Stability of asymmetric rotors with asymmetric flexible disks

2021 ◽  
pp. 107754632110004
Author(s):  
Naim Khader
Keyword(s):  
Equations Of Motion ◽  
Ritz Method ◽  
Lagrangian Approach ◽  
Governing Equations ◽  
Stability Boundaries ◽  
System Solution ◽  
Asymmetric Rotor ◽  
Constant Coefficients ◽  
The Subject ◽  
Flexible Disk

The presented work examines the dynamic behavior of an asymmetric rotor with asymmetric flexible disk, contrary to previous works on the subject, where researchers examined the effect of either rigid disk asymmetry or disk flexibility at a time. Account for the asymmetry of flexible disk in rotors constitutes the new contribution in this work. The suggested mathematical model combines Lagrangian approach with Rayleigh–Ritz method to derive the governing equations of motion of the rotor. Account for asymmetry of the flexible disk results in complicated and lengthy expressions for the potential and kinetic energies of the rotor, required in the adopted Lagrangian approach. Using symbolic computation simplified the derivation of the governing equations of motion with constant coefficients in terms of rotating coordinate system. Solution of the resulting eigenvalue problem provided numerical results for rotors with symmetric and asymmetric flexible disks, required to assess the effect of disk flexibility and asymmetry on the resulting frequencies and stability boundaries of the examined rotor system.

Analysis of Flow Induced Vibration Using the Vorticity Transport Equation

1993 ◽  
Vol 115 (3) ◽  
pp. 485-492 ◽  
Author(s):  
Jure Marn ◽  
Ivan Catton
Keyword(s):  
Parametric Analysis ◽  
Dynamic Instability ◽  
Equations Of Motion ◽  
Fluid Motion ◽  
Governing Equations ◽  
Flow Induced Vibration ◽  
The Subject ◽  
An Array Of Cylinders ◽  
Vorticity Transport ◽  
Square Array

Crossflow induced vibrations are the subject of this work. The analysis is two dimensional. The governing equations for fluid motion are solved using linearized perturbation theory and coupled with the equations of motion for cylinders to yield the threshold of dynamic instability for an array of cylinders. Parametric analysis is performed to determine the lowest instability threshold for a rotated square array and correlations are developed relating the dominant parameters. The results are compared with theoretical and experimental data for similar arrays and the discrepancies are discussed.

scholarly journals On the Modeling of Periodic Sandwich Structures with the Use of the Broken Line Hypothesis

2020 ◽  
Vol 22 (3) ◽  
pp. 761-774 ◽  
Author(s):  
Jakub Marczak
Keyword(s):  
Vibration Analysis ◽  
Sandwich Plate ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
System Of Equations ◽  
Governing Equations ◽  
Fem Model ◽  
Constant Coefficients ◽  
Plate Strip ◽  
Periodic Plate

AbstractIn this paper a dynamic analysis of sandwich plate with a certain periodic microstructure is considered. The initial system of governing equations is derived basing on the classic broken line hypothesis. As a result of transformations one can obtain a system of three differential equations of motion with periodic, highly oscillating and non-continuous coefficients. In order to derive a system of equations with constant coefficients tolerance averaging technique is applied. Eventually, in the calculation example a free vibration analysis of certain periodic plate strip is performed with the use of both the derived model and a FEM model. It can be observed that the consistency of obtained results is highly dependent on the calculation assumptions.

Blade Mistuning Coupled With Shaft Flexibility Effects in Rotor Aeroelasticity

1989 ◽  
Author(s):  
Naim Khader ◽  
Robert G. Loewy
Keyword(s):  
Equations Of Motion ◽  
Governing Equations ◽  
Aeroelastic Stability ◽  
Stability Boundaries ◽  
Coriolis Forces ◽  
Bladed Disk ◽  
Out Of Plane ◽  
Shaft Flexibility ◽  
Rotor Aeroelasticity ◽  
Plane Deformations

The effect of bladed-disk polar dissymmetry, resulting from variations in mass from one blade to another, on aeroelastic stability boundaries for a fan stage is presented. In addition to both in-plane and out-of-plane deformations of the bladed-disk, bending of the supporting shaft in two planes is considered, and the resulting Coriolis forces and gyroscopic moments are included in the analysis. A quasi-steady aerodynamics approach is combined with the Lagrangian method to develop the governing equations of motion for the flexible bladed-disk-shaft assembly. Calculations are performed for an actual fan stage.

