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.

Stability Analysis of Rotating Blade Vibration due to Torsional Excitation

2007 ◽  
Vol 13 (9-10) ◽  
pp. 1379-1391 ◽  
Author(s):  
Y.N. Al-Nassar ◽  
M. Kalyon ◽  
M. Pakdemirli ◽  
B.O. Al-Bedoor
Keyword(s):  
Stability Analysis ◽  
Blade Vibration ◽  
Rotating Blade ◽  
Torsional Excitation

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

scholarly journals An Improved Circumferential Fourier Fit (CFF) Method for Blade Tip Timing Measurements

2020 ◽  
Vol 10 (11) ◽  
pp. 3675
Author(s):  
Zhibo Liu ◽  
Fajie Duan ◽  
Guangyue Niu ◽  
Ling Ma ◽  
Jiajia Jiang ◽  
...  
Keyword(s):  
Development Program ◽  
Time Of Arrival ◽  
Blade Vibration ◽  
Vibration Measurements ◽  
Rotating Speed ◽  
Resonance Analysis ◽  
Rotating Blade ◽  
Negative Effect ◽  
Frequency Identification ◽  
Blade Tip

Rotating blade vibration measurements are very important for any turbomachinery research and development program. The blade tip timing (BTT) technique uses the time of arrival (ToA) of the blade tip passing the casing mounted probes to give the blade vibration. As a non-contact technique, BTT is necessary for rotating blade vibration measurements. The higher accuracy of amplitude and vibration frequency identification has been pursued since the development of BTT. An improved circumferential Fourier fit (ICFF) method is proposed. In this method, the ToA is not only dependent on the rotating speed and monitoring position, but also on blade vibration. Compared with the traditional circumferential Fourier fit (TCFF) method, this improvement is more consistent with reality. A 12-blade assembly simulator and experimental data were used to evaluate the ICFF performance. The simulated results showed that the ICFF performance is comparable to TCFF in terms of EO identification, except the lower PSR or more number probes that have a more negative effect on ICFF. Besides, the accuracy of amplitude identification is higher for ICFF than TCFF on all test conditions. Meanwhile, the higher accuracy of the reconstruction of ICFF was further verified in all measurement resonance analysis.

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.

scholarly journals The Spreading Residue Harmonic Balance Method for Strongly Nonlinear Vibrations of a Restrained Cantilever Beam

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Y. H. Qian ◽  
J. L. Pan ◽  
S. P. Chen ◽  
M. H. Yao
Keyword(s):  
Exact Solutions ◽  
Nonlinear Vibration ◽  
Harmonic Balance ◽  
Nonlinear Dynamical Systems ◽  
Harmonic Balance Method ◽  
Time History ◽  
Approximate Solutions ◽  
Balance Method ◽  
Lumped Mass ◽  
Strongly Nonlinear

The exact solutions of the nonlinear vibration systems are extremely complicated to be received, so it is crucial to analyze their approximate solutions. This paper employs the spreading residue harmonic balance method (SRHBM) to derive analytical approximate solutions for the fifth-order nonlinear problem, which corresponds to the strongly nonlinear vibration of an elastically restrained beam with a lumped mass. When the SRHBM is used, the residual terms are added to improve the accuracy of approximate solutions. Illustrative examples are provided along with verifying the accuracy of the present method and are compared with the HAM solutions, the EBM solutions, and exact solutions in tables. At the same time, the phase diagrams and time history curves are drawn by the mathematical software. Through analysis and discussion, the results obtained here demonstrate that the SRHBM is an effective and robust technique for nonlinear dynamical systems. In addition, the SRHBM can be widely applied to a variety of nonlinear dynamic systems.

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

The Residue Harmonic Balance Method for Duffing-Van Der Pol Oscillator with Fractional Derivative

2013 ◽  
Vol 774-776 ◽  
pp. 103-106
Author(s):  
Xin Xue ◽  
Lian Zhong Li ◽  
Dan Sun
Keyword(s):  
Fractional Derivative ◽  
Harmonic Balance ◽  
Numerical Solutions ◽  
Harmonic Balance Method ◽  
Approximate Solutions ◽  
Solution Procedure ◽  
Balance Method ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Fractional Orders

Duffing-van der Pol oscillator with fractional derivative was constructed in this paper. The solution procedure was proposed with the residue harmonic balance method. The effect of different fractional orders on resonance responses of the system in steady state were analyzed for an example without parameters. The approximate solutions were contrasted with numerical solutions. The results show that the residue harmonic balance method to Duffing-van der Pol differential equation with fractional derivative is very valid.

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