An approximate method to compute the nonlinear normal modes and bifurcation by the principle of least action
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An analytical procedure is presented to find approximately the nonlinear normal modes in conservative two-degree-of-freedom system by using the principle of least action and by assuming that the modal curve is straight. The results are compared with those of numerical experiments by utilizing the 4th order Runge-Kutta method, and it is found that there are good agreements between them. By utilizing this procedure, it is demnostrated to compute the normal modes which are analytically extended from the linearized modes and to find the generically or non-generically bifurcated modes which do not have any counterpart in the linear theory.
Key WordsNonlinear Normal Mode Generic Bifurcation Non-Generic Bifurcation Modal Curve Homogeneous System Principle of Least Action
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- Ann, Y.W., 1985, “An Approximate Method to find the Nolinear Normal Mode by Using the Least Action Principle,” M.S. Thesis, Inha Univ.Google Scholar
- Grandshteyn, I.S. and Ryzhik, I.M., 1980, Table of Integrals, Series, and Products, Academic Press, New York.Google Scholar
- Meirovitch, L., 1970, Methods of Analytical Dynamics, McGraw-Hill, Inc.Google Scholar
- Pak, C.H. and Rosenberg, R.M., 1966, “On the Existence of Normal Mode Vibrations in Nonlinear Systems,” Q. Appl. Mech., Vol. 24, pp. 177–193.Google Scholar
- Pak, C.H. and Park, S.J., 1988, “On the Modal Curves of Nonlinear Normal Modes,” KSME Journal, Vol 2, No.2, pp. 87–93.Google Scholar
- Rosenberg, R.M., 1960, “Normal Modes of Nonlinear Dual-Mass systems,” J. of Appl. Mech. ASME, pp. 263–268.Google Scholar
- Rosenberg, R.M., 1961, “On Normal Vibrations of a General Class of Nonlinear Dual-Mass Systems,” J. of Appl. Mech., ASME, pp.275–283.Google Scholar
- Rosenberg, R.M., 1966, “On Nonlinear Vibrations of Systems with Many Degrees of Freedom,” Academic Press, Appl. Mech. vol. 9, pp. 155–242.Google Scholar
- Roenberg, R.M., 1977, Analytical Dynamics of Discrete Systems, Plenum Press, New York.Google Scholar