remarks on the ambiguity in multiple scales method 多尺度法二义性的一种解释
automatical solutions of the multiple scales methods 多重尺度法的机器实现
in this paper, the governing differential equations of double pendulum is established with the lagrange methods, the stability margin of corresponding linear equations are obtained by the multiple scale method 采用拉格朗日方法建立参数激励双摆的控制微分方程,通过多尺度法对其线性化方程进行分析,获得稳定性边界。
the investigation of nonlinear oscillation is very important for the nonlinear science . many methods have been advanced to study weakly nonlinear system, including multiple scale method, kbm method, averaging method, and so on 非线性振动理论是非线性科学的一个重要研究内容,对于弱非线性常微分方程控制的动力系统已经有了许多求近似解的方法,如多尺度法、kbm法、平均法等等。
the coupling nonlinear vibration equations involving both the first in-plane and the first out-of-plane modes is generated by using the galerkin method . according to the derived equations, the internal resonance subjected to the in-plane excitation is analyzed by the multiple scale method . the results reveal that the internal resonance of the stay cables posses the characteristics of multiple values and divergence 通过galerkin方法,得到了一个反映面内一阶及面外一阶模态的耦合非线性动力系统,用多尺度法对面内激励下的内共振进行了分析,以实际桥梁拉索为例,得出了拉索模态耦合非线性振动具有多值、分叉等特点,并分析了拉索阻尼对模态耦合内共振的影响。