Affiliation:
1. Laboratory of Functional Analysis and Geometry of Spaces University of M'Sila M'Sila Algeria
2. Department of Mathematics University of M'Sila PB:166 M'Sila 28000 Algeria
Abstract
We study the small vibrations of axially moving strings described by a wave equation in an interval with two endpoints moving in the same direction with a constant speed. The solution is expressed by a series formula where the coefficients are explicitly computed in function of the initial data. We also define an energy expression for the solution that is conserved in time. Then, we establish boundary observability inequalities with explicit constants.
Subject
General Engineering,General Mathematics
Reference19 articles.
1. The free vibrations of an axially moving string in a bounded region;Ram Y. M.;Can. Appl. Math. Q.,1995
2. Analysis and Control of Transverse Vibrations of Axially Moving Strings
3. Stability of Axially Moving Materials
4. Control of Axially Moving Systems: A Review
5. Uber die bewegung eines gespannten fadens, weicher gezwungen ist durch zwei feste punkte;Skutch R.;mit einer constanten Geschwindigkeit zu gehen, und zwischen denselben in Transversal‐schwingungen von gerlinger Amplitude versetzt wird. Annalen der Physik und Chemie,1897