An Experimental Study of the Influence of Disk Flexibility and Rubbing on Rotordynamics

1993 ◽  
Author(s):  
Fangsheng Wu ◽  
George T. Flowers
Keyword(s):  
High Frequency ◽  
Analytical Study ◽  
Equations Of Motion ◽  
Frequency Component ◽  
High Amplitude ◽  
High Frequency Component ◽  
Rotor Speed ◽  
Governing Equations ◽  
Speed Range ◽  
Flexible Disk

Abstract This study is an experimental investigation of the influence of disk flexibility and rubbing on rotordynamics. The rotor rigs used in the experiments were designed to have included disk flexibility and a rubbing mechanism. The governing equations of motion are similar to those studied in analytical investigations. The system responses to imbalance were recorded and orbit trajectories were plotted at a set of different rotating speeds. The results show the rubbing response development from light forward bouncing, mixed forward bouncing, to high amplitude backward whirling heavy rubbing. The results also show that the flexible-disk rotor has the tendency of having a high frequency component at the upper rotor speed range of mixed bouncing. These agree very well with the results from an earlier analytical study.

scholarly journals Tolerance Modelling of Vibrations and Stability for Periodic Slender Visco-Elastic Beams on a Foundation with Damping. Revisiting

Materials ◽  
2020 ◽  
Vol 13 (18) ◽  
pp. 3939
Author(s):  
Jarosław Jędrysiak
Keyword(s):  
Mathematical Modelling ◽  
System Of Differential Equations ◽  
Governing Equations ◽  
Asymptotic Homogenization ◽  
Elastic Beams ◽  
Oscillating Coefficients ◽  
Constant Coefficients ◽  
Tolerance Modelling ◽  
Tolerance Method ◽  
Modelling Approach

The mathematical modelling of certain problems of vibrations and stability for periodic slender visco-elastic beams is presented in this note. To consider these problems and take into account the effect of the microstructure, the tolerance modelling approach is proposed. Using this technique, the equation with non-continuous, periodic, highly oscillating coefficients is replaced by a system of differential equations with constant coefficients. Moreover, these governing equations describe the effect of the microstructure on the overall behavior of the beams under consideration. The tolerance modelling can lead to equations of two different tolerance models—the standard and the general, under weakened assumptions. This averaging tolerance method was assessed by comparison with the asymptotic homogenization, the governing equations of which omit this effect. My considerations were limited to proposing and presenting only mathematical models describing investigated beams. In a simple analytical example, the application of the presented average models is shown.

Simulation of Engine Vibration on Nonlinear Hydraulic Engine Mounts

2005 ◽  
Author(s):  
A. R. Ohadi ◽  
G. Maghsoodi
Keyword(s):  
Equations Of Motion ◽  
Low Frequency ◽  
Governing Equations ◽  
Engine Mounts ◽  
Engine Vibration ◽  
Engine Mount ◽  
Rotational Motions ◽  
The Time Domain ◽  
Nonlinear Equations Of Motion ◽  
Four Cylinders

In this paper, vibration behavior of engine on nonlinear hydraulic engine mount including inertia track and decoupler is studied. In this regard, after introducing the nonlinear factors of this mount (i.e. inertia and decoupler resistances in turbulent region), the vibration governing equations of engine on one hydraulic engine mount are solved and the effect of nonlinearity is investigated. In order to have a comparison between rubber and hydraulic engine mounts, a 6 degree of freedom four cylinders V-shaped engine under inertia and balancing masses forces and torques is considered. By solving the time domain nonlinear equations of motion of engine on three inclined mounts, translational and rotational motions of engines body are obtained for different engine speeds. Transmitted base forces are also determined for both types of engine mount. Comparison of rubber and hydraulic mounts indicates the efficiency of hydraulic one in low frequency region.

