亚音速气流中复合材料悬臂板的非线性振动响应研究

刘艮; 张伟

doi:10.6052/0459-1879-18-336

亚音速气流中复合材料悬臂板的非线性振动响应研究

doi: 10.6052/0459-1879-18-336

刘艮,
张伟^2), ,

北京工业大学机械结构非线性振动与强度北京市重点实验室,北京 100124

基金项目: 1) 国家自然科学基金资助项目(11832002).

详细信息

通讯作者:
张伟

中图分类号: O322;
计量
- 文章访问数: 1274
- HTML全文浏览量: 230
- PDF下载量: 288
- 被引次数: 0
出版历程
- 收稿日期: 2018-10-15
- 刊出日期: 2019-05-18

NONLINEAR VIBRATIONS OF COMPOSITE CANTILEVER PLATE IN SUBSONIC AIR FLOW

Gen Liu,
Wei Zhang^{2)
, ,}

Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, Beijing University of Technology, Beijing 100124, China

摘要

摘要: 随着材料科学的发展,越来越多的新型材料应用到了工程实践中.在气流激励的作用下,对于以航空航天工程为背景、采用复合材料的板壳结构的非线性动力学问题仍是动力学领域的研究热点.本文研究了复合材料悬臂板在亚音速气流条件下的非线性振动和响应.根据理想不可压缩流体的流动条件和 Kutta--Joukowski升力定理,基于升力面理论,利用涡格法计算了三维有限长平板机翼上的亚音速气动升力.将亚音速气动力施加到复合材料悬臂板上,利用Hamilton原理,考虑Reddy三阶剪切变形理论并引入冯$\cdot$卡门非线性应变位移关系,建立了有限长平板的非线性动力学微分方程.利用有限元方法考察了不同几何参数下层合板悬臂板的固有特性,通过比较不同材料和几何参数的线性系统的固有频率,得到不同比例的内共振关系.利用Galerkin方法将偏微分方程截断为两自由度非线性常微分方程,在这里考虑了1:2的内部共振关系并利用多尺度法进行了摄动分析.对应多个选取参数,得到了频率响应曲线.结果展示了硬化弹簧型行为和跳跃现象.
- 亚音速气动力 /
- 涡格法 /
- 非线性振动 /
- 硬弹簧特性
Abstract: With the development of materials science, more and more new materials have been applied to engineering practice. Under the action of airflow excitation, the nonlinear dynamics of plate and shell structures with composite materials based on aerospace engineering is still a hot research topic. In this work, the nonlinear vibrations and responses of a laminated composite cantilever plate under subsonic air flow are investigated. According to the flow condition of ideal incompressible fluid and the Kutta--Joukowski lift theorem, the subsonic aerodynamic lift on the three-dimensional finite length flat wing is calculated by using the Vertex Lattice (VL) method, which is applied to the cantilever plate. The finite length flat wing is modeled as a laminated composite cantilever plate based on the Reddy's third-order shear deformation plate theory, moreover the von Karman geometry nonlinearity is introduced. The nonlinear partial differential governing equations of motion for the laminated composite cantilever plate subjected to the subsonic aerodynamic force are established via Hamilton's principle. The partial differential equations are separated into two nonlinear ordinary differential equations via Galerkin method. Through comparing the natural frequencies of the system with different material and geometry parameters, the 1:2 internal resonance is considered here using multiple scales method. Corresponding to several selected parameters, the frequency-response characteristics are obtained. The hardening-spring-type behaviors and jump phenomena are exhibited.
- subsonic air flow /
- vertex lattice method /
- nonlinear vibration /
- hardening-spring-type behaviors

HTML全文

参考文献(1)

