Accurate approximate analytical solutions for multi-degree-of-freedom coupled van der Pol-Duffing oscillators by homotopy analysis method

Qian, Youhua; Chen, Sheng-Min

doi:10.1016/j.cnsns.2009.11.027

Cited by 21 publications

(7 citation statements)

References 31 publications

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“…17 The HAM is completely independent of small physical parameters of a system, which provides a good way to solve the family of basic functions with multiple degrees of freedom (MDOF), especially for nonlinear systems. Qian and Chen 18 applied the HAM to establish an approximate analytical solution of a nonlinear coupled oscillator with MDOF. Yuan and Li 19 calculated the first-order resonance approximation solution of the forced Duffing equation by the HAM.…”

Section: Introductionmentioning

confidence: 99%

Periodic solutions of delay nonlinear system by multi-frequency homotopy analysis method

Qiang

Qian

Guo

2019

Journal of Low Frequency Noise, Vibration and Active Control

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A two-degree-of-freedom coupled Duffing system with time delay is studied by a modified homotopy analysis method. First, a detailed calculation is given for the system. Second, single periodic and period-doubling solutions are obtained by solving the constructed nonlinear algebraic equation. Third, upon comparison of the periodic solution obtained by the multi-frequency homotopy analysis method with the numerical solutions obtained by the numerical method, it is found that the approximate solution agrees well with the numerical solution for the system. Finally, we discuss the convergence control parameters and convergence control function.

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Section: Introductionmentioning

confidence: 99%

Periodic solutions of delay nonlinear system by multi-frequency homotopy analysis method

Qiang

Qian

Guo

2019

Journal of Low Frequency Noise, Vibration and Active Control

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“…In practical case, such a nonlinear component may represent a fault (Peng et al, 2007). The MDOF vibrating system can be described as the following equation (Lang and Peng, 2008;Qian and Chen, 2010):…”

Section: Power Cable Insulationmentioning

confidence: 99%

A nonlinear frequency analysis based approach for power cable insulation fault detection

Chen

Zhai

Lang

et al. 2012

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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PurposeThe present study is concerned with the application of a nonlinear frequency analysis approach to the detection and location of water tree degradation of power cable XLPE insulation without turning off electric power.Design/methodology/approachThe use of power cable system responses to power line carrier signals are proposed to conduct the required signal analysis for damage location purpose. This technique is based on the fact that the water tree degradation in power cables can make the system behave nonlinearly. Consequently, the location of water tree degradation can be determined by detecting the position of nonlinear components in power cable systems.FindingsA novel method has been proposed for locating water tree degradation in power cable systems; numerical simulation studies have demonstrated the effectiveness of the new technique.Originality/valueThe proposed technique has the potential to be applied in practice to more effectively resolve the power cable damage location problem.

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“…Also, the homotopy-Padé technique was proposed to accelerate the convergence of HAM series, [25]. In order to obtain the [m, n] Pade approximation of the HAM series, one should first compute all (m+n)th-order HAM approximations.…”

Section: Homotopy-padé Techniquementioning

confidence: 99%

Highly Accurate Solution of Limit Cycle Oscillation of an Airfoil in Subsonic Flow

Zhang

Chen

Liu

et al. 2011

Advances in Acoustics and Vibration

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The homotopy analysis method (HAM) is employed to propose a highly accurate technique for solving strongly nonlinear aeroelastic systems of airfoils in subsonic flow. The frequencies and amplitudes of limit cycle oscillations (LCOs) arising in the considered systems are expanded as series of an embedding parameter. A series of algebraic equations are then derived, which determine the coefficients of the series. Importantly, all these equations are linear except the first one. Using some routine procedures to deduce these equations, an obstacle would arise in expanding some fractional functions as series in the embedding parameter. To this end, an approach is proposed for the expansion of fractional function. This provides us with a simple yet efficient iteration scheme to seek very-high-order approximations. Numerical examples show that the HAM solutions are obtained very precisely. At the same time, the CPU time needed can be significantly reduced by using the presented approach rather than by the usual procedure in expanding fractional functions.

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Accurate approximate analytical solutions for multi-degree-of-freedom coupled van der Pol-Duffing oscillators by homotopy analysis method

Cited by 21 publications

References 31 publications

Periodic solutions of delay nonlinear system by multi-frequency homotopy analysis method

Periodic solutions of delay nonlinear system by multi-frequency homotopy analysis method

A nonlinear frequency analysis based approach for power cable insulation fault detection

Highly Accurate Solution of Limit Cycle Oscillation of an Airfoil in Subsonic Flow

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