Grazing phenomena in a periodically forced, friction-induced, linear oscillator

@article{citeulike:596504, abstract = {The criterion for grazing motions in a dry-friction oscillator is obtained from the local theory of non-smooth dynamical systems on the connectable and accessible domains. The generic mappings for such a dry-friction oscillator are also introduced. The sufficient and necessary conditions for grazing at the final states of mappings are expressed. The initial and final switching sets of grazing mapping, varying with system parameters, are illustrated for the grazing parametric characteristics. The initial and grazing, switching manifolds in the switching sets are defined through grazing mappings. Finally, numerical illustrations of grazing motions are very easily carried out with help of the analytical predictions. This paper provides a comprehensive investigation of grazing motions in the dry-friction oscillator for a better understanding of the grazing mechanism of such a discontinuous system. The investigation based on the local singularity theory is more intuitive and efficient than the discontinuous mapping techniques.}, author = {Luo, Albert C. and Gegg, Brandon C. }, citeulike-article-id = {596504}, doi = {10.1016/j.cnsns.2004.12.006}, journal = {Communications in Nonlinear Science and Numerical Simulation}, keywords = {bifurcation}, month = {October}, number = {7}, pages = {777--802}, posted-at = {2006-04-24 01:14:15}, priority = {2}, title = {Grazing phenomena in a periodically forced, friction-induced, linear oscillator}, url = {http://dx.doi.org/10.1016/j.cnsns.2004.12.006}, volume = {11}, year = {2006} }

TY - JOUR ID - citeulike:596504 L3 - citeulike-article-id:596504 TI - Grazing phenomena in a periodically forced, friction-induced, linear oscillator JF - Communications in Nonlinear Science and Numerical Simulation VL - 11 IS - 7 SP - 777 EP - 802 N2 - The criterion for grazing motions in a dry-friction oscillator is obtained from the local theory of non-smooth dynamical systems on the connectable and accessible domains. The generic mappings for such a dry-friction oscillator are also introduced. The sufficient and necessary conditions for grazing at the final states of mappings are expressed. The initial and final switching sets of grazing mapping, varying with system parameters, are illustrated for the grazing parametric characteristics. The initial and grazing, switching manifolds in the switching sets are defined through grazing mappings. Finally, numerical illustrations of grazing motions are very easily carried out with help of the analytical predictions. This paper provides a comprehensive investigation of grazing motions in the dry-friction oscillator for a better understanding of the grazing mechanism of such a discontinuous system. The investigation based on the local singularity theory is more intuitive and efficient than the discontinuous mapping techniques. KW - bifurcation AU - Luo, Albert AU - Gegg, Brandon PY - 2006/10// UR - http://dx.doi.org/10.1016/j.cnsns.2004.12.006 ER -