مطالعه پارامتری پاسخ دینامیکی تیرهای خمیده در صفحه افق تحت تحریک جرم متحرک با در نظر گرفتن مؤلفه لنگر پیچشی

عبدوس, هاتف; فیوضات, محمد علی; خالو, علیرضا

doi:10.22065/jsce.2023.368612.2964

مطالعه پارامتری پاسخ دینامیکی تیرهای خمیده در صفحه افق تحت تحریک جرم متحرک با در نظر گرفتن مؤلفه لنگر پیچشی

نوع مقاله : علمی - پژوهشی

نویسندگان

¹ دانشکده مهندسی عمران، دانشگاه صنعتی شریف، تهران، ایران

² استادیار، دانشکده مهندسی عمران، دانشگاه صنعتی شریف، تهران، ایران

³ استاد، دانشکده مهندسی عمران، دانشگاه صنعتی شریف، تهران، ایران.

10.22065/jsce.2023.368612.2964

چکیده

در این مطالعه، به اثرات ناشی از لنگر پیچشی بر پاسخ دینامیکی خارج از صفحه تیرهای خمیده در صفحه افق و متکی بر بستر ویسکو-الاستیک پرداخته می شود که تحت تحریک جرم متحرک قرار دارند. ابتدا در معادلات تعادل دینامیکی حاکم بر تیرهای خمیده در صفحه افق، اثرات ناشی از اینرسی دورانی، شتاب کوریولیس و نیروی مرکزگر لحاظ شده، و سپس بر اساس روش ماتریس انتقال حل عددی آن ارائه شده است. دقت مدل نیمه تحلیلی این پژوهش بر اساس مطالعات موجود در ادبیات فنی ارزیابی شد که مؤید عملکرد مطلوب آن در برآورد پاسخ دینامیکی خارج از صفحه تیرهای خمیده در صفحه افق است. در بخش مطالعات پارامتری، به چگونگی تأثیر شعاع انحنای تیر و زاویه مرکزی آن، و نیز جرم و سرعت جسم متحرک بر طیف پاسخ جابه جایی خارج از صفحه و لنگر خمشی اشاره شد. با مشاهده طیف پاسخ، در حالت کلی، با افزایش شعاع انحنا و زاویه مرکزی تیر، مقادیر جابه جایی خارج از صفحه و لنگر خمشی حداکثر روند کاهشی داشته است. همچنین، با افزایش جرم و سرعت جسم متحرک، سیستم جابه جایی و لنگر بیشتری را تجربه می کند. در انتها، به منظور تعیین میزان اثرگذاری مؤلفه لنگر پیچشی بر پاسخ دینامیکی سیستم، طیف پاسخ در حالت با و بدون اثر لنگر پیچشی مقایسه شدند که بر اساس مقادیر بررسی شده در این مقاله، به ترتیب حداکثر تا 6 و 5 درصد می تواند بیشینه جابه‌جایی و لنگر خمشی تیرهای خمیده در صفحه افق را افزایش دهد. در نتیجه، در نظر گرفتن لنگر پیچشی می تواند ارزیابی واقع بینانه تری از رفتار دینامیکی سیستم تیرخمیده-جرم متحرک داشته باشد و موجبات تحلیل و طراحی ایمن تری را به همراه آورد.

کلیدواژه‌ها

موضوعات

دینامیک سازه، زلزله و لرزه شناسی

عنوان مقاله [English]

Parametric study on the dynamics of horizontally curved beams due to a moving inertial load considering the induced torsional moment

نویسندگان [English]

Hatef Abdoos ¹
Mohammad Ali Foyouzat ²
Ali Reza Khaloo ³

¹ Department of civil engineering, Sharif University of Technology, Tehran, Iran

² Assistant Professor, Department of civil engineering, Sharif University of Technology, Tehran, Iran

³ Distinguished Professor, Department of civil engineering, Sharif University of Technology, Tehran, Iran.

چکیده [English]

This paper is devoted to investigating the effect of applied torsional moment on the out-of-plane behavior of horizontally curved beams (HCBs) subjected to the excitation induced by a moving mass. As the mass travels along the top surface of HCBs, a torsional moment will be introduced into the system due to the eccentricity of the in-plane centrifugal action with respect to the shear center of the HCB section. The differential equations governing the HCB-moving mass system are first established considering the effect of mass inertia, Coriolis and centrifugal forces, and then numerically solved within the transition matrix approach. Thereafter, a parametric study is conducted to evaluate the influence of radius of curvature and central subtended angle of HCB, as well as the mass and velocity of the moving object. In general, with an increase in the values of radius of curvature and subtended angle of HCBs, a decreasing effect in the response of the system is observed. Moreover, a general magnifying effect is essentially experienced due to an increase in the mass and velocity of the moving object. As the results suggest, the magnifying effect of the induced torsional moment due to the in-plane centrifugal force is at most six percent for the results studied herein. For long-span HCBs, the torsional effect can be deemed as insignificant on the out-of-plane response of HCB-moving mass systems. In conclusion, it is indicated that considering the contribution of the torsional moment can offer a more realistic response estimation regarding the dynamics of HCBs acted upon by a moving inertial load.

