scholarly journals Higher Accuracy Approximate Solution for Oscillations of a Mass Attached to a Stretched Elastic Wire by Rational Harmonic Balance Method

2009 ◽  
Vol 10 (4) ◽  
Author(s):  
E. Gimeno ◽  
M. L. Álvarez ◽  
M. S. Yebra ◽  
J. Rosa-Herranz ◽  
A. Beléndez
Keyword(s):  
Approximate Solution ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method

Analysis of the Periodic Damping Coefficient Equation Based on Floquet Theory

2017 ◽  
Author(s):  
Fatemeh Afzali ◽  
Gizem D. Acar ◽  
Brian F. Feeny
Keyword(s):  
Approximate Solution ◽  
Harmonic Balance ◽  
Floquet Theory ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Damping Coefficient ◽  
Harmonic Series ◽  
Periodic Part ◽  
Damped System ◽  
Linear Differential

In this paper, we study the response of a linear differential equation, for which the damping coefficient varies periodically in time. We use Floquet theory combined with the harmonic balance method to find the approximate solution and capture the stability criteria. Based on Floquet theory the approximate solution includes the exponential part having an unknown exponent, and a periodic part, which is expressed using a truncated series of harmonics. After substituting the assumed response in the equation, the harmonic balance method is applied. We use the characteristic equation of the truncated harmonic series to obtain the Floquet exponents. The free response and stability characteristics of the damped system for a set of parameters are shown.

Analysis of Oscillator Injection Locking by Harmonic Balance Method

2008 ◽  
Author(s):  
M.M. Gourary ◽  
S.G. Rusakov ◽  
S.L. Ulyanov ◽  
M.M. Zharov ◽  
B.J. Mulvaney ◽  
...  
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Injection Locking ◽  
Balance Method

Closed-Form Expression for the Exact Period of a Nonlinear Oscillator Typified by a Mass Attached to a Stretched Wire

2011 ◽  
Vol 3 (6) ◽  
pp. 689-701
Author(s):  
Malik Mamode
Keyword(s):  
Harmonic Balance ◽  
Nonlinear Oscillator ◽  
Harmonic Balance Method ◽  
Elliptic Functions ◽  
Oscillatory System ◽  
Balance Method ◽  
Closed Form Expression ◽  
Form Expression ◽  
Polynomial Potential ◽  
Exact Analytical Expression

AbstractThe exact analytical expression of the period of a conservative nonlinear oscillator with a non-polynomial potential, is obtained. Such an oscillatory system corresponds to the transverse vibration of a particle attached to the center of a stretched elastic wire. The result is given in terms of elliptic functions and validates the approximate formulae derived from various approximation procedures as the harmonic balance method and the rational harmonic balance method usually implemented for solving such a nonlinear problem.

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