On the detection of artifacts in Harmonic Balance solutions of nonlinear oscillators
On the detection of artifacts in Harmonic Balance solutions of nonlinear oscillators
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DOI：
10.1016/j.apm.2018.08.013
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发表时间：
2019
影响因子：
5
通讯作者：
U. Wagner;L. Lentz
中科院分区：
文献类型：
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作者：
U. Wagner;L. Lentz
谐波平衡法是非线性动力学中一种非常流行的半解析方法。它很容易应用，并且众所周知，在许多例子中产生了良好的结果。考虑到忽略的项，添加误差标准允许对结果进行评估。查看因此确定的增加ansatz阶数的错误，可以评估解是否真的存在或是人工产物。对于低误差解，还进行了稳定性分析，将解分为三类，即大误差解、低误差稳定解和低误差不稳定解。文中所考虑的例子是经典Duffing振子和具有非线性阻尼和激励的扩展Duffing振子。与数值积分相比，该方法能更快地计算已有的多个解及其性质。
Harmonic Balance is a very popular semi-analytic method in nonlinear dynamics. It is easy to apply and is known to produce good results for numerous examples. Adding an error criterion taking into account the neglected terms allows an evaluation of the results. Looking on the therefore determined error for increasing ansatz orders, it can be evaluated whether a solution really exists or is an artifact. For the low-error solutions additionally a stability analysis is performed which allows the classification of the solutions in three types, namely in large error solutions, low error stable solutions and low error unstable solution. Examples considered in this paper are the classical Duffing oscillator and an extended Duffing oscillator with nonlinear damping and excitation. Compared to numerical integration, the proposed procedure offers a faster calculation of existing multiple solutions and their character.