NDLI: Complexification-averaging method via the averaged Lagrangian

Content Provider	Springer Nature Link
Author	Zhang, Xinhua
Copyright Year	2013
Abstract	In this paper, the complexification-averaging (CX-A) method for multi-DOF nonlinear vibratory systems is rederived in a new way based upon the averaged Lagrangian. The complex variables are introduced to represent the original displacements and velocities, and then the fast–slow decomposition of the complex variables is made. The time averaging of the Lagrangian over the fast variables is performed. Two different expressions for the kinetic energy are presented, and this results in two schemes for deriving the governing equations of the slow variables. For the scheme I, through the order analysis of the derivatives of the slow variables, it is shown that the second-order terms appeared in the averaged Lagrangian can be omitted, and thus a reduced averaged Lagrangian is obtained. Via the reduced averaged Lagrangian, the corresponding Lagrangian equations are derived. For the scheme II, through time averaging, the averaged Lagrangian is obtained, and then the corresponding equations for the slow variables can be obtained. Finally, two nonlinear vibratory systems with two-DOF and four-DOF, respectively, are given as examples to illustrate the new procedure for the CX-A method. The loci of nonlinear normal modes on the potential surface are studied in the first example, and the frequency-energy plot is investigated in the second example.
Starting Page	429
Ending Page	437
Page Count	9
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	75
Issue Number	3
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2013-09-25
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Complexification-averaging method Averaged Lagrangian Lagrangian equation Fast–slow partition Loci of nonlinear normal mode Frequency-energy plot Vibration, Dynamical Systems, Control Mechanics Mechanical Engineering Automotive Engineering
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

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