纤维增强复合薄板非线性内共振表征测试方法研究
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摘要
提出了基于整数倍协调法的纤维增强复合薄板非线性内共振的表征测试方法。首先,为使复合薄板的前两阶固有频率呈现1∶2、1∶3等整数倍关系,基于该方法推导出复合薄板内共振固有频率的显示表达式,预先确定符合内共振形成条件的尺寸参数。然后,阐述了纤维增强复合薄板非线性内共振的表征测试原理,并总结概括出一套合理、规范的测试流程。最后,以TC300碳纤维/树脂基复合薄板作为研究对象,并对其1∶2内共振现象进行了表征测试研究。结果表明,当以第二阶固有频率进行激励时,可发现该类型复合薄板1∶2内共振的非线性振动能量传递行为。但随着激励幅度的增加,其低阶固有频率处的共振幅值相对于高阶固有频率处的共振幅值在逐渐减小,即内共振现象在逐渐减弱,其振动形态逐渐变为单倍周期运动。
The characterization test method of nonlinear internal resonance for a fiber-reinforced composite thin plate(FRCP) based on integer-multiple coordination technique was proposed. Firstly, in order to make the first two natural frequencies of such a composite plate have a ratio of 1∶2 or 1∶3, the explicit expressions of internal resonance frequencies were derived, and the dimension parameters conforming to the formation condition of internal resonance phenomenon were also pre-determined. Then, the characterization test principle of internal resonance of FRCP was illustrated, so that a reasonable and standard test procedure can be summarized. Finally, the TC300 carbon fiber/resin composite plate was taken as a research object, and its 1∶2 internal resonance phenomenon was studied. It has been found that when the composite plate was excited by the second natural frequency, the nonlinear vibration energy transfer behavior can be discovered under 1∶2 internal resonance state. However, with the increase of exciting level, the resonance amplitude at the lower natural frequency would decrease, compared with the one of higher natural frequency, i.e., the internal resonance phenomenon of FRCP was becoming weak, and its vibration motion gradually changed into a singular period.
The characterization test method of nonlinear internal resonance for a fiber-reinforced composite thin plate(FRCP) based on integer-multiple coordination technique was proposed. Firstly, in order to make the first two natural frequencies of such a composite plate have a ratio of 1∶2 or 1∶3, the explicit expressions of internal resonance frequencies were derived, and the dimension parameters conforming to the formation condition of internal resonance phenomenon were also pre-determined. Then, the characterization test principle of internal resonance of FRCP was illustrated, so that a reasonable and standard test procedure can be summarized. Finally, the TC300 carbon fiber/resin composite plate was taken as a research object, and its 1∶2 internal resonance phenomenon was studied. It has been found that when the composite plate was excited by the second natural frequency, the nonlinear vibration energy transfer behavior can be discovered under 1∶2 internal resonance state. However, with the increase of exciting level, the resonance amplitude at the lower natural frequency would decrease, compared with the one of higher natural frequency, i.e., the internal resonance phenomenon of FRCP was becoming weak, and its vibration motion gradually changed into a singular period.
引文
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[3]Sayed M,Kamel M.1∶2 and 1∶3 internal resonance active absorber for non-linear vibrating system[J].hI_Applied Mathematic Modelling,2012,36(1):310-322.
[4]Wang X,Qin Z.Nonlinear modal interactions in composite thin-walled beam structures with simultaneous1:2 internal and 1∶1 external resonances[J].Nonlinear Dynamics,2016,86(2):1381-1405.
[5]Witt A,Gorelik A.Oscillations of an elastic pendulum as an example of the oscillations of two parametrically coupled linear systems[J].Journal of Technical Physics,1933,3(2/3):294-307.
[6]Kyoyul Oh.A theoretical and experimental study of modal interactions in metallic and laminated composite plates[D].Virginia Polytechnic Institute and State University,1994,12.
[7]Abe A,Kobayashi Y,Yamada G.Nonlinear dynamic behaviors of clamped laminated shallow shells with one-to-one internal resonance[J].Journal of Sound and Vibration,2007,304:957-968.
[8]Zhang W,Yao Z,Yao M.Periodic and chaotic dynamics of composite laminated piezoelectric rectangular plate with one-to-two internal resonance[J].Science China Technological Sciences,2009,52(3):731-42.
[9]Sayed M,Mousa A A.Second-order approximation of angle-ply composite laminated thin plate under combined excitations[J].Communications in Nonlinear Science&Numerical Simulation,2012,17(12):5201-5216.
[10]Chen J,Zhang W,Sun M,et al.Parametric study on nonlinear vibration of composite truss core sandwich plate with internal resonance[J].Journal of Mechanical Science&Technology,2016,30(9):4133-4142.
[11]王延庆,梁力,郭星辉,等.基于多元L-P法的复合材料圆柱壳内共振分析[J].工程力学,2012,29(7):29-34.Wang Yanqing,Liang Li,Guo Xinghui,et al.Analysis of internal resonance of composite circular cylindrical shells based on the multidimensional L-P method[J].Engineering Mechanics,2012,29(7):29-34.(in Chinese)
[12]陶斐,冯志华,陈汐,等.复合材料层合板的动力学建模与1∶3内共振[J].噪声与振动控制,2015,35(1):78-82.Tao Fei,Feng Zhihua,Chen Xi,et al.Dynamic modeling and 1∶3 internal resonances of composite laminated plates[J].Noise and Vibration Control,2015,35(1):78-82.(in Chinese)
[13]郝育新,张伟.四边简支FGM矩形板非线性振动中的内共振[J].振动与冲击,2009,28(6):153-154.Hao Yuxin,Zhang Wei.Nonlinear vibration of functionally graded material plate under different internal resonance[J].Journal of Vibration and Shock,2009,28(6):153-154.(in Chinese)
[14]高慧.复合材料悬臂板的非线性研究[D].北京:北京工业大学,2009.Gao Hui.Nonlinear dynamics of composite laminated cantilever plate[D].Beijing:Beijing University of Technology,2009.(in Chinese)
[15]李晖,吴怀帅,薛鹏程,等.纤维增强悬臂复合薄板固有特性分析与验证[J].东北大学学报(自然科学版),2017,38(12):1731-1735.Li Hui,Wu Huaishuai,Xue Pengcheng,et al.Analysis and verification of natural characteristic of fiber-reinforced thin cantilever plate[J].Journal of Northeastern University(Natural Science),2017,38(12):1731-1735.(in Chinese)