应用非线性Galerkin方法求解微梁的动态响应
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国家自然科学基金(10772056)和哈尔滨市科技创新人才研究专项资金 (2007RFLXG009) 资助项目


Dynamical responses of microbeams using nonlinear galerkin method
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    摘要:

    分析在电场力驱动下微共振器的非线性动力学特性.取前3阶模态,利用非线性Galerkin方法得到单自由度的降阶模型.用多尺度法计算降阶模型的动态响应,并得出了稳态响应的幅频特性曲线,与利用传统Galerkin方法直接取1阶模态所得的结果比较.以数值积分法求解3自由度模型得到的微共振器动力学响应为参考标准,验证了非线性Galerkin方法与传统Galerkin方法相比具有较高的精度.

    Abstract:

    The nonlinear dynamic behaviour of a microresonator driven by electric force was investigated. The first three modes were used to get a model with singledegreeoffreedom in terms of the nonlinear Galerkin method. The multiple scales method was employed to obtain the dynamic responses of the reduced order model. The amplitudefrequency curve of stationary responses was depicted out and used to compare with the results obtained by the traditional Galerkin method where only the first mode is considered. Taking the dynamic responses obtained numerically from the model with threedegreesoffreedom as a reference, it can be concluded that the nonlinear Galerkin method has higher accuracy in comparison with the traditional Galerkin method.

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宋敉淘,曹登庆.应用非线性Galerkin方法求解微梁的动态响应[J].动力学与控制学报,2009,7(3):205~211; Song Mitao, Cao Dengqing. Dynamical responses of microbeams using nonlinear galerkin method[J]. Journal of Dynamics and Control,2009,7(3):205-211.

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  • 收稿日期:2008-07-28
  • 最后修改日期:2008-12-15
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