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

• Published in: Journal of sound and vibration Vol. 267; no. 5; pp. 1007 - 1027
• Main Authors: Suweken, G., Van Horssen, W.T.
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 06.11.2003; 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; Mode coupling; Initial value problem; Numerical method; Modeling; Varying speed; Beam(mechanics); Natural frequency; Perturbation method; Boundary value problem; Dynamic stability; Resonance; Belt conveyor; Asymptotic approximation; Bending vibration; Structural analysis
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/S0022-460X(03)00219-0

In this paper, initial–boundary-value problems for a beam equation (with string effect) 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. In this paper, the belt is assumed to move with a time-varying velocity V(t)=ε(V 0+α sin(Ωt)) . Formal asymptotic approximations of the solutions are constructed to show the complicated dynamical behaviour of the belt. Complicated dynamical behaviour of the belt system occurs when the frequency Ω is the sum or difference of any two natural frequencies of the system with zero belt velocity. For special values of the belt parameters these sum type and difference type of internal resonances coincide giving rise to even more complicated dynamical behaviour. Some examples (including detuning cases) have been studied in detail.