A Stability Analysis of Constrained Rotating Disks With Different Boundary Conditions

2007 ◽  
Author(s):  
Ramin M. H. Khorasany ◽  
Stanley G. Hutton
Keyword(s):  
Boundary Conditions ◽  
High Speed ◽  
Equations Of Motion ◽  
Order Partial Differential Equation ◽  
Rotating Disks ◽  
Different Boundary Conditions ◽  
The Difference ◽  
The Stability ◽  
The Galerkin Method ◽  
Mass Spring

The vibration behavior of constrained high speed rotating disks is of interest in industries as diverse as: aerospace, computer disk manufacture and saw design and usage. The purpose of this study is to investigate the stability behavior of guided circular disks with different boundary conditions. The equations of motion are developed for circular rotating disks constrained by space fixed linear, mass, spring, damper systems. The resulting equation of motion is a two dimensional fourth order partial differential equation that requires numerical solution. The Galerkin Method is employed using the eigenfunctions of the stationary non-constrained disk as approximation functions. Of interest is the effect on stability of conditions at the inner boundary. In particular the difference in behavior for centrally clamped, and splined disks (those disks that run on a spline arbor) is investigated. Also discussed is the effect of constraints on the flutter and divergence instability boundaries. Preliminary experimental results are presented for constrained splined disks, and these results are compared with the analytical predictions.

scholarly journals Effect of Torsional Element towards High-Speed Rotating Shaft’s Critical Speed at Different Boundary Conditions

2019 ◽  
Vol 8 (4) ◽  
pp. 6787-6792
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
High Speed ◽  
Critical Speed ◽  
Element Model ◽  
Accurate Estimation ◽  
Fe Model ◽  
Rotating Shaft ◽  
Different Boundary Conditions ◽  
The Difference

Efficiency improvement that can be provided by the high-speed rotating equipment becomes a concern for designers nowadays. Since the high-speed rotating machinery was capable of rotating at very near to critical speed, the accurate estimation of critical speed needs to be considered. This paper investigated the effect of torsional element towards critical speed of high-speed rotating shaft system for pinned-pinned (P-P), clamped-free (C-F) and clamped-free (C-F) boundaries condition. The Nelson’s finite element model that considers the torsional effect was developed for formulating the finite element (FE) model. This FE model was used to derive Mathieu-Hill’s equation and then solved by applying the Bolotin’s theory. From the solution, the Campbell’s diagram of the high-speed shaft was plotted. It was found that torsional motion has significant effect on the critical speed for different boundary conditions. The difference between critical speed of 4DOF and 5DOF models can be as high as 6.91 %.

Dynamic Stability of a Spinning Timoshenko Beam Subjected to a Moving Mass-Spring-Damper Unit

2010 ◽  
Author(s):  
T. H. Young ◽  
M. S. Chen
Keyword(s):  
Dynamic Stability ◽  
Timoshenko Beam ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Axial Direction ◽  
Longitudinal Axis ◽  
Moving Mass ◽  
The Stability ◽  
The Galerkin Method ◽  
Mass Spring

This paper investigates the dynamic stability of a finite Timoshenko beam spinning along its longitudinal axis and subjected to a moving mass-spring-damper (MSD) unit traveling in the axial direction. The mass of the moving MSD unit makes contact with the beam all the time during traveling. Due to the moving MSD unit, the beam is acted upon by a periodic, parametric excitation. In this work, the equations of motion of the beam are first discretized by the Galerkin method. The discretized equations of motion are then partially uncoupled by the modal analysis procedure suitable for gyroscopic systems. Finally the method of multiple scales is used to obtain the stability boundaries of the beam. Numerical results show that if the displacement of the MSD unit is equal to only one of the two transverse displacements of the beam, very large unstable regions may appear at main resonances.

scholarly journals Temperature Effects on Nonlinear Vibration Behaviors of Euler-Bernoulli Beams with Different Boundary Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Yaobing Zhao ◽  
Chaohui Huang
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Temperature Effects ◽  
Multiple Scales ◽  
Approximate Solutions ◽  
Response Curves ◽  
Different Boundary Conditions ◽  
The Stability ◽  
The Galerkin Method ◽  
Close Form

