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Abstract

The dynamic stability of a uniform cantilever column under a tip-concentrated subtangential follower force is examined. The governing two-point boundary value problem is converted to an initial value problem. A simple numerical iterative scheme is followed to generate a load versus frequency curve (eigencurve) in order to study the critical and post-critical behavior of the columns subjected to a tip-concentrated follower force. For the load rotation parameter greater than $\frac{1}{2}$ , the coalesce frequency and the corresponding critical load are obtained. The deformed configurations of cantilever columns are generated for different load rotation parameters. The details of the critical load parameter, tip angle and tip coordinates of the columns for the specified load rotation parameter are presented. The critical load parameter increases with the load rotation parameter.

Keywords

Cantilever column large deflections tip-concentrated load tip angle subtangential parameter

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References

Timoshenko

Gere

. Theory of elastic stability. New York: McGraw-Hill, 1961.

Bolotin

. Nonconservative problems of the theory of elastic stability. New York: Pergamon Press, 1963.

Ziegler

. Principles of structural stability. Toronto, ON: Blaisdell Publication Co., 1968.

Nageswara Rao

Venkateswara Rao

. Some studies on buckling and post-buckling of cantilever columns subjected to conservative or nonconservative loads. J Aeronaut Soc India 1989; 41: 165–181.

Nageswara Rao

Venkateswara Rao

. Post-critical behaviour of a tapered cantilever column subjected to a tip-concentrated follower force. Z Angew Math Mech 1991; 71: 471–473.

Zakharov

YuV

Okhotkin

Skorobogatov

. Bending of bars under a follower load. J Appl Mech Tech Phys 2004; 45: 756–763.

Langthjem

Sugiyama

. Dynamic stability of columns subjected to follower loads: a survey. J Sound Vib 2000; 238: 809–851.

Elishakoff

. Controversy associated with the so-called ‘Follower Forces’: Critical overview. Appl Mech Rev 2005; 58: 117–142.

Kikuchi

. A finite element method for non-self adjoint problems. Int J Numer Meth Eng 1973; 6: 39–54.

10.

Vitaliani

Gasparini

Saetta

. Finite element solution of the stability problem for nonlinear undamped and damped systems under nonconservative loading. Int J Solid Struct 1997; 34: 2497–2516.

11.

Langthjem

Sugiyama

. Optimum design of cantilevered columns under the combined action of conservative and nonconservative loads. Part I. The undamped case. Comput Struct 2000; 74: 385–398.

12.

Anderson

Thomsen

. Post-critical behaviour of Beck’s column with a tip mass. Int J Nonlinear Mech 2002; 37: 135–151.

13.

Kwasniewski

. Numerical verification of post-critical Beck’s column behavior. Int J Nonlinear Mech 2010; 45: 242–255.

14.

Navaee

Elling

. Equilibrium configurations of cantilever beams subjected to inclined end loads. Trans ASME J Appl Mech 1992; 59: 572–579.

15.

Navaee

Elling

. Possible ranges of end slope for cantilever beams. ASCE J Eng Mech 1993; 119: 630–635.

16.

Raboud

Lipsett

Faulkner

. Stability evaluation of very flexible cantilever beams. Int J Nonlinear Mech 2001; 36: 1109–1122.

17.

Batista

Kosel

. Cantilever beam equilibrium configurations. Int J Solid Struct 2005; 42: 4663–4672.

18.

Mutyalarao

Bharathi

Nageswara Rao

. On the uniqueness of large deflections of a uniform cantilever beam under a tip-concentrated rotational load. Int J Nonlinear Mech 2010; 45: 433–441.

19.

Mutyalarao

Bharathi

Nageswara Rao

. Large deflections of a cantilever beam under an inclined end load. Appl Math Comput 2010; 217: 3607–3613.

Dynamic stability of cantilever columns under a tip-concentrated subtangential follower force

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