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    王跃方

    • 教授     博士生导师   硕士生导师
    • 性别:男
    • 毕业院校:大连理工大学
    • 学位:博士
    • 所在单位:力学与航空航天学院
    • 学科:动力学与控制. 工程力学. 计算力学
    • 办公地点:大连理工大学,力学楼505室。
    • 联系方式:电子邮件:yfwang@dlut.edu.cn,QQ号:1043160457。
    • 电子邮箱:yfwang@dlut.edu.cn

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    A Matrix-Based Computational Scheme of Generalized Harmonic Balance Method for Periodic Solutions of Nonlinear Vibratory Systems

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    论文类型:期刊论文

    发表时间:2015-01-01

    发表刊物:Journal of Applied Nonlinear Dynamics

    收录刊物:Scopus

    卷号:4

    期号:4

    页面范围:379-389

    摘要:A matrix-based computational scheme is developed based on the Generalized Harmonic Balance method for periodic solutions of nonlinear dynamical systems. The nonlinear external loading is expanded into a Taylor's series as a function of displacement and velocity, and is then expressed as a combination of Fourier harmonics through the Generalized Harmonic Balance method. Using the Newton-Raphson's approach, an iteration scheme is formulated to obtain the solution of harmonic coefficients for the displacement. The present scheme is a general purpose realization of the Generalized Harmonic Balance method in the sense that it does not need an analytical Fourier expansion of loadings, and all of the coefficient matrices involved with the scheme are created in a standard way. An example of a periodically forced Duffing oscillator is provided to demonstrate the performance of the present scheme. Numerical solutions of period-1 motion from the present scheme are compared with numerical results given by the Runge-Kutta method. The numerical results agree well with analytical predictions by Luo et al. ? 2015 L & H Scientific Publishing, LLC.