کلیدواژه‌ها [English]

Horizontally curved beam
Moving mass
Torsional moment
Dynamic response
Parametric study
Visco-elastic foundation

مراجع

[1] Frýba, L. (1972). Vibration of solids and structures under moving loads.

[2] Ouyang, H. (2011). Moving-load dynamic problems: a tutorial (with a brief overview), Mechanical systems and Signal Processing, 25(6), pp. 2039–2060.

[3] Tan, C. P. and Shore, S. (1968). Response of horizontally curved bridge to moving load, Journal of Structural Devision.

[4] Wang, T. M. and Brannen, W. F. (1982). Natural frequencies for out-of-plane vibrations of curved beams on elastic foundations, Journal of Sound and Vibration, 84, pp. 241–246.

[5] Issa, M. S. (1988). Natural frequencies of continuous curved beams on Winkler-type foundation, Journal of Sound and Vibration, 127(2), pp. 291–301.

[6] Issa, M. S., Nasr, M. E., and Naiem, M. A. (1990). Free vibrations of curved Timoshenko beams on Pasternak foundations, International Journal of Solids and Structures, 26(11), pp. 1243–1252.

[7] Kang, K., Bert, C. W., and Striz, A. G. (1996). Vibration analysis of horizontally curved beams with warping using DQM, Journal of Structural Engineering., 122(6), pp. 657–662.

[8] Huang, D., Wang, T.-L., and Shahawy, M. (1998). Vibration of horizontally curved box girder bridges due to vehicles, Computers and Structures, 68(5), pp. 513–528.

[9] Howson, W. P. and Jemah, A. K. (1999). Exact out-of-plane natural frequencies of curved Timoshenko beams, Journal of Engineering Mechanics, 125(1), pp. 19–25.

[10] Lee, B. K., Mo, J. M., Jin, T. K., and Lee, J. M. (2000). Free Vibrations of Horizontally Curved Beams Resting on Winkler Type Foundation, Computing in Civil and Building Engineering, pp. 74–81.

[11] Yang, Y.-B., Wu, C.-M., and Yau, J.-D. (2001). Dynamic response of a horizontally curved beam subjected to vertical and horizontal moving loads, Journal of Sound and Vibration, 242(3), pp. 519–537.

[12] Shamalta, M. and Metrikine, A. V. (2003). Analytical study of the dynamic response of an embedded railway track to a moving load, Archive of Applied Mechanics, 73(1–2), pp. 131–146.

[13] Wu, J.-S. and Chiang, L.-K. (2003). Out-of-plane responses of a circular curved Timoshenko beam due to a moving load, International Journal of Solids and Structures, 40(26), pp. 7425–7448.

[14] Nallasivam, K., Dutta, A., and Talukdar, S. (2007). Dynamic analysis of horizontally curved thin-walled box-girder bridge due to moving vehicle, Shock and Vibration, 14(3), pp. 229–248.

[15] Khaloo, A. R. and Kafimosavi, M. (2007). Enhancement of flexural design of horizontally curved prestressed bridges, Journal of Bridg Engineering, 12(5), pp. 585–590.

[16] Kim, N.-I., Fu, C. C., and Kim, M.-Y. (2007). Dynamic stiffness matrix of non-symmetric thin-walled curved beam on Winkler and Pasternak type foundations, Advances in Engineering Software, 38(3), pp. 158–171.

[17] Çalım, F. F. and Akkurt, F. G. (2011). Static and free vibration analysis of straight and circular beams on elastic foundation”, Mechanics Research Communications, 38(2), pp. 89–94.

[18] Li, K. F., Liu, W. N., Markine, V., and Han, Z. W. (2013). Analytical study on the dynamic displacement response of a curved track subjected to moving loads, Journal of Zhejiang University SCIENCE A, 14(12), pp. 867–879.

[19] Dai, J. and Ang, K. K. (2015). Steady-state response of a curved beam on a viscously damped foundation subjected to a sequence of moving loads, Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 229(4), pp. 375–394.

[20] Kutlu, A., Ermis, M., Eratlı, N., and Omurtag, M. H. (2017). Forced Vibration of a Planar Curved Beam on Pasternak Foundation, International Journal of Structural and Construction Engineering, 11(7), pp. 981–987.

[21] Du, L., Liu, W., Liu, W., and Ma, L. (2017). Study on dynamic characteristics of a curved track subjected to harmonic moving loads, Procedia Engineering, 199, pp. 2639–2644.

