The multi-level residue harmonic balance solutions of multi-mode nonlinearly vibrating beams on an elastic foundation
Author(s)
Author(s)
Hasan, A. S. M. Z.
Lee, Y.-Y.
Date Issued
2016
Publisher
Sage Publications
Journal
Journal of Vibration and Control
Volume
22
Issue
14
Start page
3218
End page
3235
Abstract
In this paper, an efficient analytical solution method, namely, multi-level residue harmonic balance, is introduced and developed for the nonlinear vibrations of multi-mode flexible beams on an elastic foundation subject to external harmonic excitation. The main advantage of this solution method is that only one set of nonlinear algebraic equations is generated in the zero level solution procedure while the higher level solutions for any desired accuracy can be obtained by solving a set of linear algebraic equations. In other words, the computation effort to find more accurate nonlinear solutions is much less. In this paper, a multi-mode formulation, which represents the nonlinear beam vibration, is derived and set up. Then, the solution procedures are developed for obtaining the nonlinear multi-mode solution. The results from the multi-level residue harmonic balance method agree well with those from a numerical integration method. The effects of various parameters such as vibration amplitude, foundation modulus coefficient, damping factor and excitation level etc., on the nonlinear behaviors are examined. A convergence study is also performed to verify the solutions. The stability analysis is conducted using the virtue of Floquet theory and steady-state solutions are investigated.
SFU Affiliated Publication
No
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