%0 Journal Article %1 suweken2003weakly %A Suweken, G. %A van Horssen, W. T. %D 2003 %J Nonlinear Dynamics %K 74h10-deformable-solids-dynamical-problems-analytic-approximation 74h45-vibrations 74h55-solids-dynamics-stability conveyor-belts %N 2 %P 197--223 %R 10.1023/A:1022053131286 %T On the Weakly Nonlinear, Transversal Vibrations of a Conveyor Belt with a Low and Time-Varying Velocity %U https://link.springer.com/article/10.1023/A:1022053131286 %V 31 %X In this paper the weakly nonlinear, transversal vibrations of aconveyor belt will be considered. The belt is assumed to move witha low and time-varying speed. Using Kirchhoff's approach a singleequation of motion will be derived from a coupled system ofpartial differential equations describing the longitudinal andtransversal vibrations of the belt. A two time-scalesperturbation method is then applied to approximate the solutionsof the problem. It will turn out that the frequencies of the belt speed fluctuations play an important role in the dynamic behaviourof the belt. It is well-known in linear systems that instabilitiescan occur if the frequency of the belt speed fluctuations is thesum of two natural frequencies. However, in the weakly nonlinearcase as considered in this paper this is no longer true. It turns out that the weak nonlinearity stabilizes the system.

@article{suweken2003weakly, abstract = {In this paper the weakly nonlinear, transversal vibrations of aconveyor belt will be considered. The belt is assumed to move witha low and time-varying speed. Using Kirchhoff's approach a singleequation of motion will be derived from a coupled system ofpartial differential equations describing the longitudinal andtransversal vibrations of the belt. A two time-scalesperturbation method is then applied to approximate the solutionsof the problem. It will turn out that the frequencies of the belt speed fluctuations play an important role in the dynamic behaviourof the belt. It is well-known in linear systems that instabilitiescan occur if the frequency of the belt speed fluctuations is thesum of two natural frequencies. However, in the weakly nonlinearcase as considered in this paper this is no longer true. It turns out that the weak nonlinearity stabilizes the system.}, added-at = {2022-09-15T06:42:52.000+0200}, author = {Suweken, G. and van Horssen, W. T.}, biburl = {https://www.bibsonomy.org/bibtex/2857a64c75922d1d3116b5123b55e799c/gdmcbain}, day = 01, doi = {10.1023/A:1022053131286}, interhash = {8752447fb18df30151af325ed6170dd8}, intrahash = {857a64c75922d1d3116b5123b55e799c}, issn = {1573-269X}, journal = {Nonlinear Dynamics}, keywords = {74h10-deformable-solids-dynamical-problems-analytic-approximation 74h45-vibrations 74h55-solids-dynamics-stability conveyor-belts}, month = jan, number = 2, pages = {197--223}, timestamp = {2022-09-15T06:45:13.000+0200}, title = {On the Weakly Nonlinear, Transversal Vibrations of a Conveyor Belt with a Low and Time-Varying Velocity}, url = {https://link.springer.com/article/10.1023/A:1022053131286}, volume = 31, year = 2003 }