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 引用本文: 何昊南, 于开平, 唐宏, 李金泽, 周前坤, 张晓蕾. 有间隙折叠舵面的振动实验与非线性建模研究[J]. 力学学报, 2019, 51(5): 1476-1488.
He Haonan, Yu Kaiping, Tang Hong, Li Jinze, Zhou Qiankun, Zhang Xiaolei. VIBRATION EXPERIMENT AND NONLINEAR MODELLING RESEARCH ON THE FOLDING FIN WITH FREEPLAY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(5): 1476-1488.
 Citation: He Haonan, Yu Kaiping, Tang Hong, Li Jinze, Zhou Qiankun, Zhang Xiaolei. VIBRATION EXPERIMENT AND NONLINEAR MODELLING RESEARCH ON THE FOLDING FIN WITH FREEPLAY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(5): 1476-1488.

## VIBRATION EXPERIMENT AND NONLINEAR MODELLING RESEARCH ON THE FOLDING FIN WITH FREEPLAY

• 摘要: 针对折叠舵面内、外舵铰接处存在的间隙对地面振动响应的影响及间隙处的非线性建模方法展开研究.消除间隙,利用锤击法对线性折叠舵面进行模态实验,得到了前五阶模态参数;打开间隙,进行振动台扫频基础激励,实验结果表明间隙的存在会使结构的动力学响应产生非线性现象,如正反向扫描差异、跳跃、多谐波及频率漂移.非线性的影响主要体现在一阶弯曲模态上,激励量级的增大和间隙的减小均会使基频增大,且逐渐趋向于无间隙的结果,但对第二阶扭转模态的影响与第一阶相比较小.建立了折叠舵面的有限元模型. 提出了一种适用于具有集中非线性的折叠机构的模型缩减方法,并对舵面进行了模态缩减.根据Hertz接触理论,用具有线性和3/2次刚度组合形式的非线性扭转弹簧来模拟铰接处的间隙和接触.通过比较锤击实验与数值计算得到的前四阶频率和振型对模型的线性部分进行验证.通过Bathe两子步隐式复合算法计算基础激励下非线性结构的动力学响应,得到的传递函数可以模拟实验中出现的频率变化特征,验证了连接处非线性建模方法的合理性.

Abstract: The influence of the freeplay on ground vibration responses of the folding fin and the nonlinear modelling of the freeplay, which exists in the joints connecting the inboard fin and the outboard fin, are studied in this paper. The first five modal parameters are obtained by hammer tests of the linear structure without freeplay. The sweep base excitation is then applied to the root-fixed folding fin with adjustable freeplay. The experimental results show that the existence of freeplay can lead to some nonlinear phenomena of the structure, such as a forward and backward sweep difference, a jump, multi harmonics, and a frequency shift. This kind of lumped nonlinearity has a huge influence on the first bending mode. For example, both the increase of the excitation magnitude and the decrease of the angle of freeplay will raise the fundamental frequency which gradually tends to the result of the linear structure without freeplay, but they have little effects on the second torsion mode compared with those on the first bending mode. The finite element model of the folding fin is established in the numerical simulation analysis and it is reduced by the developed model reduction method which is suitable for similar folding structures with lumped nonlinearity. The freeplay and contact of the joints are simulated by nonlinear torsional springs with the combination of linear and 3/2 order stiffness according to the Hertz theory. The linear part of the folding fin is verified firstly via comparing the first four frequencies and mode shapes computed from numerical analysis and the above hammer test. The dynamic response of the nonlinear structure under base excitation is calculated by Bathe's two-step implicit composite algorithm. The transfer functions obtained can simulate the frequency variation characteristics in the experiments, thus verifying the proposed nonlinear modelling method of the joint.

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