نوع مقاله: مقاله پژوهشی
نویسندگان
1 دانشجوی کارشناسی ارشد مکانیک دانشکده فنی و مهندسی، دانشگاه جامع امام حسین (ع)
2 دانشیار گروه مکانیک، دانشکده فنی و مهندسی، دانشگاه جامع امام حسین(ع)
3 مربی، مهندسی هوافضا، دانشگاه جامع امام حسین (ع
4 دانشجوی کارشناسی ارشد عمران دانشکده فنی و مهندسی، دانشگاه جامع امام حسین (ع)
چکیده
رایزرهای دریایی یکی ازمهم‌ترین اعضای سازه‌ی سکوی شناورهستند. از همین رو، تحلیل ارتعاشات آن‌ها، دارای اهمیت ویژه‌ای می‌باشد. برای رسیدن به یک طراحی مناسب، درک چگونگی ارتعاشات عرضی رایزرها و به دست آوردن پاسخ فرکانسی آن‌ها بسیار مفید است. بنابراین در این مقاله، به تحلیل چگونگی ارتعاشات غیرخطی عرضی یک رایزر، تحت بار محوری متغیر با در نظر گرفتن اثر کشیدگی صفحه میانی، پرداخته شده است. برای انجام این تحقیق، از روش مقیاس زمانی چندگانه استفاده می‌شود. به منظور بررسی میزان دقت روش و صحت‌سنجی نتایج به دست آمده، مقایسه‌ای با روش عددی رانگ-کوتای مرتبه‌ی چهارم انجام شده است. بر اساس نتایج، پاسخ فرکانسی تیر بیان‌گر وجود پدیده‌ی تقسیم شدن به دو شاخه‌ی غیرخطی، در ارتعاشات سه بعدی رایزر می‌باشد.هم‌چنین، کشیدگی صفحه میانی رایزر، باعث ایجاد حالت سخت‌شوندگی در پاسخ فرکانسی می‌شود. مطالعه‌ای پارامتری انجام شده است که در آن، تأثیر پارامترهای مختلف بر نقطه شروع دو شاخگی غیرخطی بررسی شده است.
کلیدواژه‌ها
عنوان مقاله [English]
Analysis of Sub-Harmonic Resonance and Nonlinear Bifurcation Phenomena of Three-Dimensional Beams Under Parametric Excitation
نویسندگان [English]
- mahmoud pour jamshidian 1
- saed mahjob moghadas 2
- amir motalebi 3
- javad sheykhi 4
چکیده [English]
Risers are one of the main vessel structural members. So, non-linear vibration analysis of risers, is particularly important. To achieve a proper design, understanding how the transverse vibrations of risers and obtain their frequency response is very useful. In this paper, the transverse vibrations analysis of risers under variable axial load are investigated. The effects of mid-plane stretching is also considered. For this study, the method of multiple time scale is used. In order to verify the accuracy of this method, the results are compared with the results of four order Runge-Kutta numerical method, which has a good accuracy. The frequency response of the system is represented Bifurcation phenomenon. Study of frequency response indicating that there is bifurcation phenomenon in vibrational system, and also the mid-plane stretching of riser will create a hardening behavior. Parametric study is also performed that the effect of various parameters is review on the starting point of the bifurcation phenomenon.
کلیدواژه‌ها [English]
- Multiple time scales method
- frequency response
- bifurcation phenomenon
- marine riser
[1] Pattipawaej, O. “Modeling Uncertainty in the Dynamic Response of Marine Riser Using Probabilistic Finite Element Technique”, International Civil Engineering Conference, 2006.
[2] How, B. V. E., Ge, S. S., Choo, Y. S., “Active Control of Flexible Marine Risers”, Journal of Sound and Vibration, Vol. 320, No. 4, pp. 758 - 776, Mar. 2009.
[3] Kaewunruen, S., Chiravatchradej J., Chucheepsakul, S. “Nonlinear Free Vibrations of Marine Risers/Pipes Transporting Fluid”, Journal of Ocean Engineering, Vol. 32, No. 3, pp. 417 - 440, Mar. 2005.
[4] Rustad, A. M., Larsen, C. M., Sorensen, A. J., “Fem Modeling and Automatic Control for Collision Prevention of Top Tensioned Risers”, Journal of Marine Structures, Vol. 21, No. 1, pp. 80-112, Jan. 2008.
[5] API, Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms, 1st Load and Resistance Factor Design, American Petroleum Institute, July 1993.
[6] API, Recommended Practice for Planning Designing and Constructing Fixed Offshore Platform, 20th Working Stress Design, American Petroleum Institute, 2000.
[7] Guo, B, Song, S. Ghalambor, A, Lin, T. and Chacko, J., Offshore Pipelines, 1st Edition, Elsevier, April 2005.
[8] Wilson, J. F., “Dynamics of Offshore Structures”, 2nd edition, John Wiley & Sons, Inc, p. 374, 2003.
[9] Skjelbreia, L. and Hendrickson, J. “Fifth Order Gravity Wave Theory”, 7th Conference on Coastal Engineering, Netherlands, pp. 184-196, 1960.
