On the dynamic stability of a flying vehicle under the follower and transversal forces

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

Omid  Kavianipour ¹ (Young Researchers and Elite Club, Damavand Branch, Islamic Azad University, Damavand, Iran)
Majid  Sohrabian ² (Department of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran)

Received: 2017-07-07 Accepted : 2017-10-14 Published : 2017-11-19

Keywords:

Abstract :

This paper deals with the problem of the instability regions of a free-free uniform Bernoulli beam consisting of two concentrated masses at the two free ends under the follower and transversal forces as a model for a space structure. The follower force is the model for the propulsion force and the transversal force is the controller force. The main aim of this study is to analyze the effects of the concentrated masses on the beam instability. It is determined that the transverse and rotary inertia of the concentrated masses cause a change in the critical follower force. This paper also offers an approximation method as a design tool to find the optimal masses at the two tips using an artificial neural network (ANN) and genetic algorithm (GA). The results show that an increase in the follower and transversal forces leads to an increase of the vibrational motion of the beam which is not desirable for any control system and hence it must be removed by proper approaches.

References:

[1]	Ryu S-U, Sugiyama Y. Computational dynamics approach to the effect of damping on stability of a cantilevered column subjected to a follower force. Computers and Structures. 2003; 81(4): 265-271.
[2]	Detinko FM. Lumped damping and stability of Beck column with a tip mass. International Journal of Solids and Structures. 2003; 40(17): 4479-4486.
[3]	Di Egidio A, Luongo A, Paolone A. Linear and non-linear interactions between static and dynamic bifurcations of damped planar beams. International Journal of Non-Linear Mechanics. 2007; 42(1): 88-98.
[4]	Lee J-S, Kim N-II, Kim M-Y. Sub-tangentially loaded and damped Beck’s columns on two-parameter elastic foundation. Journal of Sound and Vibration. 2007; 306(3-5): 766-789.
[5]	Sugiyama Y, Langthjem MA. Physical mechanism of the destabilizing effect of damping in continuous non-conservative dissipative systems. International Journal of Non-Linear Mechanics. 2007; 42(1): 132-145.
[6]	Tomski L, Szmidla J, Uzny S. The local and global instability and vibration of systems subjected to non-conservative loading. Thin-Walled Structures. 2007; 45(10-11): 945-949.
[7]	Shvartsman BS. Large deflections of a cantilever beam subjected to a follower force. Journal of Sound and Vibration. 2007; 304(3-5): 969-973.
[8]	Katsikadelis JT, Tsiatas GC. Optimum design of structures subjected to follower forces. International Journal of Mechanical Sciences. 2007; 49(11): 1204-1212.
[9]	De Rosa MA, Auciello NM, Lippiello M. Dynamic stability analysis and DQM for beams with variable cross-section. Mechanics Research Communications. 2008; 35(3): 187-192.
[10]	Djondjorov PA, Vassilev VM. On the dynamic stability of a cantilever under tangential follower force according to Timoshenko beam theory. Journal of Sound and Vibration. 2008; 311(3-5): 1431-1437.
[11]	Attard MM, Lee J-S, Kim M-Y. Dynamic stability of shear-flexible beck’s columns based on Engesser’s and Haringx’s buckling theories. Computers and Structures. 2008; 86(21-22): 2042-2055.
[12]	Marzani A, Tornabene F, Viola E. Nonconservative stability problems via generalized differential quadrature method. Journal of Sound and Vibration. 2008; 315(1-2): 176-196.
[13]	Pirmoradian M. Dynamic stability analysis of a beam excited by a sequence of moving mass particles. Journal of Solid Mechanics in Engineering. 2015; 8(1): 41-49.
[14]	Beal TR. Dynamic stability of a flexible missile under constant and pulsating thrusts. AIAA Journal. 1965; 3(3): 486-494.
[15]	Wu JJ. On the stability of a free-free beam under axial thrust subjected to directional control. Journal of Sound and Vibration. 1975; 43(1): 45-52.
[16]	Park YP, Mote CD. The maximum controlled follower force on a free-free beam carrying a concentrated mass. Journal of Sound and Vibration. 1984; 98(22): 247-256.
[17]	Park YP. Dynamic stability of a free Timoshenko beam under a controlled follower force. Journal of Sound and Vibration. 1987; 113(3): 407-415.
[18]	Sato K. On the governing equation for vibrating and stability of a Timoshenko beam: Hamilton's Principle. Journal of Sound and Vibration. 1991; 145(2): 338-340.
[19]	Mladenov KA, Sugiyama Y. Stability of a jointed free-free beam under end rocket thrust. Journal of Sound and Vibration. 1997; 199(1): 1-15.
[20]	Kim JH, Choo YS. Dynamic stability of a free-free Timoshenko beam subjected to a pulsating follower force. Journal of Sound and Vibration. 1998; 216(4): 623-636.
[21]	Kim KH, Kim JH. Effect of Crack on the Dynamic Stability of a Free-Free Beam Subjected to a Follower Force.  Journal of Sound and Vibration.  2000; 233(1): 119-135.
[22]	Wang Q. A comprehensive stability analysis of a cracked beam subjected to follower compression. International Journal of Solids and Structures.  2004; 41(18-19): 4875-4888.
[23]	Caddemi S, Caliò I, Cannizzaro F. Flutter and divergence instability of the multi-cracked cantilever beam-column. Journal of Sound and Vibration. 2014; 333(6): 1718-1733.
[24]	Sohrabian M, Ahmadian H, Fathi R. Flutter Instability of Timoshenko Cantilever Beam Carrying Concentrated Mass on Various Locations. Latin American Journal of Solids and Structures. 2016; 13(16): 3005-3021.
[25]	Irani S, Kavianipour O. Effects of a flexible joint on instability of a free-free jointed bipartite beam under the follower and transversal forces. Journal of Zhejiang University SCIENCE A. 2009; 10(9): 1252-1262.
[26]	Kavianipour O, Sadati SH. Effects of damping on the linear stability of a free-free beam subjected to follower and transversal forces. Structural Engineering and Mechanics. 2009, 33(6): 709-724.
[27]	Kavianipour O, Khoshnood AM, Sadati SH. Reduction of the actuator oscillations in the flying vehicle under a follower force. Structural Engineering and Mechanics. 2013; 47(2): 149-166.
[28]	Meirovitch L. Principles and Techniques of Vibrations. Prentice-Hall International, Inc., New Jersey, 1997.
[29]	Hodges DH, Pierce GA. Introduction to Structural Dynamics and Aeroelasticity. The Press Syndicate of The University of Cambridge, Cambridge, 2002.
[30]	Craig RR, Kurdila AJ. Fundamentals of Structural Dynamics. 2nd edn John Wiley & Sons, Inc., New Jersey, 2006.