A MODIFIED MODEL FOR THE VIBRATIONS OF A TWO-DEGREE-OF-FREEDOM HYDROFOIL-ROD SYSTEM CONSIDERING 3D EFFECT

Wang Renfeng; You Yunxiang; Chen Ke; Duan Jinlong

doi:10.6052/0459-1879-17-042

Volume 49 Issue 4

Turn off MathJax

Article Contents

Abstract

References

Chinese Journal of Theoretical and Applied Mechanics > 2017 > 49(4): 920-928. > DOI: 10.6052/0459-1879-17-042 CSTR: 32045.14.0459-1879-17-042

Wang Renfeng, You Yunxiang, Chen Ke, Duan Jinlong. A MODIFIED MODEL FOR THE VIBRATIONS OF A TWO-DEGREE-OF-FREEDOM HYDROFOIL-ROD SYSTEM CONSIDERING 3D EFFECT[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(4): 920-928. DOI: 10.6052/0459-1879-17-042

Citation:

PDF (1909 KB)

A MODIFIED MODEL FOR THE VIBRATIONS OF A TWO-DEGREE-OF-FREEDOM HYDROFOIL-ROD SYSTEM CONSIDERING 3D EFFECT

Wang Renfeng^{*, †},
You Yunxiang^{*, †, ,},
Chen Ke^{*, †},
Duan Jinlong^{*, †}

*.
Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai Jiao Tong University, Shanghai 200240, China
†.
State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

Received Date: February 16, 2017
Available Online: April 26, 2017

Graphical Abstract

Abstract

Abstract

The classical Theodorsen equation for the motions of two-degree-of-freedom foils is modified with associated mass parameter ε and circulation parameter δ by considering the 3D effect of low aspect ratios, and the comparison between the calculation and classical experimental values demonstrates the modified equation is effective. According to the shape of V-g curve which varies with the mass ratio μ, two types (Type Ⅰ and Type Ⅱ) of flutter are defined. The influences of the bracing stiffness k_h, the torsional stiffness k_α, the locations of the center of gravity x_α and the angle of attack AOA on the characteristics of the flutter of a hydrofoil-rod system have been analyzed, and the comparison with experimental values shows that the numerical results are reasonable. The calculation shows the significant impacts of k_h, k_α, x_α and AOA on the flutter speed V_F. When the values of the parameters are in certain ranges respectively, flutter Type Ⅱ may occur. Specifically, a larger kh or a smaller AOA leads into a larger V_F. While, V_F first increases and then decreases with the increase of k α or x_α. Moreover, V_F only exists in a relatively narrow range of x_α, which reflects that the vibration pattern of the hydrofoil-rod system is high sensitive to x_α. Therefore, the probability of the occurrence of flutter can be reduced by avoiding the narrow range of x_α during design phase. On the other hand, according to the slow reaction of V_F to k_h and k_α, once flutter occurs, flutter can be eliminated by locking the rigid shaft with hydraulic devices.
- two-degree-of-freedom system,
- flutter,
- low mass ratio,
- experiment

FullText(HTML)

References (30)

