Sage Journals: Discover world-class research

Abstract

The subharmonic wave solutions of axially travelling, prebuckled and post-buckled plates are developed analytically, and the conditions for resonant and stationary waves are presented. From this investigation, the plate buckling caused by translation motion and compressive loading is different, and the local buckling motion for travelling plates cannot be obtained. The small motion of travelling buckled plates will jump to large motion with increasing translation speed. The phenomena can be observed in axially travelling shell structures. The prediction of resonant and stationary waves in travelling structures is useful for experimental measurement, observation and structural design. In addition, the procedure presented in this paper is applicable for investigation of non-linear structural vibrations.

Keywords

resonant wave stationary wave travelling plates non-linear vibration

Get full access to this article

View all access options for this article.

References

Mote

C. D.

A study of band saw vibrations

J. Franklin Inst., 1965, 279, 430–444.

Wang

Numerical analysis of moving orthotropic thin plates

Computer and Struct., 1999, 70, 467–486.

Luo

Hutton

S. G.

Formulation of a three-node traveling triangle plate element subjected to gyroscopic and in-plane forces

Computer and Struct., 2002, 80, 1935–1944.

von Karman

Festigkeitsprobleme im mashinenbau

Encyklopadie der Mathematischen Wissenschaften, 1910, 4 (4), 348-352 (Teubner, Leipzig).

Levy

Large deflection theory for rectangular plate. Proceedings of 1st Symposium on Applied Mathematics, 1942, Vol. 1, pp. 197–210.

Chia

C. Y.

Nonlinear Analysis of Plates, 1980 (McGraw-Hill, New York).

Shen

H. S.

Thermomechanical post-buckling analysis of imperfect laminated plates using a higher-order shear-deformation theory

Computers and Struct., 1998, 66 (4), 395–409.

Herrmann

Influence of large amplitudes on flexural motions of elastic plates. NACA technical note 3578, 1955.

Luo

A. C. J.

An approximate theory for geometrically nonlinear thin plates

Int. J. Solids and Struct., 2000, 37, 7655–7670.

10.

Lamb

Southwell

R. V.

The vibration of a spinning disc

Proc. Roy. Soc. (Lond.), 1921, 99, 272–280.

11.

Campbell

The protection of steam-turbine disk wheel from axial vibration

Trans. Am. Soc. Mech. Engrs, 1924, 46, 33–160.

12.

von Freudenreich

Vibration of steam turbine discs

J. Engng, 1925, 119, 31–34.

13.

Tobias

S. A.

Arnold

R. N.

The influence of dynamical imperfection on the vibration of rotating discs

Proc. Instn Mech. Engrs, 1957, 171, 669–690.

14.

Advani

S. H.

Stationary waves in a thin spinning disc

Int. J. Mech. Sci., 1967, 9, 307–313.

15.

Nayfeh

T. A.

Vakakis

A. F.

Subharmonic traveling waves in a geometrically nonlinear circular plate

Int. J. Nonlinear Mechanics, 1994, 29, 233–245.

16.

Raman

Mote

C. D.

Effects of imperfection on the non-linear oscillations of circular plates spinning near critical speed

Int. J. Nonlinear Mechanics, 2001, 36, 261–289.

17.

Raman

Mote

C. D.

Experimental studies on the nonlinear oscillations of circular plates spinning near critical speed

Int. J. Nonlinear Mechanics, 2001, 36, 291–305.

18.

Luo

A. C.J.

Mote

C. D.

Nonlinear vibration of rotating thin disks

Trans. ASME, J. Vibr. and Acoust., 2000, 122, 376–383.

19.

Luo

A. C.J.

Tan

C. A.

Resonant and stationary waves in rotational disks

Nonlinear Dynamics, 2001, 24, 357–372.

20.

Luo

A. C.J.

Hamidzadeh

H. R.

Equilibrium solutions and buckling stability for axially moving plates

Communs in Nonlinear Sci. and Numer. Simulation, 2002, in press.

21.

Chu

H. N.

Herrmann

Influence of large amplitudes on free flexural vibrations of rectangle elastic plates

Trans. ASME, J. Appl. Mechanics, 1956, 23, 532–540.

22.

Pasic

Hermann

Nonlinear free vibrations of buckled plates with deformable loaded edges

J. Sound and Vibr., 1983, 87 (1), 105–114.

Resonant and stationary waves in axially travelling thin plates

Abstract

Abstract

Keywords

Get full access to this article

References