Home / Regular Issue / JST Vol. 30 (1) Jan. 2022 / JST-2976-2021

 

Reinvestigation on Assessing the Stability of Mullagulov Tested Steel Rods under Follower Forces

Jakkana Peter Praveen and Boggarapu Nageswara Rao

Pertanika Journal of Science & Technology, Volume 30, Issue 1, January 2022

DOI: https://doi.org/10.47836/pjst.30.1.44

Keywords: Beck column, coalescence frequency parameter, concentrated tangential load, critical load parameter

Published on: 10 January 2022

Dynamic instability is an interesting topic in the mechanics of elastic structures. Though the subject has been formed by many analytical, numerical, and experimental investigations, it has many issues, as evidenced from the critical overview of Elishakoff. Furthermore, the controversial articles of Koiter and Sugiyama on unrealistic and realistic follower forces demand experimental verification. Mullagulov has proposed a device for creating the follower forces and tested steel rods under compression. This paper highlights the experimentation of Mullagulov and his observations briefly to examine the influence of material properties on the stability load estimations and to confirm the practical realization of follower forces.

  • Anderson, S. B., & Thomsen, J. J. (2002). Post-critical behavior of Beck’s column with a tip mass. International Journal of Nonlinear Mechanics, 37,135-151. https://doi.org/10.1016/S0020-7462(00)00102-5

  • Augusti, G., Roorda, J., Herrmann, G., & Levinson, M. (1967). Discussion: Experimental verification of the dynamic stability of a tangentially cantilever column. Transactions of ASME Journal of Applied Mechanics, 34, 523-524. https://doi.org/10.1115/1.3607727

  • Beck, M. (1952). Die Knicklast des einseitig eingespannten, tangential gedrückten Stabes [The buckling load of the cantilevered, tangentially pressed bar]. Zeitschrift für angewandte Mathematik und Physik ZAMP, 3(3), 225-228. https://doi.org/10.1007/BF02008828

  • Huang, N. C., Nachabar, W., & Nemat-Nasser, S. (1967). On Willems experimental verification of the critical load in Beck’s problem. Transactions of ASME Journal of Applied Mechanics, 34, 243-245. https://doi.org/10.1115/1.3607646

  • Koiter, W. T. (1996). Unrealistic follower forces. Journal of Sound and Vibration, 194(4), 636-638. https://doi.org/10.1006/jsvi.1996.0383

  • Kwasniewski, L. (2010). Numerical verification of post-critical Beck’s column behavior. International Journal of Nonlinear Mechanics, 45, 242-255. https://doi.org/10.1016/j.ijnonlinmec.2009.11.007

  • Langthjem, M. A., & Sugiyama, Y. (2000a). Optimum design of cantilevered columns under the combined action of conservative and non-conservative loads, Part-I: The undamped case. Computers and Structures, 74, 385-398. https://doi.org/10.1016/S0045-7949(99)00050-4

  • Langthjem, M. A., & Sugiyama, Y. (2000b). Dynamic stability of columns subjected to follower loads: A survey. Journal of Sound and Vibration, 238, 809-851. https://doi.org/10.1006/jsvi.2000.3137

  • Sugiyama, Y., Langthjem, M. A., & Ryu, B. J. (1999). Realistic follower forces. Journal of Sound and Vibration, 225, 779-782. https://doi.org/10.1006/jsvi.1998.2290

  • Madhusudan, B. P., Rajeev, V. R., & Rao, B. N. (2003). Post-buckling of cantilever columns having variable cross-section under a combined load. International Journal of Non-linear Mechanics, 38, 1513-1522. https://doi.org/10.1016/S0020-7462(02)00086-0

  • Mascolo, I. (2019). Recent developments in the dynamic stability of elastic structures. Frontiers in Applied Mathematics and Statistics, 5, Article 516. https://doi.org/10.3389/fams.2019.00051

  • Mirko, T. (2018). Flutter instability in structural mechanics: Theory and experimental evidence (PhD thesis). University of Trento, Italy.

