), 91-97. https://doi.org/10.1121/1.1928136.
  29. Liu, Y. and Chu, F. (2012), "Nonlinear vibrations of rotating thin circular cylindrical shell", Nonlinear Dynam., 67(2), 1467-1479. https://doi.org/10.1007/s11071-011-0082-7.
  30. Lockhart, D.F. (1979), "Dynamic buckling of a damped externally pressurized imperfect cylindrical shell", ASME J. Appl. Mech., 46, 372-377. https://doi.org/10.1115/1.3424537.
  31. Madenci, E. and Ozutok, A. (2020), "Variational approximate for high order bending analysis of laminated composite plates", Struct. Eng. Mech., 73(1), 1-16. https://doi.org/10.12989/sem.2020.73.1.097.
  32. Mehdipour, I., Braghin, F., Lecis, N. O. R. A. and Galassi, C. (2016), "Analytical modeling and experimental verification of a S-shaped vibration energy harvester", ASME 2016 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, American Society of Mechanical Engineers Digital Collection, USA. https://doi.org/10.1115/SMASIS2016-9120.
  33. Mohammadian, M. and Akbarzade, M. (2017), "Higher-order approximate analytical solutions to nonlinear oscillatory systems arising in engineering problems", Arch. Appl. Mech., 87(8), 1317-1332. https://doi.org/10.1007/s00419-017-1252-y.
  34. Mohyud-Din, S.T. and Noor, M.A. (2009), "Homotopy perturbation method for solving partial differential equations", Zeitschrift fur Naturforschung A, 64(3-4), 157-170. https://doi.org/10.1515/zna-2009-3-402.
  35. Pakar, I., Bayat, M. and Cveticanin, L. (2018), "Nonlinear vibration of unsymmetrical laminated composite beam on elastic foundation", Steel Compos. Struct., 26(4), 453-461. http://dx.doi.org/10.12989/scs.2018.26.4.453.
  36. Razzak, M. A. (2016), "A simple harmonic balance method for solving strongly nonlinear oscillators", J. Assoc. Arab Universities for Basic Appl. Sci., 21, 68-76. https://doi.org/10.1016/j.jaubas.2015.10.002.
  37. Sadeghzadeh, S. A. D. E. G. H. and Kabiri, A. (2016), "Application of higher order Hamiltonian approach to the nonlinear vibration of micro electro mechanical systems", Latin American J. Solids Struct., 13(3), 478-497. https://doi.org/10.1590/1679-78252557.
  38. Shokravi, M. (2018), "Forced vibration response in nanocomposite cylindrical shells-Based on strain gradient beam theory", Steel Compos. Struct., 28(3), 381-388. https://doi.org/10.12989/scs.2018.28.3.381.
  39. Von Wagner, U. and Lentz, L. (2016), "On some aspects of the dynamic behavior of the softening Duffing oscillator under harmonic excitation", Arch. Appl. Mech., 86(8), 1383-1390. https://doi.org/10.1007/s00419-016-1123-y.
  40. Zeng, D. Q. (2009), "Nonlinear oscillator with discontinuity by the max-min approach", Chaos, Solitons Fractals, 42(5), 2885-2889. https://doi.org/10.1016/j.chaos.2009.04.029.
  41. Zhang, D. and S. Wang (2018), "Nonlinear effect of tooth-slot transition on axial vibration, contact state and speed fluctuation in traveling wave ultrasonic motor", Proceedings of the Institution of Mech. Eng., Part C J. Mech. Eng. Sci. 232(19), 3424-3438. https://doi.org/10.1177/0954406217736551.