Theoretical and experimental study on free vibration of cantilever tapered beam base on new modal function

被引：0
|
作者：
Zhou K.-T. [1 ,2 ]
Yang T. [1 ]
Ge G. [1 ]
机构：
[1] School of Mechanical Engineering, Tianjin Polytechnic University, Tianjin
[2] Engineering Training Center, Tianjin University of Technology, Tianjin
来源：
Yang, Tao (yangtao@tjpu.edu.cn) | 1600年 / Tsinghua University卷 / 37期
关键词：
Energy balance method; Modal function; Mode experiment; Nonlinearity; Tapered cantilever beam;
D O I：
10.6052/j.issn.1000-4750.2019.05.0260
中图分类号：
学科分类号：
摘要：
A new type of modal function which is a linear combination of hypergeometric and Meijer-G functions is proposed for tapered cantilever beam vibration analysis. This modal function has advantages of real coefficients, accuracy and non-approximation. Two steps are carried out to verify the effectiveness and accuracy of this modal function. In the first step, the fundamental frequency as well as the shape of the modal function is validated. In the second step, the modal function is used to perform nonlinear vibration analysis, and its effectiveness is investigated. A comparison is made among the theoretical prediction, finite element method, finite element semi-analytical method and the experimental results, which demonstrates the accuracy of the calculated frequency and the modal shape, respectively. Subsequently, substituting the modal function into the governing equation of the vibrating tapered cantilever after the Galerkin procedure, the curvature nonlinear coefficient and the inertia nonlinear coefficient are obtained. The frequency-amplitude relationship is deduced by the energy balance method which has been examined by the experiment. The results show that the displacement-time relationship of a selected point on the beam which is detected by a laser sensor perfectively coincides with the theoretical prediction which is given by the modal function and the frequency-amplitude relationship. The results show the effectiveness of the presented method in predicting the deformation of the tapered cantilever during nonlinear vibration. © 2020, Engineering Mechanics Press. All right reserved.
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页码：28 / 35
页数：7
相关论文
共 17 条
  • [11] Pan D., Lou M., Semi-analytic solution of dynamic characteristics of non-prismatic Timoshenko simply supported beams, Engineering Mechanics, 26, 8, pp. 6-9, (2009)
  • [12] Taha M.H., Abohadima S., Mathematical model for vibrations of non-uniform flexural beams, Engineering Mechanics, 15, 1, pp. 3-11, (2008)
  • [13] Duan W.H., Quek S.T., Wang Q., Generalized hypergeometric function solutions for transverse vibration of a class of non-uniform annular plates, Journal of Sound and Vibration, 287, 4-5, pp. 785-807, (2005)
  • [14] Silva C.J., Daqaq M.F., Nonlinear flexural response of a slender cantilever beam of constant thickness and linearly-varying width to a primary resonance excitation, Journal of Sound and Vibration, 389, pp. 438-453, (2017)
  • [15] Nayfeh A.H., Pai P.F., Linear and Nonlinear Structural Mechanics, (2004)
  • [16] Silva C.J., Daqaq M.F., On estimating the effective nonlinearity of structural modes using approximate modal shapes, Journal of Vibration and Control, 20, 11, pp. 1751-1764, (2014)
  • [17] He J.H., Preliminary report on the energy balance for nonlinear oscillation, Mechanics Research Communications, 29, 1-2, pp. 107-111, (2002)
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