Use of multidimensional discrete Fourier transforms in the harmonic balance method

1989 ◽  
Vol 66 (4) ◽  
pp. 613-617 ◽  
Author(s):  
S. C. CHAN ◽  
K. L. HO
Keyword(s):  
Harmonic Balance ◽  
Fourier Transforms ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Discrete Fourier Transforms

An Investigation of Steady-State Dynamic Response of a Sphere-Plane Contact Interface With Contact Loss

2006 ◽  
Vol 74 (2) ◽  
pp. 249-255 ◽  
Author(s):  
Q. L. Ma ◽  
A. Kahraman ◽  
J. Perret-Liaudet ◽  
E. Rigaud
Keyword(s):  
Steady State ◽  
Harmonic Balance ◽  
Numerical Solutions ◽  
Fourier Transforms ◽  
Damping Ratio ◽  
Harmonic Balance Method ◽  
Hertzian Contact ◽  
Contact Interface ◽  
Discrete Fourier Transforms ◽  
Plane Contact

In this study, the dynamic behavior of an elastic sphere-plane contact interface is studied analytically and experimentally. The analytical model includes both a continuous nonlinearity associated with the Hertzian contact and a clearance-type nonlinearity due to contact loss. The dimensionless governing equation is solved analytically by using multi-term harmonic balance method in conjunction with discrete Fourier transforms. The accuracy of the dynamic model and solution methods is demonstrated through comparisons with experimental data and numerical solutions for both harmonic amplitudes of the acceleration response and the phase difference between the response and the force excitation. A single-term harmonic balance approximation is used to derive a criterion for contact loss to occur. The influence of harmonic external excitation f(τ) and damping ratio ζ on the steady state response is also demonstrated.

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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