Second order averaging and bifurcations to subharmonics in duffing's equation
Second order averaging and bifurcations to subharmonics in duffing's equation
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DOI：
10.1016/s0022-460x(81)80030-2
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发表时间：
1981-09
影响因子：
4.7
通讯作者：
C. Holmes;P. J. Holmes
中科院分区：
文献类型：
--
作者：
C. Holmes;P. J. Holmes
随着激励幅值、频率和阻尼的变化，负线性刚度Duffing方程的周期运动和平衡解会发生演化、失稳和倍周期分叉。对于周期二的分叉，根据激励频率的不同，可以是亚临界的，也可以是超临界的。分析是通过平均法进行的，为了保留重要的非线性效应，必须将平均化处理到二阶。对高次次谐波作了一些评论。
Periodic motions near and equilibrium solution of Duffing's equation with negative linear stiffness can evolve, lose their stability, and undergo period doubling bifurcations as excitation amplitude, frequency and damping are varied. For bifurcations to period two it is shown that these can be either sub- or supercritical, depending upon the excitation frequency. The analysis is carried out by the averaging method, and, to retain important non-linear effects, averaging must be taken to second order. Some remarks on higher order subharmonics are made.