Non-linear, non-planar and non-periodic vibrations of a string
作者： O. O'Reilly , P.J. Holmes
DOI: 10.1016/0022-460X(92)90374-7
关键词: Integrable system 、 Vibration 、 Normal mode 、 Classical mechanics 、 Forcing (recursion theory) 、 Nonlinear system 、 C++ string handling 、 Hamiltonian system 、 Planar 、 Mathematics
摘要: Abstract We study the vibrations of a string subject to planar harmonic excitation, both experimentally and theoretically. observe multiple periodic motions, non-planar (whirling), as well quasi-periodic whirling irregularly precessing oscillations when forcing frequency is near that transverse normal mode. A two-degree-of-freedom model derived, it shown these motions can be partially understood in terms completely integrable Hamiltonian system obtained damping tend zero model.
harvard.edu
elsevier.com
sci-hub.se 参考文章(35)
Stephen Wiggins, Global Bifurcations and Chaos Applied Mathematical Sciences. ,(1988) , 10.1007/978-1-4612-1042-9
Diffeomorphisms with Many Periodic Points Princeton University Press. ,(1965) , 10.1515/9781400874842-006
John T. Cannon, Sigalia Dostrovsky, The Evolution of Dynamics: Vibration Theory from 1687 to 1742 Studies in the History of Mathematics and Physical Sciences. ,vol. 6, ,(1981) , 10.1007/978-1-4613-9461-7
A. Mielke, P. Holmes, O. O'Reilly, Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle-center Journal of Dynamics and Differential Equations. ,vol. 4, pp. 95- 126 ,(1992) , 10.1007/BF01048157
G. V. Anand, Negative resistance mode of forced oscillations of a string Journal of the Acoustical Society of America. ,vol. 54, pp. 692- 698 ,(1973) , 10.1121/1.1913650
T.C.A. Molteno, N.B. Tufillaro, Torus doubling and chaotic string vibrations: Experimental results Journal of Sound and Vibration. ,vol. 137, pp. 327- 330 ,(1990) , 10.1016/0022-460X(90)90796-3
Ray Redheffer, Jack K. Hale, Ordinary differential equations American Mathematical Monthly. ,vol. 78, pp. 1154- ,(1971) , 10.2307/2316346
Z.C. Feng, P.R. Sethna, Global bifurcation and chaos in parametrically forced systems with one-one resonance Dynamics and Stability of Systems. ,vol. 5, pp. 201- 225 ,(1990) , 10.1080/02681119008806098
A.K. Bajaj, J.M. Johnson, Asymptotic techniques and complex dynamics in weakly non-linear forced mechanical systems International Journal of Non-linear Mechanics. ,vol. 25, pp. 211- 226 ,(1990) , 10.1016/0020-7462(90)90052-B
P.J. Holmes, The dynamics of repeated impacts with a sinusoidally vibrating table Journal of Sound and Vibration. ,vol. 84, pp. 173- 189 ,(1982) , 10.1016/S0022-460X(82)80002-3