References

[1]	赵永辉.气动弹性力学与控制.北京:科学出版社, 2007:120-121 Zhao Yonghui. Mechanics and Control of Aeroelasticity. Beijing:China Science Publishing & Media Ltd, 2007:120-121
[2]	张博, 王国玉, 黄彪等.绕水翼空化非定常动力特性的时频分析.实验流体力学, 2009, 23(3):44-49 http://www.cnki.com.cn/Article/CJFDTOTAL-LTLC200903009.htm Zhang Bo, Wang Guoyu, Huang Biao, et al. Unsteady dynamics of cavitating flows around a hydrofoil. Journal of Experiments in Fluid Mechanics, 2009, 23(3):44-49 http://www.cnki.com.cn/Article/CJFDTOTAL-LTLC200903009.htm
[3]	史爱明, 杨永年, 叶正寅.带结构刚度非线性的超音速弹翼颤振分析方法研究.西北工业大学学报, 2003, 21(4):481-485 http://www.cnki.com.cn/Article/CJFDTOTAL-XBGD200304027.htm Shi Aiming, Yang Yongnian, Ye Zhengyin. An investigation of flutter characteristics of wing with nonlinear stiffness in supersonic flow. Journal of Northwestern Polytechnical University, 2003, 21(4):481-485 http://www.cnki.com.cn/Article/CJFDTOTAL-XBGD200304027.htm
[4]	张琪昌, 刘海英, 任爱娣.非线性机翼极限环颤振的研究.空气动力学学报, 2004, 22(3):332-336 http://cdmd.cnki.com.cn/Article/CDMD-10056-2004125787.htm Zhang Qichang, Liu Haiying, Ren Aidi. The study of limit cycle flutter for airfoil with nonlinearity. Acta Aerodynamica Sinica, 2004, 22(3):332-336 http://cdmd.cnki.com.cn/Article/CDMD-10056-2004125787.htm
[5]	任智毅, 金海波, 丁运亮.大展弦比机翼非线性颤振剪裁设计新方法.动力学与控制学报, 2014(3):283-288 http://www.cnki.com.cn/Article/CJFDTOTAL-DLXK201403019.htm Ren Zhiyi, Jin Haibo, Ding Yunliang. A new method on flutter tailoring techniques of high-aspect-ratio wings. Journal of Dynamics and Control, 2014(3):283-288 http://www.cnki.com.cn/Article/CJFDTOTAL-DLXK201403019.htm
[6]	Jewell DA. Hydroelastic instability of a control surface. Hydromechanics Laboratory, 1961, 1442:1-18 http://dome.mit.edu/handle/1721.3/48945
[7]	宫武旗, 贾博博, 席光.两串列扑翼的相位差对平均推力影响机理的实验研究.力学学报, 2015, 47(6):1017-1025 doi: 10.6052/0459-1879-14-378 Gong Wuqi, Jia Bobo, Xi Guang. An experimental study on the influence of the phase difference on the mean thrust of two plunging wings in tandem. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(6):1017-1025 doi: 10.6052/0459-1879-14-378
[8]	刘强, 刘周, 白鹏等.低雷诺数翼型蒙皮主动振动气动特性及流场结构数值研究.力学学报, 2016, 48(2):269-277 doi: 10.6052/0459-1879-15-188 Liu Qiang, Liu Zhou, Bai Peng, et al. Numerical study about aerodynamic characteristics and flow field structures for a skin of airfoil with active oscillation at low Reynolds number. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(2):269-277 doi: 10.6052/0459-1879-15-188
[9]	高远, 黄彪, 吴钦等.绕水翼空化流动及振动特性的实验研究.力学学报, 2015, 47(6):1009-1016 doi: 10.6052/0459-1879-15-173 Gao Yuan, Huang Biao, Wu Qin, et al. Experimental investigation of the vibration characteristics of hydrofoil in cavitating flow. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(6):1009-1016 doi: 10.6052/0459-1879-15-173
[10]	苏二龙, 罗建军.高超声速飞行器横侧向失稳非线性分岔分析.力学学报, 2016, 48(5):1192-1201 http://lxxb.cstam.org.cn/CN/abstract/abstract146016.shtml Su Erlong, Luo Jianjun. Nonlinear bifurcation analysis of lateral loss of stability for hypersonic vehicle. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(5):1192-1201 http://lxxb.cstam.org.cn/CN/abstract/abstract146016.shtml
[11]	郝子辉, 阎超, 周玲. k-ω-γ模式对转捩影响因素的预测性能研究.力学学报, 2015, 47(2):215-222 http://lxxb.cstam.org.cn/CN/abstract/abstract145231.shtml Hao Zihui, Yan Chao, Zhou Ling. Parametric study of a k-ω-γ model in predicting hypersonic boundary-layer flow transition. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(2):215-222 http://lxxb.cstam.org.cn/CN/abstract/abstract145231.shtml
[12]	张瑜. 二元机翼颤振的复杂响应. [硕士论文]. 成都: 西南交通大学, 2013 http://cdmd.cnki.com.cn/Article/CDMD-10613-1013250684.htm Zhang Y. The complex response of the two degrees freedom airfoil flutter.[Master Thesis]. Chengdu:Southwest Jiaotong University, 2013 http://cdmd.cnki.com.cn/Article/CDMD-10613-1013250684.htm
[13]	Ducoin A, Astolfi JA, Deniset F. Computational and experimental investigation of flow over a transient pitching hydrofoil. European Journal of Mechanics-B/Fluids, 2009, 28(6):728-743 doi: 10.1016/j.euromechflu.2009.06.001
