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TECHNICAL PAPERS

Improvement of Nonlinear Single Resonant Mode Method

[+] Author and Article Information
A. S. Nobari, M. Shahramyar

Aerospace Department, Amirkabir University, Tehran, Iran

J. Vib. Acoust 125(1), 59-63 (Jan 06, 2003) (5 pages) doi:10.1115/1.1523875 History: Received October 01, 2001; Revised August 01, 2002; Online January 06, 2003
Copyright © 2003 by ASME
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References

Rosenberg,  R. M., 1962, “The Normal Modes of Nonlinear n-Degree-of-Freedom Systems,” ASME J. Appl. Mech., 82, pp. 7–14.
Shaw,  W., and Pierre,  C., 1994, “Normal Modes of Vibration for Nonlinear Continuous Systems,” J. Sound Vib., 2, pp. 319–347.
Vakakis,  F., 1997, “Nonlinear Normal Modes and Their Applications in Vibration Theory: An Overview,” Mech. Syst. Signal Process., 11(1), pp. 3–22.
Setio,  S., and Jezequel,  L., 1992, “Modal Analysis of Nonlinear Multi Degree of Freedom Structure,” Int. J. of Anal. Exp. Modal Anal., 7(2), pp. 75–93.
Szemplinska,  Stupnicka, 1979, “The Modified Single Modified Method in the Investigations of the Resonant Vibrations of Nonlinear Systems,” J. Sound Vib., 63, pp. 475–489.
Szemplinska,  Stupnicka, 1983, “Nonlinear Normal Modes and Generalized Ritz Method in the Problems of Vibrations of Nonlinear Elastic Continuous Systems,” Int. J. Non-Linear Mech., 18, pp. 149–165.
Iwan,  W. D., 1973, “A Generalization of the Concept of Equivalent Linearization,” Int. J. Non-Linear Mech., 18, pp. 149–165.
Sanliturk,  , 1997, “Harmonic Balance Vibration Analysis of Turbine Blades with Friction Dampers,” ASME J. Vib. Acoust. 119, pp. 96–103.
Rao, J. S. S., 1992, Advanced Theory of Vibration, Halsted Press.
Ray, W. C., and Penzien, J., 1993, Dynamic Structures, McGraw-Hill.

Figures

Grahic Jump Location
The response around the first mode in state 1
Grahic Jump Location
The response of system in linear state
Grahic Jump Location
The response around the second mode in state 1
Grahic Jump Location
The response around the fourth mode in state 2
Grahic Jump Location
The response around the fifth mode in state 2
Grahic Jump Location
The response around the third mode in state 1
Grahic Jump Location
The response around the second mode in state 2
Grahic Jump Location
Model of 5 DOF system, m1−m5=1.0 Kg,k1−k5=1.0 N/m,c1−c5=0.02 N sec/m
Grahic Jump Location
The response around the fourth mode in state 1
Grahic Jump Location
The response around the fifth mode in state 1
Grahic Jump Location
The response around the first mode in state 2
Grahic Jump Location
The response around the third mode in state 2

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