Semi-Analytical Modeling and Vibration Control of a Geometrically Nonlinear Plate

2017 ◽  
Vol 17 (04) ◽  
pp. 1771003 ◽  
Author(s):  
Atta Oveisi ◽  
Tamara Nestorović ◽  
Ngoc Linh Nguyen
Keyword(s):  
Harmonic Balance ◽  
Vibration Suppression ◽  
External Disturbance ◽  
Nonlinear Partial Differential Equation ◽  
Harmonic Balance Method ◽  
Single Mode ◽  
Piezo Actuator ◽  
Control Law ◽  
Geometrically Nonlinear ◽  
Relationship Of

This paper presents the dynamic modeling of a piezolaminated plate considering geometrical nonlinearities. The piezo-actuator and piezo-sensor are connected via proportional derivative feedback control law. The Hamilton’s principle is used to extract the strong form of the equation of motion with the reflection of the higher order strain terms by means of the strain–displacement relationship of the von Karman type. Then the nonlinear partial differential equation (PDE) obtained is converted to a nonlinear algebraic equation by employing the combination of harmonic balance method and single-mode Galerkin’s technique. Finally, the vibration suppression performance and sensitivity of the dynamic response is evaluated for various control parameters and magnitudes of external disturbance.

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.

Nonlinear Vibration Solutions of Nano-Beams Considering Surface Effects

2013 ◽  
Author(s):  
Hassan Askari ◽  
Ebrahim Esmailzadeh ◽  
Davood Younesian
Keyword(s):  
Differential Equation ◽  
Harmonic Balance ◽  
Nonlocal Parameter ◽  
Harmonic Balance Method ◽  
Beam Theory ◽  
Surface Effects ◽  
Nonlinear Ordinary Differential Equation ◽  
Balance Technique ◽  
Governing Differential Equation ◽  
Relationship Of

Nonlinear free vibration of nanobeams considering the surface effects is studied. The governing differential equation of motion of the system employing the Euler-Bernoulli beam theory is derived. Galerkin method is utilized to obtain the nonlinear ordinary differential equation of nanobeams, which is a well-known type of the Duffing equation. The elliptical harmonic balance method, energy balance technique and the variational approach are employed to obtain the frequency-amplitude relationship of the system. The effects of different parameters, i.e., aspect ratio, nonlocal parameter and the resultant residual stress, on the natural frequency are examined. Moreover, the variation of the amplitude on the frequency response is studied. The influence of the initial amplitude on the obtained modulus from the elliptical harmonic balance has been examined. Furthermore, the exact numerical solution is determined to verify the results obtained from the analytical solutions.

On Vibration Control Using a Bistable Snap Through Absorber From a Force Balance Perspective

2013 ◽  
Author(s):  
David R. Johnson ◽  
R. L. Harne ◽  
K. W. Wang
Keyword(s):  
Vibration Control ◽  
Primary Structure ◽  
Vibration Suppression ◽  
External Disturbance ◽  
Harmonic Balance Method ◽  
Harmonic Excitation ◽  
Force Balance ◽  
Single Frequency ◽  
System Response ◽  
Primary System

One approach to vibration control is to apply a force to a primary structure which opposes excitation, effectively canceling the external disturbance. A familiar passive example of this approach is the linear tuned mass absorber. In this spirit, the utility of a bistable attachment for attenuating vibrations, especially in terms of the high-orbit, snap through dynamic, is investigated using the harmonic balance method and experiments. Analyses demonstrate the fundamental harmonic snap through dynamic, having commensurate frequency with the single-frequency harmonic excitation, may yield displacements either substantially in-phase or out-of-phase with the primary structure. During in-phase snap through, forces are generated by the bistable oscillator which reinforce the applied loading, resulting in dramatic amplification of primary system response. During out-of-phase snap through, forces are generated which are only partially opposed to the input, leading to a measure of host structure attenuation. The experiments verify the analytical findings and also uncover nonlinear dynamics not predicted by the analysis that have slightly favorable vibration suppression performance when compared with the out-of-phase, fundamental harmonic snap through action.

scholarly journals Prediction of Transient Pressure Fluctuations within a Low-Pressure Turbine Cascade Using a Lanczos-Filtered Harmonic Balance Method

2021 ◽  
Vol 6 (3) ◽  
pp. 25
Author(s):  
Jan Philipp Heners ◽  
Stephan Stotz ◽  
Annette Krosse ◽  
Detlef Korte ◽  
Maximilian Beck ◽  
...  
Keyword(s):  
Turbulence Model ◽  
Harmonic Balance ◽  
Separation Bubble ◽  
Pressure Fluctuations ◽  
Harmonic Balance Method ◽  
Low Pressure ◽  
Filter Method ◽  
Turbine Cascade ◽  
Transient Pressure ◽  
Low Pressure Turbine

Unsteady pressure fluctuations measured by fast-response pressure transducers mounted in a low-pressure turbine cascade are compared to unsteady simulation results. Three differing simulation approaches are considered, one time-integration method and two harmonic balance methods either resolving or averaging the time-dependent components within the turbulence model. The observations are used to evaluate the capability of the harmonic balance solver to predict the transient pressure fluctuations acting on the investigated stator surface. Wakes of an upstream rotor are generated by moving cylindrical bars at a prescribed rotational speed that refers to a frequency of f∼500 Hz. The excitation at the rear part of the suction side is essentially driven by the presence of a separation bubble and is therefore highly dependent on the unsteady behavior of turbulence. In order to increase the stability of the investigated harmonic balance solver, a developed Lanczos-type filter method is applied if the turbulence model is considered in an unsteady fashion.

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