[14]	Ducoin A, Astolfi JA, Sigrist JF. An experimental analysis of fluid structure interaction on a flexible hydrofoil in various flow regimes including cavitating flow. European Journal of Mechanics-B/Fluids, 2012, 36(10):63-74 https://www.researchgate.net/publication/257439194_An_experimental_analysis_of_fluid_structure_interaction_on_a_flexible_hydrofoil_in_various_flow_regimes_including_cavitating_flow
[15]	Ducoin A, Astolfi JA, Gobert ML. An experimental study of boundary-layer transition induced vibrations on a hydrofoil. Journal of Fluids & Structures, 2012, 32(3):1269-1278 https://www.researchgate.net/profile/Marie_Laure_Gobert2/publication/251600891_An_Experimental_Study_of_Boundary-Layer_Transition_Induced_Vibrations_on_a_Hydrofoil/links/550c4e5c0cf2ac2905a3c346/An-Experimental-Study-of-Boundary-Layer-Transition-Induced-Vibrations-on-a-Hydrofoil.pdf?origin=publication_detail
[16]	Liebeck RH. A class of airfoils designed for high lift in incompressible flow. Journal of Aircraft, 1973, 10(10):610-617 doi: 10.2514/3.60268
[17]	Liebeck RH. Exact method of designing airfoils with given velocity distribution in incompressible flow. Journal of Aircraft, 1975, 12(2):127-127 http://www.worldcat.org/title/exact-method-of-designing-airfoils-with-given-velocity-distribution-in-incompressible-flow-an-extension-of-the-lighthill-and-arlinger-methods/oclc/227699008
[18]	Hsiun CM, Chen C. Improved procedure for the inverse design of two-dimensional airfoils in ground effect. Journal of Aircraft, 2015, 33(6):1094-1100 https://www.researchgate.net/publication/245429542_Improved_procedure_for_the_inverse_design_of_two-dimensional_airfoils_in_ground_effect
[19]	Abdellatif Ö E, Gawad A F A. Experimental, numerical and neural investigation of the aerodynamic characteristics for two-dimensional wings in ground effect//Al-Azhar Engineering International Conference. Cairo, Egypt., 2003
[20]	Jamei S, Maimun A, Mansor S, et al. Numerical investigation on aerodynamic characteristics of a compound wing-in-ground effect. Journal of Aircraft, 2012, 49(5):1297-1305 doi: 10.2514/1.C031627
[21]	Bellamy-Knights PG. A perturbation method for surface singularity solutions for potential flow. Acta Mechanica, 1996, 117(1):81-86 doi: 10.1007/BF01181038
[22]	Lottati I. Flutter and divergence aeroelastic characteristics for composite forward swept cantilevered wing. Journal of Aircraft, 1985, 22(11):1001-1007 doi: 10.2514/3.45238
[23]	Smith EC, Chopra I. Formulation and evaluation of an analytical model for composite box-beams. Journal of the American Helicopter Society, 1990, 36(3):23-35 https://www.researchgate.net/publication/4664436_Formulation_and_Evaluation_of_An_Analytical_Model_for_Composite_Box-Beams
[24]	Wu X, Sun CT. Vibration analysis of laminated composite thinwalled beams using finite elements. AIAA Journal, 1991, 29(5):736-742 doi: 10.2514/3.10648
[25]	White MWD, Heppler GR. Vibration modes and frequencies of Timoshenko beams with attached rigid bodies. Journal of Applied Mechanics, 1995, 62(1):193-199 doi: 10.1115/1.2895902
[26]	Banerjee JR. Explicit analytical expressions for frequency equation and mode shapes of composite beams. International Journal of Solids & Structures, 2001, 38(14):2415-2426 http://www.sciencedirect.com/science/article/pii/S0020768300001001
[27]	Song Ö, Librescu L. Free vibration and aeroelastic divergence of aircraft wings modelled as composite thin-walled beams//Structures, Structural Dynamics, and Materials Conference. Baltimore, 1991, 13(13):2623-2627 https://www.researchgate.net/publication/267596466_Aeroelastic_Response_of_an_Aircraft_Wing_Modeled_as_a_Thin-Walled_Composite_Beam
[28]	Georghiades GA, Guo SJ, Banerjee JR. Flutter characteristics of laminated composite wings. Journal of Aircraft, 1996, 33(6):1204-1206 doi: 10.2514/3.47078
[29]	肖清, 谢俊超, 陈东阳.舵系统的颤振计算与分析.中国舰船研究, 2016, 11(5):48-54 http://www.cnki.com.cn/Article/CJFDTOTAL-JCZG201605008.htm Xiao Qing, Xie Junchao, Chen Dongyang. Flutter calculation and analysis of rudder system. Chinese Journal of Ship Research, 2016, 11(5):48-54 http://www.cnki.com.cn/Article/CJFDTOTAL-JCZG201605008.htm
[30]	Chu WH, Abramson HN. Further calculations of the flutter speed of a fully submerged subcavitating hydrofoil. Journal of Hydronautics, 1969, 3(4):168-174 doi: 10.2514/3.62821

