Response of fractional oscillators with viscoelastic term under random excitation
Response of fractional oscillators with viscoelastic term under random excitation
复制标题
随机激励下具有粘弹性项的分数振子的响应
DOI：
10.1115/1.4026068
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发表时间：
2014-07
期刊：
影响因子：
--
通讯作者：
Liu Di
中科院分区：
文献类型：
--
作者：
Xu Yong;Li Yongge;Liu Di
本文考虑了窄带噪声作用下的分数阶阻尼粘弹性系统。在回顾Lindstedt-Poincaré（LP）方法和多尺度方法的基础上，提出了一种获得二阶近似解析解的新方法，并从理论上推导了确定性情况下的频率-振幅响应方程和随机情况下的一阶和二阶稳态矩。数值仿真验证了该方法的有效性，仿真结果与理论分析结果吻合较好。特别地，我们发现新方法对于强非线性系统是有效的。此外，还研究了分数阶数和粘弹性参数对系统的影响，结果表明：在固定点处，系统的稳态振幅随分数阶数和粘弹性参数的增加而增加。最后，利用接收到的Fokker-Planck-Kolmogorov（FPK）方程研究了随机跳变现象，计算了概率密度函数的稳态解，其形状随噪声强度的增加由单峰变为双峰，并且随机跳变现象与频幅响应方程的解一致。
A system with fractional damping and a viscoelastic term subject to narrow-band noise is considered in this paper. Based on the revisit of the Lindstedt–Poincaré (LP) and multiple scales method, we present a new procedure to obtain the second-order approximate analytical solution, and then the frequency–amplitude response equations in the deterministic case and the first- and second-order steady-state moments in the stochastic case are derived theoretically. Numerical simulation is applied to verify the effectiveness of the proposed method, which shows good agreement with the analytical results. Specially, we find that the new method is valid for strongly nonlinear systems. In addition, the influences of fractional order and the viscoelastic parameter on the system are explored, and the results indicate that the steady-state amplitude will increase at a fixed point with the increase of fractional order or viscoelastic parameter. At last, stochastic jump is investigated via the received Fokker–Planck–Kolmogorov (FPK) equation to compute the stationary solution of probability density functions with its shape changing from one peak to two peaks with the increase of noise intensity, and the phenomena of stochastic jump is consistent with the solution of frequency–amplitude response equations.
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影响因子：
5.6
作者：
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通讯作者：
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作者：
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DOI：
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发表时间：
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影响因子：
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通讯作者：
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DOI：
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发表时间：
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期刊：
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DOI：
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发表时间：
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期刊：
IEEE Transactions on Systems, Man, and Cybernetics
影响因子：
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作者：
A. H. Nayfeh;Vimal Singh
通讯作者：
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