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Dynamic Analysis of Vibrating Systems with Nonlinearities 被引量:1

Dynamic Analysis of Vibrating Systems with Nonlinearities
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摘要 The max-min approach is applied to mathematical models of some nonlinear oscillations.The models are regarding to three different forms that are governed by nonlinear ordinary differential equations.In this context,the strongly nonlinear Duffing oscillator with third,fifth,and seventh powers of the amplitude,the pendulum attached to a rotating rigid frame and the cubic Duffing oscillator with discontinuity are taken into consideration.The obtained results via the approach are compared with ones achieved utilizing other techniques.The results indicate that the approach has a good agreement with other well-known methods.He's max-min approach is a promising technique and can be successfully exerted to a lot of practical engineering and physical problems.
出处 《Communications in Theoretical Physics》 SCIE CAS CSCD 2012年第2期183-187,共5页 理论物理通讯(英文版)
关键词 nonlinear oscillation He's max-min approach dynamic analysis 非线性振动系统 非线性常微分方程 数学模型 强非线性 物理问题 振荡器 技术 立方
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同被引文献23

  • 1JAISER A R, STEN K, and KYSLE P. A numerical solution of the nonlinear controlled Duffing oscillator by radial basis functions[J]. Computers and Mathematics with Applications, 2012(64): 2049-2065.
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  • 3MENG K L and STEVE S. Temporal and spectral responses of a softening Duffing oscillator undergoing route-to-chaos[J]. Communication Nonlinear Science Numerical Simulation, 2012(17): 5217-5228.
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  • 6IBRAHIM A M A and CHOUDHURY P K. On the Maxwell- Duffing approach to model photonic deflection sensor[J]. IEEE Photonics Journal, 2013, 5(4): 6800812.
  • 7LI Keqiang, WANG Shangjiu, and ZHAO Yonggang. Multiple periodic solutions for asymptotically linear Duffing equations with resonance[J]. Journal of Mathematical Analysis and Applications, 2013, 397: 156-160.
  • 8ALEX E. Analytical solution of the damped Helmholtz- Duffing equation[J]. Applied Mathematics Letters, 2012(25): 2349-2353.
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  • 10杨红英,叶昊,王桂增,吕琛.Duffing振子的Lyapunov指数与Floquet指数研究[J].仪器仪表学报,2008,29(5):927-932. 被引量:20

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