Determination of limit cycles for a modified van der Pol oscillator

Mechanics Research Communications - Tập 33 Số 1 - Trang 93-98 - 2006
Mario D’Acunto1
1Department of Chemical Engineering and Materials Science, University of Pisa, via Diotisalvi 2, 56126 Pisa, Italy

Tóm tắt

Từ khóa


Tài liệu tham khảo

Bogarcz, 1997, Dry friction self-excited vibrations, analysis and experiment, Eng. Trans., 45, 197

Colin, 1999, Small-amplitude limit cycle bifurcations for Liénard systems with quadratic or cubic damping or restoring forces, Nonlinearity, 12, 1099, 10.1088/0951-7715/12/4/321

D’Acunto, 2001, A Simple Model for Low Friction Systems, vol. 311

den Hartog, 1984

Depasier, 2001, Variational approach to a class of nonlinear oscillators with several limit cycles, Phys. Rev. E, 64, 05617-1-6, 10.1103/PhysRevE.64.056217

Drăgănescu, 2004, Nonlinear relaxation phenomena in polycrystalline solids, Int. J. Nonlinear Sci. Numer. Simul., 4, 219, 10.1515/IJNSNS.2003.4.3.219

Hao, 2003, Application of the Lagrange multiplier method the semi-inverse method to the search for generalised variational principle in quantum mechanics, Int. J. Nonlinear Sci. Numer. Simul., 4, 311, 10.1515/IJNSNS.2003.4.3.311

He, 1999, Variational iteration method—a kind of nonlinear analytical technique: some examples, Int. J. Nonlinear Mech., 34, 699, 10.1016/S0020-7462(98)00048-1

He, 2000, A classical variational model for micropolar elastodynamics, Int. J. Nonlinear Sci. Numer. Simul., 1, 133, 10.1515/IJNSNS.2000.1.2.133

He, 2000, A Review on some new recently developed nonlinear analytical techniques, Int. J. Nonlinear Sci. Numer. Simul., 1, 51, 10.1515/IJNSNS.2000.1.1.51

He, 2000, Variational iteration method for autonomous ordinary differential systems, Appl. Math. Comput., 114, 115, 10.1016/S0096-3003(99)00104-6

He, 2002, Preliminary report on the energy balance for nonlinear oscillations, Mech. Res. Commun., 29, 107, 10.1016/S0093-6413(02)00237-9

He, 2003, Determination of limit cycles for strongly nonlinear oscillators, Phys. Rev. Lett., 90, 10.1103/PhysRevLett.90.174301

Jackson, 1989

Liu, 2004, Variational approach to nonlinear electrochemical system, Int. J. Nonlinear Sci. Numer. Simul., 5, 95, 10.1515/IJNSNS.2004.5.1.95

Marinca, 2002, An approximate solution for x–c weakly nonlinear oscillations, Int. J. Nonlinear Sci. Numer. Simul., 3, 107, 10.1515/IJNSNS.2002.3.2.107

Nayfeh, 1979

Wazwaz, 2001, A reliable algorithm for obtaining positive solutions for nonlinear boundary value problems, Comput. Math. Appl., 41, 1237, 10.1016/S0898-1221(01)00094-3