In this study, the influence of geometrical
parameters on the curve veering phenomenon in a tor-sional system with stepped
shaft is investigated. Three approximate solutions including finite el-ement,
Rayleigh-Ritz and discretization methods, along with an exact solution are
employed to obtain the natural frequencies of the structure. The study reveals
that, under specific circumstances, the results obtained by approximate methods
are very close to the exact solution. The curve veering behavior is manifested
irrespective of the method employed. It is concluded that for the structure
studied the curve veering behavior is not because of the approximate techniques
used to compute the natural frequencies, and is an inherent behavior of the
structure.
References
[1]
Bhat, R.B. (1954) Curve Veering Behavior of Some Vibrating Systems. Shock and Vibration, 7, 241-249. http://dx.doi.org/10.1155/2000/841538
[2]
Warburton, G.B. (1974) The Vibration of Rectangular Plates. Shock and Vibration, 8, 371-384.
[3]
Leissa, A.W. (1974) On a Curve Veering Aberration. Journal of Applied Mathematics and Physics (ZAMP), 25, 99-110.
[4]
Schajer, G.S. (1984) The Vibration of a Rotating Circular String Subject to Fixed Elastic Restraint. Journal of Sound and Vibration, 92, 11-19. http://dx.doi.org/10.1016/0022-460X(84)90369-9
[5]
Wang, J.T.S., Shaw, D. and Mahrenholtz, O. (1987) Vibration of Rotating Rectangular Plates. Journal of Sound and Vibration, 112, 455-468. http://dx.doi.org/10.1016/S0022-460X(87)80111-6
[6]
Rao, C.K. (1989) Frequency Analysis of Clamped-Clamped Uniform Beam with Intermediate Elastic Supports. Journal of Sound and Vibration, 133, 502-509. http://dx.doi.org/10.1016/0022-460X(89)90615-9
[7]
Pierre, C. (1988) Mode Localization and Eigenvalue Loci Veering Phenomena in Disordered Structures. Journal of Sound and Vibration, 126, 485-502. http://dx.doi.org/10.1016/0022-460X(88)90226-X
[8]
Breslavsky, I., Avramov, K.V., Mikhlin, Y. and Kochurov, R. (2008) Nonlinear Modes of Snap-Through Motions of a Shallow Arch. Journal of Sound and Vibration, 311, 297-313. http://dx.doi.org/10.1016/j.jsv.2007.09.015
[9]
Chan, H.C. and Liu, J.K. (2000) Mode Localization and Frequency Loci Veering in Disordered Engineering Structures. Chaos, Solitons and Fractals, 11, 1493-1504. http://dx.doi.org/10.1016/S0960-0779(99)00073-9
[10]
Bois, J.L.D., Adhikari, S. and Lieven, N.A.J. (2011) On the Quantification of Eigenvalue Curve Veering: A Veering Index. Journal of Applied Mechanics, 78, 041007-1-041007-8.
[11]
Saito, A., Castanier, M.P. and Pierre, C. (2009) Estimation and Veering Analysis of Nonlinear Resonant Frequencies of Cracked Plates. Journal of Sound and Vibration, 326, 725-739. http://dx.doi.org/10.1016/j.jsv.2009.05.009
[12]
Lacarbonara, W., Arafat, H. and Nayfeh, A.H. (2005) Large Non-Linear Interactions in Imperfect Beams at Veering. International Journal of Non-Linear Mechanics, 40, 987-1003. http://dx.doi.org/10.1016/j.ijnonlinmec.2004.10.006
[13]
Vidoli, S. and Vestroni, F. (2005) Veering Phenomena in Systems with Gyroscopic Coupling. Journal of Applied Mechanics, 72, 641-647. http://dx.doi.org/10.1115/1.1940666
[14]
Chen, J.S. and Li, Y.-T. (2006) Effects of Elastic Foundation on the Snap-Through Buckling of a Shallow Arch under a Moving Point Load. International Journal of Solids and Structures, 43, 4220-4237. http://dx.doi.org/10.1016/j.ijsolstr.2005.04.040
[15]
Al-Qaisia, A.A. and Hamdan, M.N. (2013) On Nonlinear Frequency Veering and Mode Localization of a Beam with Geometric Imperfection Resting on Elastic Foundation. Journal of Sound and Vibration, 332, 4641-4655. http://dx.doi.org/10.1016/j.jsv.2013.03.031
[16]
Beddoe, B. (1965) Wave Theory of Free Torsional Vibration of Composite Systems of Shafts. Journal of Mechanical Engineering Science, 7, 48-56. http://dx.doi.org/10.1243/JMES_JOUR_1965_007_010_02
[17]
Maltbaek, J.C. (1962) Influence of a Discrete Inertia on the Free Torsional Vibrations of a Uniform Bar. International Journal of Mechanical Sciences, 4, 24-34. http://dx.doi.org/10.1016/0020-7403(62)90004-8
[18]
Maltbaek, J.C. (1967) Torsional Vibration of a Stepped Shaft. Engineer, 223, 972-974.
[19]
Rao, D.K. (1978) Torsional Frequencies of a Multi-Stepped Shaft with Rotors. International Journal of Mechanical Sciences, 20, 415-422. http://dx.doi.org/10.1016/0020-7403(78)90031-0
Leissa, A.W. and So, J.Y. (1995) Comparisons of Vibration Frequencies for Rods and Beams from One-Dimensional and Three-Dimensional Analysis. Journal of Acoustic Society, 98, 2122-2135. http://dx.doi.org/10.1121/1.414331
[22]
Thomson, W.T. and Dahleh, M.D. (1997) Theory of Vibrations with Applications. 5th Edition, Prentice Hall, Upper Saddle River.
[23]
Bhat, R.B. (1985) Natural Frequencies of Rectangular Plates Using Characteristic Orthogonal Polynomials in Rayleigh-Ritz Method. Journal of Sound and Vibration, 102, 493-499. http://dx.doi.org/10.1016/S0022-460X(85)80109-7
