تحلیل پایداری دینامیکی ارتعاشات عرضی تیر تحت عبور متوالی جرم-های متحرک

Subject Areas : Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering

مصطفی پیرمرادیان ¹

1 - 1- استادیار دانشکده مهندسی مکانیک، دانشگاه آزاد اسلامی، واحد خمینی شهر

Received: 2015-12-28 Accepted : 2015-12-28 Published : 2015-02-01

Keywords: پایداری دینامیکی, مسأله‌ی تیر-جرم متحرک, روش هارمونیک بالانس نموی, تئوری فلاکه,

Abstract :

در این مقاله تحلیل پایداری دینامیکی تیری با تکیه­گاه ساده که تحت عبور متوالی جرم­ها قرار گرفته است بررسی می­شود. چنین شرایط بارگذاری روی تیر در تحلیل مسائلی از قبیل حرکت وسائل نقلیه و قطارها از روی پل­ها، جراثقیل­های حمل بار، لوله­له­های حاوی سیال، لوله­ی انواع اسلحه­ها حایز اهمیت است. بر اثر عبور مداوم و پریودیک جرم­ها از روی تیر، یک مسأله­ی خطی پریودیک حاصل می­شود. تئوری فلاکه و روش هارمونیک بالانس نموی برای به دست آوردن مرز پایدار و ناپایدار مسأله بر حسب پارامترهای جرم­های عبوری مورد استفاده قرار می­گیرند. منحنی مشخص کننده­ی نواحی پایدار و ناپایدار حاصل شده با استفاده از بکارگیری این دو روش به خوبی با یکدیگر مطابقت داشته و شبیه­سازیهای عددی برای مقادیر عددی پارامترهای انتخابی جرم متحرک، صحت و دقت روش­های مذکور را تأیید می­کند.

References:

[1].   Willis, R., “Report of the Commissioners Appointed to inquire into the application of iron to railway structures”, Appendix B, Stationery Office, London, England, 1849.

[2].   Stokes, G.G., Sir, Discussion of a differential equation relating to the breaking of railway bridges, Mathematical and physical papers, 2^nd edition, reprinted 1966, originally printed as Transactions of Cambridge Philosophical Society, 1849.

[3].   Ayre, R.S., Jacobson, L.S., and Hsu, C.S., Transverse vibration of one and two span beams under the action of a moving mass load, Proceedings of the First U.S. National Congress on Applied Mechanics, 1952,pp. 81-90.

[4].   Inglis, C.E., “A mathematical treatise on vibrations in railway bridges”, Cambridge University Press, London, 1934.

[5].   Hillerborg, A., “Dynamic influences of smoothly running loads on simply supported girders”, Inst. of Structural Engineering and Bridge Building of the Royal Inst. of Technology, Stockholm, 1951.

[6].   Fryba, L., “Vibration of solids and structures under moving loads”, Thomas Telford Ltd., Third Edition, 1999.

[7].   Yang, Y. B., Yau, J. D. and Wu, Y. S., “Vehicle bridge interaction dynamics: with applications to high speed railways”, World Scientific Publishing Company, 2004.

[8].   Mackertich, S., Response of a beam to a moving mass”, Journal of the Acoustical Society of America, vol. 92, No. 3, 1992, pp. 1766-1769.

[9].   Gbadeyan, J. A., and Oni, S. T., “Dynamic behaviour of beams and rectangular plates under moving loads”, Journal of Sound and Vibration, vol. 182, No. 5,1995, pp.677-695.

[10].            Esmailzadeh, E. and Ghorashi, M., “Vibration analysis of a Timoshenko beam subjected to a travelling mass”, Journal of Sound and Vibration, vol. 199, No. 4, 1997, pp. 615- 628.

[11].            Foda, M.A., and Abduljabbar, Z., A dynamic green function for the response of a beam structure to a moving mass, Journal of Sound and Vibration, vol. 210, 1998, pp. 295-306.

[12].            Michaltsos, G.T. and Sophianopoulos, D., and Kounadis, A.N., The effect of moving mass and other parameters on the dynamic response of a simply supported beam”. Journal of Sound and Vibration, vol. 191, 1996, pp. 357-362.

[13].            Michaltsos ,G.T. and Kounadis, A.N., The effects of Centripetal and Coriolis forces on the dynamic response of light bridges under moving loads, Journal of Vibration and Control, vol. 7, 2001, pp.315-326.

[14].            Wu, J.J., Dynamic analysis of an inclined beam due to moving loads, Journal of Sound and Vibration,vol. 288, 2005, pp. 107-131.

 

[15].            Rao, V.G., Linear dynamics of an elastic beam under moving loads, Journal of Vibration and Acoustics,vol. 122, 2000, pp. 281-289.

[16].            Siddiqui, S.A.Q. and Golnaraghi, M.F. and Heppler, G.R., Dynamics of a flexible beam carrying a moving mass using perturbation, numerical and time frequency analysis techniques, Journal of Sound and Vibration, vol. 229, No. 5, 2000, pp. 1023-1055.

[17].            Mamandi, A. and Kargarnovin, M.H., and Farsi, S., An investigation on effects of traveling mass with variable velocity on nonlinear dynamic response of an inclined Timoshenko beam with different boundary conditions, International Journal of Mechanical Sciences, vol. 52, 2010, pp. 1694-1708.

[18].            Nikkhoo, A. and Rofooei, F.R., and Shadnam, M.R., Dynamic behavior and modal control of beams under moving mas”, Journal of Sound and Vibration, vol. 306, 2007, pp. 712- 724.

[19].            Yau, D.T.W. and Fung, E.H.K., Dynamic response of a rotating flexible arm carrying a moving mass, Journal of Sound and Vibration, vol. 257, No. 1, 2002, pp. 107-117.

[20].            Nayyeri Amiri, S., and Onyango M., Simply supported beam response on elastic foundation carrying repeated rolling concentrated loads, Journal of Engineering Science and Technology, vol. 5, No.1, 2010, pp. 52- 66.

[21].            Eftekhari, S.A. and Jafari, A.A., Coupling Ritz method and triangular quadrature rule for moving mass  problem, Journal of Applied Mechanics, vol. 79, issue 2, 2012, pp. 021018.

[22].            Nelson, H.D., and Conover, R.A., Dynamic stability of a beam carrying moving masses, Journal of Applied Mechanics, 38, Series E, 1971, pp. 1003-1006.

[23].            Benedetti, G.A., Dynamic stability of a beam loaded by a sequence of moving mass particles, Journal of Applied Mechanics, vol. 41, 1974, pp. 1069-1071.

[24].            Katz, R., Lee C.W., Ulsoy, A.G., and Scott, R.A., Dynamic stability and response of a beam subjected to a deflection dependent moving load, Journal of Vibration, Acoustics, Stress, and Reliability in Design, vol. 109, 1987, pp. 361-365.

[25].            Mackertich, S., Dynamic stability of a beam excited by a sequence of moving mass particles, Acoustical Society of America,2004, pp. 1416-1419.

[26].            Aldraihem, O.J., and Baz, A., Dynamic stability of stepped beams under moving loads, Journal of Sound and Vibration, vol. 250, No. 5, 2002, pp. 835-848.

[27].            Verichev, S.N., and Metrikine, A.V., Instability of vibrations of mass that moves uniformly along a beam on a periodically inhomogeneous foundation, Journal of Sound and Vibration, vol. 260, 2003, pp. 901-925.

[28].            Verichev, S.N., and Metrikine, A.V., Instability of a bogie moving on flexibly supported Timoshenko beam, Journal of Sound and Vibration, vol. 253, No. 3, pp. 635-668, 2002.