130 0 |
SM ISO690:2012 BANICHUK, Nikolay, BARSUK, Alexander A., JERONEN, J., TUOVINEN, Tero, NEITTAANMAKI, Pekka. Stability of Axially Moving Strings, Beams and Panels. Dusseldorf: 2020, pp. 397-483. ISSN 09250042DOI: 10.1007/978-3-030-23803-2_7 |
EXPORT metadate: Google Scholar Crossref CERIF DataCite Dublin Core |
Solid Mechanics and its Applications | ||||||
2020 | ||||||
|
||||||
DOI:https://doi.org/10.1007/978-3-030-23803-2_7 | ||||||
Pag. 397-483 | ||||||
|
||||||
Descarcă PDF | ||||||
Rezumat | ||||||
In this chapter, using analytical approaches, we consider the problems of dynamics and stability of moving elastic rods and strings, axially traveling between two supports at a constant velocity. Transverse, longitudinal and torsional vibrations of the moving structure are reduced to the same mathematical form, a hyperbolic second-order partial differential equation. The analysis is then extended to the axially traveling string with damping. An analytical free-vibration solution is obtained. It is seen external friction leads to stabilization, whereas internal friction in the traveling material will destabilize the system in a dynamic mode at the static critical point. Finally, we consider the effects of bending rigidity, which in the case of paper materials introduces a singular perturbation to the governing equation. We consider an implicit exact eigensolution for beams, the effect of elastic supports at the boundaries to the vibration behavior of a long traveling beam, and the stability of a beam traveling in a homogeneous gravitational field. |
||||||
|