[1]	杨执钧, 黄锐, 刘豪杰等. 大长细比导弹的气动弹性降阶模型. 力学学报, 2017, 49(3): 517-527
[1]	(Yang Zhijun, Huang Rui, Liu Haojie, et al.Aeroelastic model of reduced-order for a slender missile. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(3): 517-527 (in Chinese))
[2]	夏巍, 冯浩成. 热过屈曲功能梯度壁板的气动弹性颤振. 力学学报, 2016, 48(3): 609-614
[2]	(Xia Wei, Feng Haocheng.Aeroelastic flutter of post-buckled functionally graded panels. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(3): 609-614 (in Chinese))
[3]	叶柳青, 叶正寅. 激波主导流动下壁板的热气动弹性稳定性理论分析. 力学学报, 2018, 50(2): 221-220
[3]	(Ye Liuqing, Ye Zhengyin.Aeroelastic stability analysis of heated flexible panel in shock-dominated flows. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(2): 221-232 (in Chinese))
[4]	刘人怀, 薛江红. 复合材料层合板壳非线性力学的研究进展. 力学学报, 2017, 49(3): 487-506
[4]	(Liu Renhuai, Xue Jiang, Development of nonlinear mechanics for laminated composite plates and shells. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(3): 487-506 (in Chinese))
[5]	Noor AK, Burton WS.Assessment of shear deformation theories for multilayered composite plates. Applied Mechanics Reviews, 1989, 42(1): 1-13
[6]	Noor AK, Burton WS.Stress and free vibration analyses of multilayered composite plates. Composite Structures, 1989, 11(3): 183-204
[7]	Abe A, Kobayashi Y, Yamada G.Two-mode response of simply supported, rectangular laminated plates. International Journal of Non-Linear Mechanics, 1998, 33(4): 675-690
[8]	Abe A, Kobayashi Y, Yamada G.Three-mode response of simply supported, rectangular laminated plates. JSME International Journal Series C Mechanical Systems, Machine Elements and Manufacturing, 1998, 41(1): 51-59
[9]	Abe A, Kobayashi Y, Yamada G.Analysis of subharmonic resonance of moderately thick antisymmetric angle-ply laminated plates by using method of multiple scales. Journal of Sound and Vibration, 1998, 217(3): 467-484
[10]	Oh K, Nayfeh AH.Nonlinear combination resonances in cantilever composite plates. Nonlinear Dynamics, 1996, 11(2): 143-169
[11]	Pai PF, Nayfeh AH.A nonlinear composite plate theory. Nonlinear Dynamics, 1991, 2(6): 445-477
[12]	Pai PF, Nayfeh AH.A unified nonlinear formulation for plate and shell theories. Nonlinear Dynamics, 1994, 6(4): 459-500
[13]	Librescu L, Reddy JN.A few remarks concerning several refined theories of anisotropic composite laminated plates. International Journal of Engineering Science, 1989, 27(5): 515-527
[14]	Zhang W.Global and chaotic dynamics for a parametrically excited thin plate. Journal of Sound and Vibration, 2001, 239(5): 1013-1036
[15]	Kitipornchai S, Yang J, Liew KM.Semi-analytical solution for nonlinear vibration of laminated FGM plates with geometric imperfections. International Journal of Solids and Structures, 2004, 41(9-10): 2235-2257
[16]	Park T, Lee SY, Seo JW, et al.Structural dynamic behavior of skew sandwich plates with laminated composite faces. Composites Part B$:$ Engineering, 2008, 39(2): 316-326
[17]	Chien RD, Chen CS.Nonlinear vibration of laminated plates on an elastic foundation. Thin-Walled Structures, 2006, 44(8): 852-860
[18]	Singh BN, Lal A, Kumar R.Nonlinear bending response of laminated composite plates on nonlinear elastic foundation with uncertain system properties. Engineering Structures, 2008, 30(4): 1101-1112
[19]	Alijani F, Amabili M, Karagiozis K, et al.Nonlinear vibrations of functionally graded doubly curved shallow shells. Journal of Sound and Vibration, 2011, 330(7): 1432-1454
[20]	Alijani F, Bakhtiari-Nejad F, Amabili M.Nonlinear vibrations of FGM rectangular plates in thermal environments. Nonlinear Dynamics, 2011, 66(3): 251
[21]	Zhang W, Chen J, Zhang YF, et al.Continuous model and nonlinear dynamic responses of circular mesh antenna clamped at one side. Engineering Structures, 2017, 151: 115-135
[22]	Liu T, Zhang W, Wang JF.Nonlinear dynamics of composite laminated circular cylindrical shell clamped along a generatrix and with membranes at both ends. Nonlinear Dynamics, 2017, 90(2): 1393-1417
[23]	Sun Y, Zhang W, Yao MH.Multi-pulse chaotic dynamics of circular mesh antenna with 1: 2 internal resonance. International Journal of Applied Mechanics, 2017, 9(4): 1750060
[24]	Zhang W, Liu T, Xi A, et al.Resonant responses and chaotic dynamics of composite laminated circular cylindrical shell with membranes. Journal of Sound and Vibration, 2018, 423: 65-99
[25]	Dowell EH.Nonlinear oscillations of a fluttering plate. AIAA Journal, 1966, 4(7): 1267-1275
[26]	Dowell EH.Nonlinear oscillations of a fluttering plate. II. AIAA Journal, 1967, 5(10): 1856-1862
[27]	Amabili M, Pa$\imath$doussis MP. Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction. Applied Mechanics Reviews, 2003, 56(4): 349-381
[28]	Singha MK, Ganapathi M.A parametric study on supersonic flutter behavior of laminated composite skew flat panels. Composite Structures, 2005, 69(1): 55-63
[29]	Haddadpour H, Navazi HM, Shadmehri F.Nonlinear oscillations of a fluttering functionally graded plate. Composite Structures, 2007, 79(2): 242-250
[30]	Kuo SY.Flutter of rectangular composite plates with variable fiber pacing. Composite Structures, 2011, 93(10): 2533-2540
[31]	Zhao MH, Zhang W.Nonlinear dynamics of composite laminated cantilever rectangular plate subject to third-order piston aerodynamics. Acta Mechanica, 2014, 225(7): 1985-2004
[32]	Hao YX, Zhang W, Yang J, et al.Nonlinear dynamics of a functionally graded thin simply-supported plate under a hypersonic flow. Mechanics of Advanced Materials and Structures, 2015, 22(8): 619-632
[33]	Drela M. Flight Vehicle Aerodynamics.MIT Press, 2014
[34]	Nayfeh AH, Mook DT. Nonlinear Oscillations. John Wiley & Sons, 2008