Blade Vibration Suppression Using Friction Elements in Shrouding

2011 ◽  
Author(s):  
Michal Hajzˇman ◽  
Miroslav Byrtus ◽  
Vladimi´r Zeman
Keyword(s):  
Numerical Integration ◽  
Nonlinear Equations ◽  
Harmonic Balance ◽  
Vibration Suppression ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Blade Vibration ◽  
Friction Element ◽  
Nonlinear Equations Of Motion

The problem of two blades with a friction element is studied in order to analyze the effects of the friction on the undesirable vibration suppression. The simplified contact model between friction planes of the blade shrouding and the friction element is derived to be a fast computational tool comparing with a time-consuming finite element solution. The harmonic balance method is suitable for the linearization of originally nonlinear equations of motion under certain assumptions given on the excitation of the system and on its dynamic response. On the other hand the nonlinear equations of motion can be solved directly by their numerical integration, which is more time-consuming but it is not limited by given assumptions. The comparison of results of the harmonic balance method and of the numerical integration of motion equations is given in the paper.

A Study of Dynamic Instability of Plates by an Extended Incremental Harmonic Balance Method

1985 ◽  
Vol 52 (3) ◽  
pp. 693-697 ◽  
Author(s):  
C. Pierre ◽  
E. H. Dowell
Keyword(s):  
Harmonic Balance ◽  
Dynamic Instability ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Mathieu Equation ◽  
Equation System ◽  
Balance Method ◽  
Incremental Harmonic Balance Method ◽  
Incremental Harmonic Balance ◽  
Nonlinear Equations Of Motion

The dynamic instability of plates is investigated with geometric nonlinearities being included in the model, which allows one to determine the amplitude of the parametric vibrations. A modal analysis allowing one spatial mode is performed on the nonlinear equations of motion and the resulting nonlinear Mathieu equation is solved by the incremental harmonic balance method, which takes several temporal harmonics into account. When viscous damping is included, a new algorithm is proposed to solve the equation system obtained by the incremental method. For this purpose, a new characterization of the parametric vibration by its total amplitude—or Euclidian norm—is introduced. This algorithm is particularly simple and convenient for computer implementation. The instability regions are obtained with a high degree of accuracy.

Nonlinear Truck Ride Analysis

1974 ◽  
Vol 96 (2) ◽  
pp. 597-602 ◽  
Author(s):  
G. R. Potts ◽  
H. S. Walker
Keyword(s):  
Numerical Integration ◽  
Nonlinear Equations ◽  
Digital Computer ◽  
Dry Friction ◽  
Shock Absorber ◽  
Equations Of Motion ◽  
Deflection Curve ◽  
Force Velocity ◽  
Nonlinear Equations Of Motion ◽  
Dry Friction Damping

The nonlinear vibratory motions of a three-axle semitrailer truck were investigated via the use of a digital computer. The nonlinear equations of motion are presented and a method of numerical integration is discussed. The analysis allows any shape of suspension force-deflection curve (including wheel hop, suspension stops, and dry friction damping) and a similar liberality of shock absorber force-velocity characteristics. An experimental vibration study, performed on a model truck, is described and the results compare favorably with the calculated results of the numerical integration.

scholarly journals Chaotic Phenomena and Nonlinear Responses in a Vibroacoustic System

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Yiu-Yin Lee
Keyword(s):  
Numerical Integration ◽  
Governing Equation ◽  
Harmonic Balance ◽  
Integration Method ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Numerical Integration Method ◽  
Chaotic Phenomena ◽  
Nonlinear Responses ◽  
Flexible Panel

This study addresses the chaotic phenomena and nonlinear responses in a vibroacoustic system. It is the first study about the chaotic phenomena in a vibroacoustic system, which is formed by a flexible panel coupled with a cavity. A multimode formulation is developed from the acoustic governing equation and nonlinear structural governing equation. The chaotic and various nonlinear responses are computed from the multimode formulation using a numerical integration method. The results obtained from the proposed method and classical harmonic balance method are generally consistent. A set of modal convergence studies is performed to check the proposed method. The effects of various parameters on triggering the nonchaotic responses to chaotic responses in a vibroacoustic system are studied in detail.

scholarly journals Application of harmonic balance method for solving non-linear equations of motion

2018 ◽  
Vol 182 ◽  
pp. 02024
Author(s):  
Robert Kostek
Keyword(s):  
Harmonic Balance ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Harmonic Balance Method ◽  
Time History ◽  
Balance Method ◽  
Non Linear ◽  
Time Histories ◽  
History Of ◽  
Non Linear Equations

This article presents the advantages and limitations of a harmonic balance method applied for solving non-linear equations of monition. This method provides an opportunity to find stable and unstable periodic solutions, which was demonstrated for a few equations. An error of solution decreases rapidly with increase of number of harmonics for smooth time history of acceleration, which shows convergence; whereas, for discontinuous time histories, this method is not effective.

Dynamic Analysis of a Brushless D.C. Motor Using a Modified Harmonic Balance Method

1995 ◽  
Vol 117 (3) ◽  
pp. 283-291 ◽  
Author(s):  
Ming-ran Lee ◽  
Chandramouli Padmanabhan ◽  
Rajendra Singh
Keyword(s):  
Numerical Integration ◽  
Harmonic Balance ◽  
Broad Band ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Time Varying ◽  
Computationally Efficient ◽  
Dynamic Interactions ◽  
Torque Pulsations ◽  
Analytical Approaches

Analysis of brushless D.C. motor (BDCM) torque pulsations is an essential step in the diagnosis and control of vibration and noise generated by many electro-mechanical devices. The broad band spectral content of the torque pulsations, as predicted by a mathematical model which accounts for various complex effects, can often be obtained only by numerical integration which is time consuming while permitting little understanding of the dynamic interactions. Prior analytical approaches, such as the Fourier series technique or the d-q axis theory, are limited by the simplifying assumptions needed to compute the torque spectrum. This paper develops a new semi-analytical formulation for the analysis of nonlinear, time-varying BDCM’s which involve both spatial and temporal domains. A modified multi-term harmonic balance method, based on a transformation of the dual-domain problem to a spatial domain formulation, is developed here specifically to compute the magnitude of several harmonics of the pulsating torque. The interacting effects of key parameters, like dynamic eccentricity, magnetic saturation and open stator slots, on the time-varying inductances and rotor flux density distribution are included explicitly in the formulation. The predicted spectra compare very well with those obtained by direct time domain numerical integration. Yet, the proposed method is computationally efficient especially when the model dimension is reduced. It also provides better insight into the high frequency dynamics of the sample case.

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