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On the equilibria and qualitative dynamics of a forced nonlinear oscillator with contact and friction
Kinematical structural stability
1. | IBISC, UFRST-UEVE, 40, rue du Pelvoux CE 1455 Courcouronnes, 91020 Evry Cedex, France |
2. | South Britain University, LIMATB -UBS -Lorient Research Center, Rue de Saint Maudé - BP 92116, 56321 Lorient cedex, France, France, France |
References:
[1] |
D. Bigoni and G. Noselli, Experimental evidence of flutter and divergence instabilities induced by dry friction, Journal of the Mechanics and Physics of Solids, 59 (2011), 2208-2226.
doi: 10.1016/j.jmps.2011.05.007. |
[2] |
V. V. Bolotin, Non-conservative Problems of the Theory of Elastic Stability, Pergamon Press, 1963. |
[3] |
N. Challamel, F. Nicot, J. Lerbet and F. Darve, Stability of non-conservative elastic structures under additional kinematics constraints, Engineering Structures, 32 (2010), 3086-3092.
doi: 10.1016/j.engstruct.2010.05.027. |
[4] |
K. E. Gustafson and D. K. M. Rao, Numerical Range. The field of Values of Linear Operators and Matrices, Universitext, Springer, 1997.
doi: 10.1007/978-1-4613-8498-4. |
[5] |
R. Hill, A general theory of uniqueness and stability in elastic-plastic solids, Journal of the Mechanics and Physics of Solids, 6 (1958), 236-249.
doi: 10.1016/0022-5096(58)90029-2. |
[6] |
R. Hill, Some basic principles in the mechanics of solids without a natural time, J. Mech. Phys. Solids, 7 (1959), 209-225.
doi: 10.1016/0022-5096(59)90007-9. |
[7] |
O. N. Kirillov and F. Verhulst, Paradoxes of dissipation-induced destabilization or who opened Withney's umbrella?, Z. Angew.Math. Mech., 90 (2010), 462-488.
doi: 10.1002/zamm.200900315. |
[8] |
J. Lerbet, M. Aldowaji, N. Challamel, F. Nicot, F. Prunier and F. Darve, P-positive definite matrices and stability of nonconservative systems, Z. Angew. Math. Mech., 92 (2012), 409-422.
doi: 10.1002/zamm.201100055. |
[9] |
J. Lerbet, M. Aldowaji, N. Challamel, F. Nicot, O. Kirillov and F. Darve, Geometric degree of nonconservativity, Math. and Mech. of Complex Systems, 2 (2014), 123-139.
doi: 10.2140/memocs.2014.2.123. |
[10] |
T. Tarnai, Paradoxical behaviour of vibrating systems challenging Rayleigh's theorem, 21st International Congress of Theoretical and Applied Mechanics, Warsaw, 2004. |
[11] |
J. M. T. Thompson, 'Paradoxical' mechanics under fluid flow, Nature, 296 (1982), 135-137.
doi: 10.1038/296135a0. |
show all references
References:
[1] |
D. Bigoni and G. Noselli, Experimental evidence of flutter and divergence instabilities induced by dry friction, Journal of the Mechanics and Physics of Solids, 59 (2011), 2208-2226.
doi: 10.1016/j.jmps.2011.05.007. |
[2] |
V. V. Bolotin, Non-conservative Problems of the Theory of Elastic Stability, Pergamon Press, 1963. |
[3] |
N. Challamel, F. Nicot, J. Lerbet and F. Darve, Stability of non-conservative elastic structures under additional kinematics constraints, Engineering Structures, 32 (2010), 3086-3092.
doi: 10.1016/j.engstruct.2010.05.027. |
[4] |
K. E. Gustafson and D. K. M. Rao, Numerical Range. The field of Values of Linear Operators and Matrices, Universitext, Springer, 1997.
doi: 10.1007/978-1-4613-8498-4. |
[5] |
R. Hill, A general theory of uniqueness and stability in elastic-plastic solids, Journal of the Mechanics and Physics of Solids, 6 (1958), 236-249.
doi: 10.1016/0022-5096(58)90029-2. |
[6] |
R. Hill, Some basic principles in the mechanics of solids without a natural time, J. Mech. Phys. Solids, 7 (1959), 209-225.
doi: 10.1016/0022-5096(59)90007-9. |
[7] |
O. N. Kirillov and F. Verhulst, Paradoxes of dissipation-induced destabilization or who opened Withney's umbrella?, Z. Angew.Math. Mech., 90 (2010), 462-488.
doi: 10.1002/zamm.200900315. |
[8] |
J. Lerbet, M. Aldowaji, N. Challamel, F. Nicot, F. Prunier and F. Darve, P-positive definite matrices and stability of nonconservative systems, Z. Angew. Math. Mech., 92 (2012), 409-422.
doi: 10.1002/zamm.201100055. |
[9] |
J. Lerbet, M. Aldowaji, N. Challamel, F. Nicot, O. Kirillov and F. Darve, Geometric degree of nonconservativity, Math. and Mech. of Complex Systems, 2 (2014), 123-139.
doi: 10.2140/memocs.2014.2.123. |
[10] |
T. Tarnai, Paradoxical behaviour of vibrating systems challenging Rayleigh's theorem, 21st International Congress of Theoretical and Applied Mechanics, Warsaw, 2004. |
[11] |
J. M. T. Thompson, 'Paradoxical' mechanics under fluid flow, Nature, 296 (1982), 135-137.
doi: 10.1038/296135a0. |
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