Theoretical study on travelling web dynamics and instability under non-homogeneous tension

Abstract

Problems of dynamics and stability of a moving web, travelling between two rollers at a constant velocity, are studied using analytical approaches. Transverse vibrations of the web are described by a partial differential equation small inhomogeneities in the tension may have a large effect on the divergence forms.

Estimates for Divergence Velocities of Axially Moving Orthotropic Thin Plates

“…It can be seen that the smaller the value of the shear modulus is, the lower the critical velocity V cr 0 becomes. This effect was found also in the case of the isotropic plate (Banichuk et al, 2013a). The critical velocity for an orthotropic plate with G 12 = G H and homogeneous tension (α = 0) is V cr 0 = 83.4461 m/s (by keeping other parameter values the same).…”

“…The result for constant tension and the first estimate in (51) in the case of an ideal membrane were also discussed in Banichuk et al (2013a), here however in a slightly different manner using complex analysis.…”

“…The case of orthotropic plates, specifically, has been studied by Biancolini et al (2005) Tension inhomogeneities and their effects on the divergence instability of moving plates have been studied in Banichuk et al (2013a). A linearly inhomogeneous tension profile, with the axial tension varying across the cross direction, was considered in the case of a moving isotropic plate.…”

Nonlinear dynamical behaviors of a moving membrane under external excitation

“…26 Nguyen and Hong 27 presented a control algorithm for suppression of the transverse vibration of an axially moving web system via regulation of axial velocity. Banichuk et al 28 analyzed the dynamics and stability of a moving web under nonhomogeneous tension by using analytical approaches. The natural frequencies of a specially orthotropic rectangular membrane were examined with respect to its design parameters by Wetherhold and Padliya.…”

Vibrations of a continuous web on elastic supports

“…In our previous studies (see, e.g., [3][4][5][6][7][8], we have considered mathematical modelling of the mechanical aspects of the paper making process, using analytical and numerical approaches. The processing of paper, steel, fabric or rubber, and looping systems such as band saws and timing belts, all belong to the class of systems known as axially moving materials.…”