Dynamic behaviour of an axially moving plate undergoing small cylindrical deformation submerged in axially flowing ideal fluid

Abstract

The out-of-plane dynamic response of a moving plate, travelling between two rollers at a constant velocity, is studied, taking into account the mutual interaction between the vibrating plate and the surrounding, axially flowing ideal fluid. Transverse displacement of the plate (assumed cylindrical), is described by an integrodifferential equation that includes a local inertia term, Coriolis and centrifugal forces, the aerodynamic reaction of the external medium, the vertical projection of membrane tension, the bending resistance, and external perturbation forces. In the two-dimensional model thus set up, the aerodynamic reaction is found analytically as a functional of the cylindrical displacement, using the techniques of complex analysis. The resulting integro-differential problem is discretized in space with the Fourier-Galerkin method, and integrated in time with the diagonalization method. Examples are computed with physical parameters corresponding to air and some paper materials. The effects of the surrounding fluid on the critical velocity and first natural frequency are investigated, for stationary air, for an air mass moving with the plate, and for some arbitrary axial fluid velocities. The obtained results are applicable for both an ideal membrane and a plate with nonzero bending rigidity.

The origin of in-plane stresses in axially moving orthotropic continua

“…by (6) and the definition ρ 0 ≡ M/V 0 . Let us assume that the material is subjected to pure axial stress.…”

“…In their studies, it was found that the surrounding air significantly reduces the eigenfrequencies and critical velocities of the web, when compared to the vacuum case. Chang and Moretti [9] studied membranes using potential flow theory, and Banichuk et al [5,6] used the flat panel model coupled with potential flow. This research was extended by Jeronen [31], where the eigenfrequency spectra were investigated for this model and for the moving string with damping.…”

Modeling and dynamic analysis of axially moving variable fractional order viscoelastic plate

“…The research on the vibration characteristics of viscoelastic plate structure is an important subject in many fields, such as aerospace, shipbuilding, machinery, and civil engineering [5][6][7]. Viscoelastic moving plate is a common model of axially moving materials [8,9].…”

On Travelling Web Stability Including Material Viscoelasticity and Surrounding Air

“…Kulachenko modelled the uid-structure interaction on the basis of acoustic theory nding also that the presence of air reduces the eigenfrequencies of the web compared to the vacuum case [6]. Recently, Banichuk et al studied the interaction between the moving web and owing air using a panel model (a plate with cylindrical deformation) and an analytical expression for the aerodynamic reaction pressure [14,15]. The aerodynamic reaction was solved analytically for potential ow in the complex plane where the panel was represented as a cut.…”