摘要: Abstract In this paper, we derive a class of analytical solution the damped Helmholtz–Duffing oscillator that is based on recently developed exact for undamped case. Our procedure indicates holds specific system parametric choice values.
core.ac.uk
sci-hub.se 参考文章(10)
Y.Z. Chen, X.Y. Lin, Several numerical solution techniques for nonlinear eardrum-type oscillations Journal of Sound and Vibration. ,vol. 296, pp. 1059- 1067 ,(2006) , 10.1016/J.JSV.2006.03.019
E. Bonisoli, A. Vigliani, Passive elasto-magnetic suspensions: nonlinear models and experimental outcomes Mechanics Research Communications. ,vol. 34, pp. 385- 394 ,(2007) , 10.1016/J.MECHRESCOM.2007.02.005
W. Han, M. Petyt, Geometrically nonlinear vibration analysis of thin, rectangular plates using the hierarchical finite element method—I: The fundamental mode of isotropic plates Computers & Structures. ,vol. 63, pp. 295- 308 ,(1997) , 10.1016/S0045-7949(96)00345-8
M Senthilvelan, M Lakshmanan, V K Chandrasekar, New aspects of integrability of force-free duffing-van der Pol oscillator and related nonlinear systems Journal of Physics A. ,vol. 37, pp. 4527- 4534 ,(2004) , 10.1088/0305-4470/37/16/004
Zhaosheng Feng, Monotonous property of non-oscillations of the damped Duffing’s equation Chaos, Solitons & Fractals. ,vol. 28, pp. 463- 471 ,(2006) , 10.1016/J.CHAOS.2005.07.006
S.K. Lai, J. Harrington, Y. Xiang, K.W. Chow, Accurate analytical perturbation approach for large amplitude vibration of functionally graded beams International Journal of Non-linear Mechanics. ,vol. 47, pp. 473- 480 ,(2012) , 10.1016/J.IJNONLINMEC.2011.09.019
Alex Elías-Zúñiga, Exact solution of the quadratic mixed-parity Helmholtz–Duffing oscillator Applied Mathematics and Computation. ,vol. 218, pp. 7590- 7594 ,(2012) , 10.1016/J.AMC.2012.01.025
F.I. Compeán, D. Olvera, F.J. Campa, L.N. López de Lacalle, A. Elías-Zúñiga, C.A. Rodríguez, Characterization and stability analysis of a multivariable milling tool by the enhanced multistage homotopy perturbation method International Journal of Machine Tools & Manufacture. ,vol. 57, pp. 27- 33 ,(2012) , 10.1016/J.IJMACHTOOLS.2012.01.010
Juan A Almendral, Miguel A F Sanju n, Integrability and symmetries for the Helmholtz oscillator with friction Journal of Physics A. ,vol. 36, pp. 695- 710 ,(2003) , 10.1088/0305-4470/36/3/308
V K Chandrasekar, M Senthilvelan, M Lakshmanan, New aspects of integrability of force-free Duffing-van der Pol oscillator and related nonlinear systems arXiv: Exactly Solvable and Integrable Systems. ,(2004) , 10.1088/0305-4470/37/16/004