理论与应用力学分享 http://blog.sciencenet.cn/u/sunwp 主要从事非线性振动、动力学控制等领域的研究。sunwp@jlu.edu.cn

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博士毕业两年内的主要工作-非线性系统瞬态响应的高精度逼近

已有 2881 次阅读 2010-7-28 06:32 |个人分类:生活|系统分类:论文交流|关键词:学者| 强非线性, 解析逼近, 瞬态响应

  An analytical approximate method for strongly nonlinear damped oscillators is proposed. By introducing phase and amplitude of oscillation as well as a bookkeeping parameter, we rewrite the governing equation into a partial differential equation with solution being a periodic function of the phase. Based on combination of the Newton’s method with the harmonic balance method, the partial differential equation is transformed into a set of linear ordinary differential equations in terms of harmonic coefficients, which can further be converted into systems of linear algebraic equations by using the bookkeeping parameter expansion. Only a few iterations can provide very accurate approximate analytical solutions even if the nonlinearity and damping are significant. The method can be applied to general oscillators with odd nonlinearities as well as even ones even without linear restoring force.



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