TY - JOUR
T1 - A new method for approximate analytical solutions to nonlinear oscillations of nonnatural systems
AU - Wu, B. S.
AU - Lim, C. W.
AU - He, L. H.
PY - 2003/4
Y1 - 2003/4
N2 - This paper deals with nonlinear oscillations of a conservative, nonnatural, single-degree-of-freedom system with odd nonlinearity. By combining the linearization of the governing equation with the method of harmonic balance, we establish approximate analytical solutions for the nonlinear oscillations of the system. Unlike the classical harmonic balance method, the linearization is performed prior to proceeding with harmonic balancing thus resulting in linear algebraic equations instead of nonlinear algebraic equations. Hence, we are able to establish the approximate analytical formulas for the exact period and periodic solution. These approximate solutions are valid for small as well as large amplitudes of oscillation. Two examples are presented to illustrate that the proposed formulas can give excellent approximate results.
AB - This paper deals with nonlinear oscillations of a conservative, nonnatural, single-degree-of-freedom system with odd nonlinearity. By combining the linearization of the governing equation with the method of harmonic balance, we establish approximate analytical solutions for the nonlinear oscillations of the system. Unlike the classical harmonic balance method, the linearization is performed prior to proceeding with harmonic balancing thus resulting in linear algebraic equations instead of nonlinear algebraic equations. Hence, we are able to establish the approximate analytical formulas for the exact period and periodic solution. These approximate solutions are valid for small as well as large amplitudes of oscillation. Two examples are presented to illustrate that the proposed formulas can give excellent approximate results.
KW - Harmonic balance method
KW - Linearization
KW - Nonlinear oscillation
KW - Nonnatural system
KW - Odd nonlinearity
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-0037769060&origin=recordpage
U2 - 10.1023/A:1024223118496
DO - 10.1023/A:1024223118496
M3 - RGC 21 - Publication in refereed journal
VL - 32
SP - 1
EP - 13
JO - Nonlinear Dynamics
JF - Nonlinear Dynamics
SN - 0924-090X
IS - 1
ER -