Reduction of Noise Inside a Cavity by Piezoelectric Actuators

2003 ◽  
Vol 125 (1) ◽  
pp. 12-17 ◽  
Author(s):  
I. Hagiwara ◽  
D. W. Wang ◽  
Q. Z. Shi ◽  
R. S. Rao
Keyword(s):  
Sound Pressure ◽  
Control Mechanism ◽  
Equations Of Motion ◽  
Piezoelectric Actuators ◽  
Governing Equations ◽  
Control Laws ◽  
Modal Coupling ◽  
Modal Amplitude ◽  
Global And Local ◽  
Fully Coupled

A new analytical model is developed for the reduction of noise inside a cavity using distributed piezoelectric actuators. A modal coupling method is used to establish the governing equations of motion of the fully coupled acoustics-structure-piezoelectric patch system. Two performance functions relating “global” and “local” optimal control of sound pressure levels (SPL) respectively are applied to obtain the control laws. The discussions on associated control mechanism show that both the mechanisms of modal amplitude suppression and modal rearrangement may sometimes coexist in the implementation of optimal noise control.

Numerical Investigation of a Fiber Web Effect on the Pressure Drop and Particles Collection in a Microchannel

2009 ◽  
Author(s):  
Alireza Dastan ◽  
Omid Abouali
Keyword(s):  
Pressure Drop ◽  
Flow Field ◽  
Numerical Investigation ◽  
Particle Motion ◽  
Particle Deposition ◽  
Hydraulic Diameter ◽  
Lagrangian Approach ◽  
Computational Domain ◽  
Governing Equations ◽  
Eulerian Approach

In this paper pressure drop and particle deposition in a microchannel with a hydraulic diameter of 225 micrometer is investigated numerically. Several hundred micron length fibers caught at the entrance of the channels making a “fiber web” also is modeled in this research. Governing equations for the flow field are solved with an Eulerian approach while the equations of particle motion in the flow are solved by a Lagrangian approach. Assuming the symmetry in the domain, one channel and the corresponding plenum are studied in the computational domain. For studying the effects of fibers in the flow, two fiber webs with four and six solid fibers are studied. The increase of pressure drop in the microchannel because of the entrance fiber web is computed and discussed. Also deposition and collection of the particles with various diameters at the fiber webs are also presented.

Influence of Material Damping on In-Plane Modal Parameters for Rotating Disks

2012 ◽  
Author(s):  
Hamid R. Hamidzadeh ◽  
Ehsan Sarfaraz
Keyword(s):  
Elastic Moduli ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Elastic Stability ◽  
Rotating Disks ◽  
Governing Equations ◽  
Annular Disk ◽  
Stress Theory ◽  
Hysteretic Damping ◽  
Circumferential Wave

The linear in-plane free vibration of a thin, homogeneous, viscoelastic, rotating annular disk is investigated. In the development of an analytical solution, two dimensional elastodynamic theory is employed and the viscoelastic material for the medium is allowed by assuming complex elastic moduli. The general governing equations of motion are derived by implementing plane stress theory. Natural frequencies are computed for several modes at specific radius ratios with fixed-free boundary conditions and modal loss factors for different damping ratios are determined. The computed results were compared to previously established results. It was observed that the effects of rotational speed and hysteretic damping ratio on natural frequency and elastic stability of the rotating disks were related to the mode of vibration and type of circumferential wave occurring.

scholarly journals Conducting dusty fluid flow through a constriction in a porous medium

2016 ◽  
Vol 5 (1) ◽  
pp. 29
Author(s):  
Madhura K R ◽  
Uma M S
Keyword(s):  
Porous Medium ◽  
Hartmann Number ◽  
Equations Of Motion ◽  
Fluid Phase ◽  
Dust Particles ◽  
Governing Equations ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Flow Through ◽  
Constricted Channel

<p><span lang="EN-IN">The flow of an unsteady incompressible electrically conducting fluid with uniform distribution of dust particles in a constricted channel has been studied. The medium is assumed to be porous in nature. The governing equations of motion are treated analytically and the expressions are obtained by using variable separable and Laplace transform techniques. The influence of the dust particles on the velocity distributions of the fluid are investigated for various cases and the results are illustrated by varying parameters like Hartmann number, deposition thickness on the walls of the cylinder and the permeability of the porous medium on the velocity of dust and fluid phase.</span></p>

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