Nonlinear Vibration Characteristics Analysis of a Cantilever Beam with Slant Crack
MA Hui1, ZENG Jin1, LANG Ziqiang2, TAI Xingyu3
1. Northeastern University, School of Mechanical Engineering & Automation, Shenyang 110819, China;
2. The University of Sheffield, Department of Automatic Control and Systems Engineering, Sheffield S1 3JD, UK;
3. Shenyang Blower Works Group Corporation, Shenyang, 110869, PR China
Aiming at the slant crack fault of cantilever bar or beam, this paper analyzes the nonlinear dynamic characteristics of a cantilever beam with slant crack based on ANSYS software. Assuming that only bending vibration of the cantilever beam is considered, a finite element (FE) model is established by using mixed elements. In the model, the plane elements (Plane 183) are adopted in the crack region and the contact elements are used to simulate the breathing effect of the slant crack. Moreover, beam elements are utilized in the regions which are far away from the crack region. By comparing with the FE model composed by full plane elements, the accuracy of the developed model is verified firstly, in addition, the calculation efficiency is also evaluated. Finally, the effects of crack angles and the amplitude of excitation force on the vibration responses of the system are also analyzed. The results show that the nonlinear characteristics caused by slant crack are more obvious with the increasing crack angles. Among the vibration responses, the amplitudes of base frequency and its multiple frequencies has a linear relationship with the amplitudes of excitation force.
马辉1,?，曾劲1，郎自强2, 太兴宇3. 斜裂纹悬臂梁非线性振动特性分析[J]. 振动与冲击, 2016, 35(12): 86-91.
MA Hui1, ZENG Jin1, LANG Ziqiang2, TAI Xingyu3. Nonlinear Vibration Characteristics Analysis of a Cantilever Beam with Slant Crack. JOURNAL OF VIBRATION AND SHOCK, 2016, 35(12): 86-91.
[1] Volovoi V V, Hodges D H. Assessment of beam modeling methods for rotor blade applications [J]. Mathematical and Computer Modelling, 2001, 33: 1099-1112.
[2] Dimarogonas A D. Vibration of cracked structures: a state of the art review [J]. Engineering Fracture Mechanics, 1996, 55(5): 831-857.
[3] Bovsunovsky A, Surace C. Non-linearities in the vibration of elastic structures with a closing crack: A state of the art review [J]. Mechanical Systems and Signal Processing, DOI: http://dx.doi.org/10.1016/j.ymssp.2015.01.021, 2015.
[4] Ghondros T G, Dimarogonas A D. Vibration of a cracked cantilever beam [J]. ASME Journal of Vibration and Acoustics, 1998, 120(3): 742-746.
[5] Ghondros T G, Dimarogonas A D, J. Yao. A continuous cracked beam vibration theory [J]. Journal of Sound and Vibration, 1998: 215(1): 17-34.
[6] 李帅. 含呼吸式裂纹的叶盘系统动态特性研究[D]. 长沙: 中南大学, 2012.
Li Shuai. Study of dynamic characteristics of bladed disk with breathing crack [D]. Changsha: Central South University, 2012.
[7] 胡家顺, 冯新, 李昕, 等. 裂纹梁振动分析和裂纹识别方法研究进展[J]. 振动与冲击, 2007, 26(11): 146-152.
Hu Jiashun, Feng Xin, Li Xin, et al. State-of-art of vibration analysis and crack identification of cracked beams[J]. Journal of Vibration and Shock, 2007, 26(11): 146-152.
[8] Ghondros T G, Dimarogonas A D, J. Yao. Vibration of a beam with a breathing crack [J]. Journal of Sound and Vibration, 2001, 239(1): 57-67.
[9] Andreaus U, Casini P, Vestroni F. Non-linear dynamics of a cracked cantilever beam under harmonic excitation [J]. International Journal of Non-linear Mechanics, 2007, 42: 566-575.
[10] Andreaus U, Baragatti P. Cracked beam identification by numerically analysing the nonlinear behaviour of the harmonically forced response [J]. Journal of Sound and Vibration, 2011, 330: 721-742.
[11] 胡家顺, 冯新, 周晶. 呼吸裂纹梁非线性动力学特性研究[J]. 振动与冲击, 2009, 28(1): 76-80.
Hu Jiashun, Feng Xin, Zhou Jing. Study on nonlinear dynamic response of a beam with a breathing crack [J]. Journal of Vibration and Shock, 2009, 28(1): 76-80.
[12] 崔韦, 王建军. 共振条件下的裂纹梁振动与裂纹扩展耦合分析[J]. 推进技术, 2014, 35(10): 1404-1411.
Cui Wei, Wang Jianjun. Coupling analysis of vibration and crack propagation for a cracked beam at resonant state [J]. Journal of Propulsion Technology, 2014, 35(10): 1404-1411.
[13] Bouboulas A S, Anifantis N K, Georgantzinos S K. Vibration Analysis of Cracked Beams Using the Finite Element Method[M]. INTECH Open Access Publisher, 2012.
[14] Qin F, Chen L, Li Y, et al. Fundamental frequencies of turbine blades with geometry mismatch in fir-tree attachments [J]. ASME Journal of Turbomachinery, 2006, 128: 512-516.
[15] Ma H, Shi C Y, Han Q K, et al. Fixed-point rubbing fault characteristic analysis of a rotor system based on contact theory [J]. Mechanical Systems and Signal Processing, 2013, 38(1): 137-153.
[16] Ma H, Zhao Q B, Zhao X Y, et al. Dynamic characteristics analysis of a rotor-stator system under different rubbing forms [J]. Applied Mathematical Modelling, 2015, 39(8): 2392-2408.
