Use of the Method of Harmonic Balance for Controlling the Condition of Permanent Magnets

2020 ◽  
Vol 61 (9-10) ◽  
pp. 569-571
Author(s):  
A. M. Lankin ◽  
M. V. Lankin ◽  
I. M. Lankin
Keyword(s):  
Harmonic Balance ◽  
Permanent Magnets ◽  
Method Of Harmonic Balance

scholarly journals Functional analysis and the method of harmonic balance

1975 ◽  
Vol 32 (4) ◽  
pp. 457-464 ◽  
Author(s):  
C. A. Borges ◽  
L. Cesari ◽  
D. A. Sánchez
Keyword(s):  
Functional Analysis ◽  
Harmonic Balance ◽  
Method Of Harmonic Balance

Analysis of Rotating Blade Forced Vibration Due to Torsional Excitation Using the Method of Harmonic Balance

2002 ◽  
Author(s):  
B. O. Al-Bedoor ◽  
A. A. Al-Qaisia
Keyword(s):  
Forced Vibration ◽  
Harmonic Balance ◽  
Approximate Solutions ◽  
Coefficient Matrix ◽  
Blade Vibration ◽  
Varying Coefficients ◽  
Rotating Blade ◽  
Method Of Harmonic Balance ◽  
Torsional Excitation ◽  
Truncated Fourier Series

This paper presents an analysis of the forced vibration of rotating blade due to torsional excitation. The model analyzed is a multi-modal forced second order ordinary differential equation with multiple harmonically varying coefficients. The method of Harmonic Balance (HB) is employed to find approximate solutions for each of the blade modes in the form of truncated Fourier series. The solutions have shown multi resonance response for the first blade vibration mode. The examination of the determinant of the harmonic balance solution coefficient matrix for stability purposes has shown that the region between the two resonance points is an unstable vibration region. Numerical integration of the equations is conducted at different frequency ratio points and the results are discussed. This solution provides a very critical operation and design guidance for rotating blade with torsional vibration excitation.

scholarly journals Resonant Stellar Orbits in Spiral Galaxies

1975 ◽  
Vol 69 ◽  
pp. 237-244
Author(s):  
P. O. Vandervoort
Keyword(s):  
Excellent Agreement ◽  
Spiral Galaxy ◽  
Harmonic Balance ◽  
Spiral Galaxies ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Analytic Solutions ◽  
Stellar Orbits ◽  
Method Of Harmonic Balance ◽  
Resonance Phenomena

This paper reviews a series of investigations of the orbits of stars in the regions of the Lindblad resonances of a spiral galaxy. The analysis is formulated in an epicyclic approximation. Analytic solutions of the epicyclic equations of motion are obtained by the method of harmonic balance of Bogoliubov and Mitropolsky. These solutions represent the resonance phenomena exhibited by the orbits in generally excellent agreement with numerical solutions.

A generalization of the method of harmonic balance

1987 ◽  
Vol 116 (3) ◽  
pp. 591-595 ◽  
Author(s):  
J. Garcia-Margallo ◽  
J.Diaz Bejarano
Keyword(s):  
Harmonic Balance ◽  
Method Of Harmonic Balance

Frictional Damping of Flutter: Microslip Versus Macroslip

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
Robert Hudson ◽  
Alok Sinha
Keyword(s):  
Harmonic Balance ◽  
Function Method ◽  
Friction Model ◽  
Describing Function ◽  
Friction Dampers ◽  
Method Of Harmonic Balance ◽  
Frictional Damping ◽  
Negative Damping ◽  
Describing Function Method ◽  
Microslip Friction

Friction dampers are utilized in turbomachinery to reduce blade vibrations resulting from aeroelastic interactions. In this paper, the microslip friction model is applied to a blade with blade to ground damper and subjected to negative damping. Analysis using the describing function method, also known as the method of harmonic balance, is used to identify the behavior of the system and the maximum negative damping that can be stabilized by such a damper. These results are compared to those for the macroslip friction model.

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