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Dynamical Analysis Of Transverse Vibrations Of Axially Moving Viscoelastic Beams

Posted on:2006-03-15Degree:DoctorType:Dissertation
Country:ChinaCandidate:X D YangFull Text:PDF
GTID:1100360155460304Subject:General and Fundamental Mechanics
Abstract/Summary:PDF Full Text Request
The class of systems with axially moving materials involves power transmission chains, band saw blades, aerial cableways and paper sheets during processing. Transverse vibration of such systems is generally undesirable although characteristic of operation at high transport speeds. The study of the vibration response of the axially moving materials is of great significance. Through a convective acceleration component, the governing equations of motion for axially moving materials are skew-symmetric in the state space formulation. The research of the transverse vibration in that case may pay contribution to the context of continuous gyroscopic systems.The nonlinear effect cannot be neglected if the transverse displacement of the axially moving beam is rather large. When transverse motion is treated for axially moving beams, there are two types of nonlinear models, a partial-differential equation or an integro-partial-differential equation. The partial-differential equation is derived from considering the transverse displacement only, and the integro-partial-differential equation is traditionally derived from decoupling the governing equation of coupled longitudinal and transverse motion under the quasi-static stretch assumption that supposes the influence of longitudinal inertia can be neglected.The modeling of dissipative mechanisms is an important research topic of axially moving material vibrations. Viscoelasticity is an effective approach to model the damping mechanism. In present investigation, the Kelvin viscoelastic model will be adopted in the studying of the free vibration, parametric resonance, and the forced vibration of the axially moving beam.Vibrations of continuous systems are always modeled in the form of a partial differential equation with small nonlinear or perturbed terms. The perturbation methods may be applied directly to the partial differential equation system. This approach is called direct-perturbation method. The direct-perturbation method produces more accurate results than the discretization method because the eigenfunctions represent the real system better in the case of the direct-perturbation method.In fact, many real systems could be represented by the axially moving materials with pulsating speed. That is, the axial transport speed is a constant mean velocity with small periodic fluctuations. In some other case, if the foundations supporting the axially moving materials are not motionless, the forced transverse vibration must be considered. The method of multiple scales can be used in those governing equations. The amplitude...
Keywords/Search Tags:axially moving beam, viscoelaticity, partial differential equation, nonlinear vibration, averaging method, method of multiple scales, Galerkin method, numerical method, bifurcation, chaos
PDF Full Text Request
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