POD降阶方法在含局部非线性悬臂梁中的适应性分析

Adaptability analysis of reduction model of a nonlinearbeam based on POD method

在非线性结构的振动控制设计中结构模型的阶数不宜过高,为此,本研究以含局部非线性的悬臂梁为研究对象,开展影响POD降阶方法所得低阶模型精度的研究。着重分析了非线性强弱、降阶模型的阶数、POD模态获取源信号的激振类型、响应信号的采样频率和响应信号采样时长等因素对降阶模型响应预测精度的影响。结果表明:对于强非线性的局部非线性悬臂梁系统,POD方法同样适用;在选取源信号的激振类型时,应避免选取脉冲激励信号;响应的采样频率与时长不一定要选取过大。最后,提出了一种针对含有噪声信号应用POD方法的解决方案,可为工程应用提供有益的参考。

In the vibration control design of nonlinear structures,the order of the structure model should not be too high.For this reason,this paper takes the cantilever beam with local nonlinearity as the research object to carry out the research on the low-order model accuracy obtained by the POD reduction method.The analysis focuses on the influence of factors such as the strength of nonlinearity,the order of the reduced-order model,the excitation type of the source signal obtained by the POD mode,the sampling frequency of the response signal and the sampling duration of the response signal and other factors on the response prediction accuracy of the reduced-order model.For strongly nonlinear local nonlinear cantilever beam systems,the POD method is also applicable.When selecting the excitation type of the source signal,it is necessary to avoid the conclusion that the sampling frequency and duration of the pulse excitation signal and response selected should not be too large.Finally,a solution for applying the POD method to noisy signals is proposed,which can provide a useful reference for engineering applications.