ARTICLE
Experimental study of the nonlinear dynamics of a smooth and discontinuous oscillator with different smoothness parameters and initial values
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1
Shijiazhuang Tiedao University, Shijiazhuang, China
 
2
State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang
 
3
Beijing Feb.7th Locomotive Industry Co., Ltd
 
 
Submission date: 2018-06-24
 
 
Acceptance date: 2019-05-25
 
 
Online publication date: 2019-10-15
 
 
Publication date: 2019-10-15
 
 
Journal of Theoretical and Applied Mechanics 2019;57(4):935-946
 
KEYWORDS
ABSTRACT
The dynamic response of a nonlinear system is very sensitive to initial conditions. Both the irrational nonlinearity and the large displacement of a smooth and discontinuous (SD) oscillator have been studied in this paper. An experimental study has been conducted on a model of the SD oscillator with different initial conditions and smoothness parameters. Experimental results indicate that tiny variation in the initial displacement will lead to different kinds of vibrations, and the system exhibits a wide range of nonlinear dynamical phenomena with the change of smoothness parameters. All experimental results are in good conformity with numerical simulation results.
 
REFERENCES (19)
1.
Léger A., Pratt E., Cao Q., 2012, A fully nonlinear oscillator with contact and friction, Nonlinear Dynamics, 70, 511-522.
 
2.
Cao Q., Wang D., Chen Y., Wiercigroch M., 2012, Irrational elliptic functions and the analytical solutions of SD oscillator, Journal of Theoretical and Applied Mechanics, 50, 3, 701-715.
 
3.
Cao Q., Wiercigroch M., Pavlovskaia E.E., Grebogi C., Thompson J.M., 2006, Archetypal oscillator for smooth and discontinuous dynamics, Physical Review E, 74, 1-5, DOI: 10.1103/PhysRevE.74.046218.
 
4.
Cao Q., Wiercigroch M., Pavlovskaia E.E., Grebogi C., Thompson J.M., 2008a, The limit case response of the archetypal oscillator for smooth and discontinuous dynamics, International Journal of Nonlinear Mechanics, 43, 462-473, DOI: 10.1016/j.ijnonlinmec.2008.01.003.
 
5.
Cao Q.,Wiercigroch M., Pavlovskaia E.E., Thompson J.M., Grebogi C., 2008b, Piecewise linear approach to an archetypal oscillator for smooth and discontinuous dynamics, Philosophical Transactions of the Royal Society –Mathematical Physical and Engineering Sciences, 1865, 366, 635-652, DOI: 10.1098/rsta.2007.2115.
 
6.
Cao Q., Xiong Y., Wiercigroch M., 2008c, Resonances of the SD oscillator due to the discontinuous phase, Journal of Applied Analysis and Computation, 1, 2, 183-191.
 
7.
Filippov A.F., 1988, Differential Equations with Discontinuous Right-hand Sides, Dordrecht, The Netherlands: Kluwer Academic Publishers.
 
8.
Gatti G., Kovacic I., Brennan M.J., 2010, On the response of a harmonically excited two degree-of-freedom system consisting of a linear and a nonlinear quasi-zero stiffness oscillator, Journal of Sound of Vibration, 329, 1832-1835, DOI: 10.1016/j.jsv.2009.11.019.
 
9.
Gourdon E., Alexander N.A., Taylor C.A., Lamarque C.H., Pernot S., 2010, Nonlinear energy pumping under transient forcing with strongly nonlinear coupling: Theoretical and experimental results, Journal of Sound of Vibration, 300, 2007, 522-551, DOI: 10.1016/j.jsv.2006.06.074.
 
10.
Han Y.W., Cao Q.J., Chen Y.S., Wiercigroch M., 2012, A novel smooth and discontinuous oscillator with strong irrational nonlinearities, Science China-Physical Mechanics and Astronomy, 55, 10, 1832-1843, DOI: 10.1007/s11433-012-4880-9.
 
11.
Kunze M., 2000, Non-Smooth Dynamical Systems, New York: Springer-Verlag.
 
12.
Shaw S.W, Holmes P.J., 1983, A periodically forced piecewise linear oscillator, Journal of Sound and Vibration, 90, 1, 129-155, DOI: 10.1016/0022-460X(83)90407-8.
 
13.
Thompson J.M.T., Hunt G.W., 1973, A General Theory of Elastic Stability, London: John Wiley & Sons.
 
14.
Tian R.L., Cao Q.J., Li Z.X., 2010a, Hopf bifurcations for the recently proposed smooth-and-discontinuous oscillator, Chinese Physical Letters, 27, 7, 074701-074704, DOI: 10.1088/0256-307x/27/7/074701.
 
15.
Tian R.L., Cao Q.J., Yang S.P., 2010b, The codimension-two bifurcation for the recent proposed SD oscillator, Nonlinear Dynamics, 59, 1-2, 19-27, DOI: 10.1007/s11071-009-9517-9.
 
16.
Tian R.L., Wu Q.L., Liu Z.J., Yang X.W., 2012, Dynamic analysis of the smooth-and-discontinuous oscillator under constant excitation, China Physical Letters, 29, 8, 084706-084711, DOI: 10.1088/0256-307x/29/8/084706.
 
17.
Tian R.L., Wu Q.L., Yang X.W., Si C.D., 2013, Chaotic threshold for the smooth-and-discontinuous oscillator under constant excitations, European Physical Journal Plus, 128, 7, 801-812, DOI: 10.1140/epjp/i2013-13080-6.
 
18.
Zhang H.X., Zhang W., Yao M.H., et al., 2007, Experimental research on nonlinear vibration of an axially moving visco-elastic belt, Journal of Dynamics and Control, 5, 4, 361-364.
 
19.
Zhang Y., Luo G., Cao Q., Lin M., 2014, Wada basin dynamics of a shallow arch oscillator with more than 20 coexisting low-period periodic attractors, International Journal of Non-Linear Mechanics, 58, 151-161, DOI: 10.1016/j.ijnonlinmec.2013.09.009.
 
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