Error Estimates for Harmonic-Balance Solutions of Nonlinear Dynamical Systems

Error Estimates for Harmonic-Balance Solutions of Nonlinear Dynamical Systems
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非线性动力系统谐波平衡解的误差估计

DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
M. Leamy
M. Leamy
中科院分区：
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文献类型：
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作者：
A. Ferri;M. Leamy

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谐波平衡法通常用于线性和非线性系统，以近似其对周期激励的稳态响应。本文提出了谐波平衡法的后验误差估计。误差估计的性能研究使用两个例子：Duffing方程具有光滑，非线性和库仑阻尼系统具有不连续的非线性。误差估计是非常容易计算，并与时间积分得到的RMS误差进行比较。结果发现，误差估计与均方根误差相比，特别是对于Duffing方程。
The harmonic balance method is commonly applied to linear and nonlinear systems to approximate their steady-state response to periodic excitation. This paper presents an a posteriori error estimate for harmonic balance solution techniques. The performance of the error estimate is studied using two examples: a Duffing equation having a smooth, cubictype nonlinearity and a Coulomb-damped system having a discontinuous nonlinearity. The error estimate is shown to be very easy to calculate and is compared with RMS errors obtained from time integration. It is found that the error estimate compares favorably with the RMS error, especially for the Duffing equation.