Sing the exact finite strip method, a precise solution for linear free vibration and stability of an axially moving plate subjected to plane stresses is obtained. The plate may travel over multiple line supports. Exact natural frequencies and the speed at the onset of instability in the travelling plate can be identified for different boundary conditions and plate dimensions. In addition, a semi-analytical finite strip formulation has been developed for traveling plates with arbitrary boundary conditions and various in-plane loads. Modelling with a system of elastic springs, allows interior point and line supports for the plates to be taken into account. For moving plates, the effect of dimensional ratio in-plane loads and boundary conditions on free vibration, and stability characteristics of the plates were investigated and are described in this article. The influence of speed of plate motion and interior supports on the vibration frequency of the moving plates has also been studied and is illustrated with examples.
AzhariM. and BradfordM.A. (1995). “The use of bubble functions for the post-local buckling of plate assemblies by the finite strip method”, International Journal for Numerical Methods in Engineering, Vol. 38, pp. 995–968.
2.
AzhariM.HoshdarS. and BradfordM.A. (2000). “On the use of bubble functions in the local buckling analysis of plate structures by the spline finite strip method”, International Journal for Numerical Methods in Engineering, Vol. 48, pp. 583–593.
3.
BathR.B. (1991). “Vibration of rectangular plates on point and line supports using characteristic orthogonal polynomials in the Rayleigh-Ritz method”, Journal of Sound and Vibration, Vol. 149, No. 1, pp. 170–172.
4.
CheungY.K. (1968). “The finite strip method in the analysis of elastic plates with two opposite simply supported ends”, Proceedings of the Institution of Civil Engineers, Vol. 40, pp. 1–7.
5.
CheungY.K. and ThamL.G. (1998). The Finite Strip Method, USA: CRC Press.
6.
DaweD.J. (1978). “Finite strip model for vibration of mindlin plates”, Journal of Sound and Vibration, Vol. 59, pp. 441–452.
7.
GormanD.J. (1981). “An analytical solution for the free vibration analysis of rectangular plates resting on symmetrically distributed point supports”, Journal of Sound and Vibration, Vol. 79, No. 6, pp. 561–574.
8.
HintonE. and ZienkiewiezO.C. (1977). “A note on a simple thick finite strip”, International Journal for Numerical Methods in Engineering, Vol. 11, pp. 905–909.
9.
KimC.S. and DickinsonS.M. (1987). “The flexural vibration of rectangular plates with point supports”, Journal of Sound and Vibration, Vol. 117, No. 2, pp. 294–261.
10.
KimJ.ChoJ.LeeU. and ParkS. (2003). “Modal spectral element formulation for axially moving plates subjected to in-plane axial tension”, Computers and Structures, Vol. 81, pp. 2011–2020.
11.
LeeH.P. and NgT.Y. (1994). “Effects of support configuration on parametric excitation of a plate”, International Journal of Solids and Structures, Vol. 31, pp. 835–848.
12.
LengocL. and McCallionH. (1995). “Wide bandsaw blade under cutting conditions, part I: Vibration of a plate moving in its plane while subjected to tangential edge loading”, Journal of Sound and Vibration, Vol. 186, No. 1, pp. 125–142.
13.
LinC.C. (1997). “Stability and vibration characteristics of axially moving plates”, International Journal of Solids and Structures, Vol. 34, No. 24, pp. 3179–3190.
14.
LinC.C. and MoteC.D.Jr. (1995). “Equilibrium displacement and stress distribution in a two-dimensional, axially moving web under transverse loading”, Journal of Applied Mechanics, Vol. 62, pp. 772–779.
15.
LuoA.C.J. and HamidzadehH.R. (2004). “Equilibrium and buckling stability for axially traveling plates”, Communications in Nonlinear Science and Numerical Simulation, Vol. 9, pp. 343–360.
16.
LuoZ. and HuttonS.G. (2002). “Formulation of a three-node traveling triangular plate element subjected to gyroscopic and in-plane forces”, Computers and Structures, Vol. 80, pp.1935–1944.
17.
MoteC.D.Jr. (1966). “On the nonlinear oscillation of an axially moving string”, Journal of Applied Mechanics, pp. 463–464.
18.
SaadatpourM.M.AzhariM. and BradfordM.A. (1998). “Buckling of arbitrary quadrilateral plates with intermediate supports by the Galerkin method”, Computer Methods in Applied Mechanics and Engineering, Vol. 164, pp. 297–306.
19.
SaadatpourM.M.AzhariM. and BradfordM.A. (2000). “Vibration analysis of simply supported plates of general shape with internal point and line supports using the Galerkin method”, Engineering Structures, Vol. 22, No. 9, pp. 1180–1188.
20.
SackR.A. (1953). “Transverse oscillations in traveling strings”, British Journal of Applied Physics, pp. 224–226.
21.
SreeramT.R. and SivaneriN.T. (1998). “FE-analysis of a moving beam using Lagrangian multiplier method”, International Journal of Solids and Structures, Vol. 35, No. 28, pp. 3675–3694.
22.
StylianouM. and TabarrokB. (1994). “Finite element analysis of an axially moving beam part II: Stability analysis”, Journal of Sound and Vibration, Vol. 178, No. 4, pp. 455–481.
23.
ThurmanA.L. and MoteC.D.Jr. (1969). “Free periodic nonlinear oscillation of an axially moving strip”, Journal of Applied Mechanics, pp. 83–91.
24.
UlsoyA.G. and MoteC.D.Jr. (1982). “Vibration of wide band saw blades”, Journal of Engineering for Industry, Vol. 104, pp. 71–78.
25.
WickertJ.A. (1992). “Non-linear vibration of a traveling tensioned beam”, Journal of Non-Linear Mechanics, Vol. 27, No. 3, pp. 503–507.
26.
WickertJ.A. and MoteC.D.Jr. (1990). “Classical vibration analysis of axially moving continua”, Journal of Applied Mechanics, Vol. 57, pp. 738–744.
27.
WilliamsF.W. and WittrickW.H. (1968). “Computational procedures for a matrix analysis of the stability and vibration of thin-walled structures in compression”, International Journal of Mechanical Science, Vol. 11, pp. 979–998.
28.
WittrickW.H. and WilliamsF.W. (1971). “A general algorithm for computing natural frequencies of elastic structures”, Quarterly Journal of Mechanics and Applied Mathematics, Vol. 24, pp. 263–284.
