Publisher : The Korean Society for Noise and Vibration Engineering
DOI : 10.5050/KSNVE.2016.26.3.281
Title & Authors
Modal Analysis for the Rotating Cantilever Beam with a Tip Mass Considering the Geometric Nonlinearity Kim, Hyoungrae; Chung, Jintai;
In this paper, a new dynamic model for modal analysis of a rotating cantilever beam with a tip-mass is developed. The nonlinear strain such as von Karman type and the corresponding linearized stress are used to consider the geometric nonlinearity, and Euler-Bernoulli beam theory is applied in the present model. The nonlinear equations of motion and the associated boundary conditions which include the inertia of the tip-mass are derived through Hamilton's principle. In order to investigate modal characteristics of the present model, the linearized equations of motion in the neighborhood of the equilibrium position are obtained by using perturbation technique to the nonlinear equations. Since the effect of the tip-mass is considered to the boundary condition of the flexible beam, weak forms are used to discretize the linearized equations. Compared with equations related to stiffening effect due to centrifugal force of the present and the previous model, the present model predicts the dynamic characteristic more precisely than the another model. As a result, the difference of natural frequencies loci between two models become larger as the rotating speed increases. In addition, we observed that the mode veering phenomenon occurs at the certain rotating speed.
Hoa, S. V., 1979, Vibration of a Rotating Beam with Tip Mass, Journal of Sound and Vibration, Vol. 67, No. 3, pp. 369~381.
Huang, C. L., Lin, W. Y. and Hsiao, K. M., 2010, Free Vibration Analysis of Rotating Euler Beams at High Angular Velocity, Vol. 88, No. 17-18, pp. 991-1001.
Banerjee, J. R. and Kennedy, D., 2014, Dynamic Stiffness Method for In-plane Free Vibration of Rotating Beams Including Coriolis Effects, Vol. 333, No. 26, pp. 7299-7312.
Kim, M. and Kang, N., 2010, Vibration Analysis of a Rotating Cantilever Beam with Tip Mass using DTM, Transactions of the Korean Society for Noise and Vibration Engineering, Vol. 20, No. 11, pp. 1058~1063.
Meirovitch, L., 1967, Analytical Methods in Vibrations, Macmillan Publishing Co., Inc., New York, Chap. 10.
Kane, T. R., Ryan, R. R. and Banerjee, A. K., 1987, Dynamics of a Cantilever Beam Attached to a Moving Base, Journal of Guidance, Control, and Dynamics, Vol. 10, No. 2, pp. 139~151.
Yoo, H. H., Ryan, R. R. and Scott, R. A., 1995, Dynamics of Flexible Beams Undergoing Overall Motions, Journal of Sound and Vibration, Vol. 181, No. 2, pp. 261~278.
Yoo, H. H., Seo, S. and Huh, K., 2002, The Effect of a Concentrated Mass on the Modal Characteristics of a Rotating Cantilever Beam, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering, Vol. 216, No. 2, pp. 151~163.
Lee, K. B. and Yoo, H. H., 2013, Free Vibration Analysis of a Rotating Cantilever Beam Made-up of Functionally Graded Materials, Transactions of the Korean Society for Noise and Vibration Engineering, Vol. 23, No. 8, pp. 742~751.
Kwon, S. and Yoo, H. H., 2015, Mode and Transient Response Localization Occurred in Rotating Multi-Packet Blade Systems due to Random Mistuning, International Journal of Precision Engineering and Manufacturing, Vol. 16, No. 10, pp. 2063~2071.
Simo, J. C. and Vu-quoc, L., 1987, The Role of Non-linear Theories in Transient Dynamic Analysis of Flexible Structures, Journal of Sound and Vibration, Vol. 119, No. 3, pp. 487~508.
Pesheck, E., Pierre, C. and Shaw, S. W., 2001, Accurate Reduced-order Models for a Simple Rotor Blade Model Using Nonlinear Normal Modes, Mathematical and Computer Modelling, Vol. 33, No. 10-11, pp. 1085~1097.
Sharf, I., 1996, Geometrically Non-linear Beam Element for Dynamics Simulation of Multibody Systems, Internationals Journal for Numerical Methods in Engineering, Vol. 39, No. 5, pp. 763~786.
Wang, F. X., 2013, Model Reduction with Geometric Stiffening Nonlinearities for Dynamic Simulations of Multibody Systems, International Journal of Structural Stability and Dynamics, Vol. 13, No. 8, pp. 1~27.
Kim, H., Yoo, H. H. and Chung, J., 2013, Dynamic Model for Free Vibration and Response Analysis of Rotating Beams, Journal of Sound and Vibration, Vol. 332, No. 22, pp. 5917~5928.