Local nonlinear attachments can affect the global dynamics of their linear host structures through modal interactions. This was shown previously in experimental and computational studies of a model airplane with local nonlinear attachments at its wings, under impulsive forcing. Here we study nonlinear modal interactions in the model airplane subject to harmonic excitation. We consider the case of both attachments locked (L-L – baseline linear system), and compare it to two nonlinear cases, i.e., left-wing attachment unlocked (U-L), and both attachments unlocked (U-U). Nonlinear output response functions are used to study the nonlinear modal interactions due to the local attachments in the frequency domain; these are detected only in a certain frequency band. Proper orthogonal decomposition, in conjunction with a weighted modal assurance criterion, are used to quantify these modal interactions. At some frequency bands the nonlinearities facilitate energy transfer to non-resonant airplane modes, despite being widely separated in frequency from resonant modes. Our findings apply to general linear systems with local nonlinear attachments.

局部非线性附件可以通过模态相互作用影响其线性主体结构的整体动力学。先前在对一架带有机翼局部非线性附件的模型飞机进行冲击力的实验和计算研究中已经证明了这一点。在这里，我们研究模型飞机在受到谐波激励的情况下的非线性模态相互作用。我们考虑两个附件均处于锁定状态（LL –基线线性系统）的情况，并将其与两种非线性情况进行比较，即左翼附件未锁定（UL）和两个附件均已解锁（UU）。非线性输出响应函数用于研究由于频域中的局部附件引起的非线性模态相互作用。这些仅在特定频带中被检测到。适当的正交分解，结合加权模态保证准则，用于量化这些模态相互作用。在某些频带上，尽管在频率上与共振模式相距甚远，但非线性仍有助于将能量转移至非共振飞机模式。我们的发现适用于具有局部非线性附件的一般线性系统。