[22] Liu, W., Du, L., Liu, W., and Thompson, D. J., “Dynamic response of a curved railway track subjected to harmonic loads based on the periodic structure theory”, Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit, 232(7), pp. 1932–1950 (2018).

[23] Li, S. H. and Ren, J. Y. (2018). Analytical study on dynamic responses of a curved beam subjected to three-directional moving loads, Applied Mathematical Modelling, 58, pp. 365–387.

[24] Abdoos, H., Khaloo, A. R., and Foyouzat, M. A. (2020). On the out-of-plane dynamic response of horizontally curved beams resting on elastic foundation traversed by a moving mass, Journal of Sound and Vibration, p. 115397.

[25] Luo, J., Zhu, S., and Zhai, W. (2022). Formulation of curved beam vibrations and its extended application to train-track spatial interactions, Mechanical systems and Signal Processing, 165, p. 108393.

[26] Piovan, M. T., Cortinez, V. H., and Rossi, R. E. (2000). Out-of-plane vibrations of shear deformable continuous horizontally curved thin-walled beams, Journal of Sound and Vibration, 237(1), pp. 101–118.

[27] Yau, J.-D., Wu, Y.-S., and Yang, Y.-B. (2001). Impact response of bridges with elastic bearings to moving loads, Journal of Sound and Vibration, 248(1), pp. 9–30.

[28] Yang, Y.-B. and Kuo, S.-R. (1987). Effect of curvature on stability of curved beams, Journal of Structural Engineering, 113(6), pp. 1185–1202.

[29] Cannon, D. F., Edel, K., Grassie, S. L., and Sawley, K. (2003). Rail defects: an overview, Fatigue and Fracture of Engineering materials & Structures, 26(10), pp. 865–886.

[30] Jeong, D. Y. (2003). Correlations between rail defect growth data and engineering analyses, Part II: Field tests.

[31] Foyouzat, M. A., Abdoos, H., Khaloo, A. R., and Mofid, M. (2022). “In-plane vibration analysis of horizontally curved beams resting on visco-elastic foundation subjected to a moving mass”, Mechanical systems and Signal Processing, 172, p. 109013.

[32] Yang, Y.-B., Yau, J. D., Yao, Z., and Wu, Y. S. (2004). Vehicle-Bridge Interaction Dynamics: With Applications to High-Speed Railways, World Scientific.

[33] Foyouzat, M. A., Estekanchi, H. E., and Mofid, M. (2018). An analytical-numerical solution to assess the dynamic response of viscoelastic plates to a moving mass, Applied Mathematical Modelling, 54, pp. 670–696.

[34] Hirzinger, B., Adam, C., and Salcher, P. (2020). Dynamic response of a non-classically damped beam with general boundary conditions subjected to a moving mass-spring-damper system, International Journal of Mechanical Sciences, 185, p. 105877.

[35] Moradi, S., Azam, S. E., and Mofid, M. (2021). On Bayesian active vibration control of structures subjected to moving inertial loads, Engineering Structures, 239, p. 112313.

[36] Azam, S. E., Didyk, M. M., Linzell, D., and Rageh, A. (2022). Experimental validation and numerical investigation of virtual strain sensing methods for steel railway bridges, Journal of Sound and Vibration, 537, p. 117207.

[37] Alile, M. R., Foyouzat, M. A., and Mofid, M. (2022). Vibration of a Circular plate on Pasternak foundation with variable modulus due to moving mass, Structural Engineering and Mechanics, 83, pp. 757-770.

[38] Khaloo, A. R., Foyouzat, M. A., Abdoos, H., and Mofid, M. (2023). Axial force contribution to the out-of-plane response of horizontally curved beams under a moving mass excitation. Applied Mathematical Modelling, 115, pp. 148–172.

[39] Brogan, W. L. (1991). Modern Control Theory, Pearson education india.

[40] Foyouzat, M. A. (2023). Separation/recontact investigation of a travelling oscillator over a plate with inclusion of surface roughness, Thin-Walled Structures, 183, p. 110373.

[41] Vitez, I., Krumes, D., and Vitez, B. (2005). UIC-recommendations for the use of rail steel grades, Metalurgija, 44(2), pp. 137–140.

[42] Square, E., & Dingwall, P. (1998). Track Standards Manual - Section 8: Track Geometry.

[43] Division, T. P. (2009). MOD UK Railways Permanent Way Design and Maintenance Policy and Standards Issue 4, (4).

[44] Barboteo, J. (2011). The sustainable freight railway : Designing the freight vehicle – track system for higher delivered tonnage with improved availability at reduced cost OVERVIEW OF COMMON FREIGHT WAGON VEHICLES, pp. 1–30.

[45] Zarfam, R. and Khaloo, A. R. (2012). Vibration control of beams on elastic foundation under a moving vehicle and random lateral excitations, Journal of Sound and Vibration, 331(6), pp. 1217–1232.