[10] Emam, S. A., “A Theoretical and Experimental Study of Nonlinear Dynamics of Buckled Beams”, PH.D Thesis, Engineering Mechanics, Virginia Polytechnic Institute and State University, 2002.
[11] Kim, Y. C., “Non-Linear Vibration of Long Slender Beams”, PH.D Thesis, Massachusetts Institute of Technology, Departement of Ocean Engineering, 1983.
[12] Malatkar, P., “Non-Linear Vibrations of Cantilever Beams and Plates”, PH.D Thesis, Engineering Mechanics, Virginia Polytechnic Institute and State University, 2003.
[13] Athisakul, C., “Large-Strain Static Analysis of Marine Risers with a Variational Approach”, 12th International Offshore and Polar Engineering Conference, Vol. 2, pp. 164-170, 2002.
[14] Irani, M. B., Modi, V. J. and Weit, F. “Riser Dynamics with Internal Flow and Nutation Damping”, 6th International Offshore Mechanics and Arctic Engineering Conference, Vol. 3, pp. 119-125, 1987.
[15] Kirk, C. L., “Dynamic and Static Analysis of a Marine Riser”, Applied Ocean Research, Vol. 1, No. 3, pp. 1-8, 1979.
[16] J. Leklong, “Dynamic Responses of Marine Risers/Pipes Transporting Fluid Subject to Top End Excitations”, The International Society of Offshore and Polar Engineer, Vol. 14, No. 12, 2008.
[17] Patel, M. H., “Review of Flexible Riser Modelling and Analysis Techniques, Engineering Structures”, Vol. 17, No. 4, pp. 293-304, 1995.
[18] Zhang, W., Feng, X. W. and Jean, W. Z. , “Local Bifurcations and Codimension-3 Degenerate Bifurcations of a Quintic Nonlinear Beam Under Parametric Excitation”, Journal of Chaos Solitons Fractals, Vol. 24, No. 4, pp. 977–998, Sep. 15, 2005.
[19] Rafieipo, H., Lotfavar, A. and Shalamzari, S. H., “Non-Linear Vibration Analysis of Functionally Graded Beam on Winkler-Pasternak Foundation Under Mechanical and Thermal Loading via Homotopy Analysis Method”, Journal of Mechanics Modares, Vol. 12, pp. 87-101, 2012.
[20] Ahmadian, M. T., Mojahedi, M., “Free Vibration Analysis of a Nonlinear Beam Using Homotopy and Modified Lindstedt-Poincare Methods”, Journal of Solid Mechanic, Vol. 1, pp. 29-36, Mar. 2009.
[21] Pirbodaghi, T., and Ahmadian, M. T., “On the homotopy analysis method for Non-Linear Vibration of Beams”, Mechanics Research Communications, Vol 36, No. 2, pp. 143- 148, 2009.
[22] Sedighi, H. M., Shirazi, K. H. and Zare, J., “An Analytic Solution of Transversal Oscillation of Quantic Non-Linear Beam With Homotopy Analysis Method”, International Journal of Non-Linear Mechanics Vol. 47, pp. 777-784, Apr. 2012.
[23] Rafiee, R., “Analysis of Nonlinear Vibrations of a Carbon Nanotube Using Perturbation Technique”, Journal of Mechanics Modares, Vol. 12, pp. 60-67, 2012.
[24] Xua, M. R., “Determination of Natural Frequencies of Fluid-Conveying Pipes Using Homotopy Perturbation Method, Computers and Mathematics With Applications”, Vol. 60, pp. 520-527, 2010.
[25] Rao, S. S., Mechanical Vibrations, 5th Revised edition, Prentice Hall, p. 1112, 2011.
[26] Nayfeh, A. H., “Introduction to Perturbation Techniques”, 1st edition, Wiley-VCH, p. 536, July 1993.
[27] Nayfeh, A. H. and Mook, D. T. “Non-Linear Oscillations”, John Wiley & Sons, 1979.
[28] Abdelhafez, H. M., “Resonance of a Non-Linear Forced System with Two-Frequency Parametric and Self-Excitations”, Mathematics and Computers in Simulation, Vol. 66, No. 2, pp. 69–83, Mar. 2004.
[29] EL-Bassiouny, A. F., “Principal Parametric Resonances of Non-Linear Mechanical System with Two-Frequency and Self-Excitations”, Mechanics Research Communications, Vol. 32, pp. 337–350, Nov. 2005.
[30] Fengn, Z. H., Zhu, X. D. and Lan, X. J., “Stochastic Jump and Bifurcation of a Slender Cantilever Beam Carrying Alumped Mass Under Narrow-Band Principal Parametric Excitation”, International Journal of Non-Linear Mechanics, Vol. 46, pp. 1330–1340, Jan. 2011.
[31] Ghayesh, M. H. and Khadem, S. E. “Rotary Inertia and Temperature Effects on Non-Linear Non-Linear Vibration, Steady-State Response and Stability of an Axially Moving Beam With Time-Dependent Velocity”, International Journal of Mechanical Sciences, Vol. 50, pp. 389–404, Oct. 28, 2008.
[32] Nayfeh, A. H. and Balachandran, B., “Applied Non-Linear Dynamics Analytical, Computational, and Experimental Methods”, 1 edition Wiley-Vch, p. 704, 2004.
