On the transversal vibrations of a conveyor belt with a low and time-varying velocity. Part I: the string-like case

• Published in: Journal of sound and vibration Vol. 264; no. 1; pp. 117 - 133
• Main Authors: Suweken, G., Van Horssen, W.T.
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 26.06.2003; Elsevier
• Subjects: Applied sciences; Continuous conveyors: mechanical, hydraulic, pneumatic, etc; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Material handling, hoisting. Storage. Packaging; Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Vibrations and mechanical waves; Wave equation; Time varying system; Perturbation method; Boundary value problem; Initial value problem; Numerical method; Belt conveyor; Asymptotic approximation; String; Modeling; Varying speed; Bending vibration
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/S0022-460X(02)01168-9

In this paper initial-boundary-value problems for a linear wave (string) equation are considered. These problems can be used as simple models to describe the vertical vibrations of a conveyor belt, for which the velocity is small with respect to the wave speed and is assumed to move with a time-varying speed. Formal asymptotic approximations of the solutions are constructed to show the complicated dynamical behavior of the conveyor belt. It will also be shown that the truncation method cannot be applied to this problem in order to obtain approximations valid on long time scales.