[1]	Zhao Feng, Kang Yanhong, Cao Xinyu, Du Wenliao, Cao Shuqian. SINGLE-STAGE AND MULTI-STAGE CONSECUTIVE CONSTANT QUASI-ZERO STIFFNESS FOR VIBRATION ISOLATION AT LOW FREQUENCY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2025, 57(6): 1-16. DOI: 10.6052/0459-1879-25-046
[2]	Chen Shuo, Wang Tai, Su Shuo, Xie Yingbai, Liu Chuntao. EXPERIMENTAL INVESTIGATION ON RISING BEHAVIOR OF SINGLE BUBBLE UNDER THE EFFECT OF UNIFORM DC ELECTRIC FIELD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(10): 2736-2744. DOI: 10.6052/0459-1879-21-352
[3]	Luo Yue, Wang Lei, Dang Leining, Liu Jinbo, Zhang Jun, Liu Sen. ARCJET ABLATION EXPERIMENT TO SIMULATE THE CHELYABINSK ASTEROID ENTRY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1362-1370. DOI: 10.6052/0459-1879-20-081
[4]	Hu Jianjun, Zhu Qing, Wang Meid, Jin Yaolan, Wang Simin, Kong Xiangdong. PIV MEASUREMENT OF CLOSE IMPINGING JET ON FLAT PLATE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1350-1361. DOI: 10.6052/0459-1879-20-142
[5]	Kang Houjun, Guo Tieding, Zhao Yueyu. REVIEW ON NONLINEAR VIBRATION AND MODELING OF LARGE SPAN CABLE-STAYED BRIDGE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(3): 519-535. DOI: 10.6052/0459-1879-15-436
[6]	Guo Wei, Hu Zhiming, Zuo Luo, Gao Shusheng, Yu Rongze, Zeng Bo. GAS DESORPTION-DIFFUSION-SEEPAGE COUPLED EXPERIMENT OF SHALE MATRIX AND MATHEMATIC MODEL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(6): 916-922. DOI: 10.6052/0459-1879-15-068
[7]	Shiping Wang Aman Zhang Yunlong Liu Chao Wang. Experimental study on interaction of inphase bubbles[J]. Chinese Journal of Theoretical and Applied Mechanics, 2012, 44(1): 56-64. DOI: 10.6052/0459-1879-2012-1-lxxb2010-772
[8]	Tong Zhao Longxiang Chen Guoping Cai. Theoretical and experimental studies of H∞ control for a flexible plate with time delay[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(6): 1043-1053. DOI: 10.6052/0459-1879-2011-6-lxxb2011-076
[9]	Longxiang Chen, Guoping Cai. Experimental study on active control of a rotating flexible beam with time delay[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(4): 520-527. DOI: 10.6052/0459-1879-2008-4-2008-010

Cited By

Cited by

Periodical cited type(1)

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. 力学学报. 2019(05): 1476-1488 .

本站查看

Other cited types(2)

Get Citation

PDF

XML

Article Metrics

Article views (1213) PDF downloads (393) Cited by(3)

A MODIFIED MODEL FOR THE VIBRATIONS OF A TWO-DEGREE-OF-FREEDOM HYDROFOIL-ROD SYSTEM CONSIDERING 3D EFFECT