  • Mullagulov, M. K. (1994). Experimental-theoretical study of the stability of rods, compressed by follower forces. Strength of Materials, 26(6), 441-446. https://doi.org/10.1007/BF02209415

  • Mutyalarao, M., Bharathi, D., & Rao, B. N. (2012). Dynamic stability of cantilever columns under a tip-concentrated sub tangential follower force. Mathematics and Mechanics of Solids, 18(5), 449-463. https://doi.org/10.1177/1081286512442436

  • Mutyalarao, M., Bharathi, D., Narayana, K. L., & Rao, B. N. (2017). How valid are Sugiyama’s experiments on follower forces? International Journal of Non-linear Mechanics, 93, 122-125. https://doi.org/10.1016/j.ijnonlinmec.2014.12.007

  • Praveen, J. P., Rao, B. N., Harnath, Y., Rao, B. V., Narayana, C., & Mahaboob, B. (2021). Revisited the critical load assessment of Huang et al. on the Willems tested Beck column. Pertanika Journal of Science and Technology, 29(1), 251-262. https://doi.org/10.47836/pjst.29.1.14

  • Praveen, J. P., Rao, B. N., Mahaboob, B., Rajaiah, M., Harnath, Y., & Narayana, C. (2020). On the simulation of Beck column through a simple Xiong-Wang-Tabarrok experimental model of centripetally loaded column. International Journal of Emerging Trends in Engineering Research, 8(9), 5100-5103. https://doi.org/10.30534/ijeter/2020/35892020

  • Rao, B. N., & Rao, G.V. (1989a). Post-critical behaviour of a uniform cantilever column under a tip concentrated follower force. Journal of Sound and Vibration, 132,350-352. https://doi.org/10.1016/0022-460X(89)90604-4

  • Rao, B. N., & Rao, G. V. (1989b). Some studies on buckling and post- buckling of cantilever columns subjected to conservative or non conservative loads. The Journal of the Aeronautical Society of India, 41(2), 165-182.

  • Rao, B. N., & Rao, G. V. (1990). Stability of tapered cantilever columns subjected to a tip concentrated sub tangential follower force. Forschung Im Ingenieurwesen, 56(3), 93-96. https://doi.org/10.1007/BF02560974

  • Rao, B. N., & Rao, G. V. (1991). Post-critical behaviour of a tapered cantilever column subjected to a tip concentrated follower force. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 71(11), 471-473. https://doi.org/10.1002/zamm.19910711116

  • Sugiyama, Y. (2002). Experimental approach to non-conservative stability problems. In A. P. Seyranian & I. Elishakoff (Eds.), Modern Problems of Structural Stability (pp. 341-394). Springer. https://doi.org/10.1007/978-3-7091-2560-1_7

  • Sugiyama, Y., Katayama, K., & Kiriyama, K. (2000). Experimental verification of dynamic stability of vertical cantilever columns subjected to a sub tangential force. Journal of Sound and Vibration, 236(2), 193-207. https://doi.org/10.1006/jsvi.1999.2969

  • Sugiyama, Y., Langthjem, M. A., & Katayama, K. (2019). Dynamic stability of columns under non-conservative forces: Theory and experiments. Springer International Publishing. https://doi.org/10.1007/978-3-030-00572-6_2

  • Timoshenko, S. P., & Gere, J. M. (2012). Theory of elastic stability. Tata McGraw-Hill Education Private Limited.

  • Tomski, L., & Uzny, S. (2008). Free vibration and the stability of a geometrically nonlinear column loaded by a follower force directed towards the positive pole. International Journal of Solids and Structures, 45(1), 87-112. https://doi.org/10.1016/j.ijsolstr.2007.07.011

  • Willems, N. (1966). Experimental verification of the dynamic stability of a tangentially loaded cantilever column. Transactions of ASME Journal of Applied Mechanics, 33, 460-461. https://doi.org/10.1115/1.3625073

  • Xiong, Y., Wang, T. K., & Tabarrok, B. (1989). On a centripetally loaded model simulating Beck’s column. International Journal of Solids and Structures, 25(10), 1107-1113. https://doi.org/10.1016/0020-7683(89)90070-X

  • Zahharov, Y. V., Okhotkin, K. G., & Skorobogatov, A. D. (2004). Bending of bars under a follower load. Journal of Applied Mechanics and Technical Physics, 45, 756-763. https://doi.org/10.1023/B:JAMT.0000037975.91152.01

ISSN 0128-7680

e-ISSN 2231-8526

Article ID

JST-2976-2021

Download Full Article PDF

Share this article

Recent Articles