This paper is concerned with temperature effects on the modeling and vibration characteristics of Euler-Bernoulli beams with symmetric and nonsymmetric boundary conditions. It is assumed that in the considered model the temperature increases/decreases instantly, and the temperature variation is uniformly distributed along the length and the cross-section. By using the extended Hamilton’s principle, the mathematical model which takes into account thermal and mechanical loadings, represented by partial differential equations (PDEs), is established. The PDEs of the planar motion are discretized to a set of second-order ordinary differential equations by using the Galerkin method. As to three different boundary conditions, eigenvalue analyses are performed to obtain the close-form eigenvalue solutions. First four natural frequencies with thermal effects are investigated. By using the Lindstedt-Poincaré method and multiple scales method, the approximate solutions of the nonlinear free and forced vibrations (primary, super, and subharmonic resonances) are obtained. The influences of temperature variations on response amplitudes, the localisation of the resonance zones, and the stability of the steady-state solutions are investigated, through examining frequency response curves and excitation response curves. Numerical results show that response amplitudes, the number and the stability of nontrivial solutions, and the hardening-spring characteristics are all closely related to temperature changes. As to temperature effects on vibration behaviors of structures, different boundary conditions should be paid more attention.

A comparative study on the breakup of Newtonian and viscoelastic liquid films

2018 ◽  
Vol 32 (12n13) ◽  
pp. 1840032
Author(s):  
Lijuan Qian ◽  
Shaobo Song ◽  
Lisha Jiang ◽  
Xiaolu Li ◽  
Jianzhong Lin
Keyword(s):  
Liquid Film ◽  
High Speed ◽  
Liquid Films ◽  
Viscoelastic Liquid ◽  
Ligament Length ◽  
Time Resolved ◽  
Liquid Bubble ◽  
Mean Size ◽  
The Difference ◽  
The Stability

The breakup of viscoelastic liquid films are investigated experimentally and analytically. The breakup phenomena of viscoelastic liquid film are recorded by the time resolved high speed camera. Video images reveal the difference behavior of liquid bubble breakup for Newtonian and viscoelastic liquid. For the Newtonian liquid, cylindrical ligaments are stretched into droplets with large distributions of drop size. For the viscoelastic liquid, the pinch-off point is located on the liquid connections to the nozzle and finally the main part of the ligament no longer elongates. Furthermore, a dispersion relation based on the stability analysis is involved to predict the ligament length and drop mean size after breakup for liquid film. The calculated ligament length is validated by the measured drop mean size at higher air-to-liquid mass flow ratio.

scholarly journals Research on Thermal Insulation Performance of Lightweight Thermal Protection Materials for High Speed Aircraft under Different Boundary Conditions

2018 ◽  
Vol 179 ◽  
pp. 02001
Author(s):  
Feng Wang ◽  
Dafang Wu ◽  
Haoyuan Ren
Keyword(s):  
Boundary Conditions ◽  
Thermal Insulation ◽  
High Speed ◽  
Thermal Protection ◽  
Different Boundary Conditions ◽  
Flight Vehicles ◽  
Calculation Results ◽  
Different Temperatures ◽  
Insulation Performance

The determination of thermal insulation performance of thermal protection materials or structures is an indispensable and important step in the safety design of high speed flight vehicles. To obtain the temperature difference of the radiating surface for plate specimens under three different boundary conditions in heat insulation experiments (the specimens were placed either vertically or horizontally with the radiating surface facing down or horizontally with the radiating surface facing up), three thermal test setups were established to test the thermal insulation performance of light-weight ceramic specimens at different temperatures. The results show that the radiating surface temperature was the highest when the specimen was placed horizontally with the radiating surface facing down, while it was the lowest when the specimen was placed horizontally with the radiating surface facing up.The numerical calculation results agreed very well with the experimental ones, confirming the credibility and accuracy of the experimental results. The different thermal insulation performances of the plate specimens obtained under three different boundary conditions will provide important guidance for designers in the design of thermal protection systems for large cabins of high speed flight vehicles.

Stability Analysis of High-Speed Railway Vehicle Based on Multibody Dynamics Analysis

2013 ◽  
Vol 392 ◽  
pp. 156-160
Author(s):  
Ju Seok Kang
Keyword(s):  
Stability Analysis ◽  
Multibody Dynamics ◽  
High Speed ◽  
Equations Of Motion ◽  
Contact Forces ◽  
Design Parameters ◽  
Railway Vehicle ◽  
Dynamics Analysis ◽  
Contact Points ◽  
The Stability

Multibody dynamics analysis is advantageous in that it uses real dimensions and design parameters. In this study, the stability analysis of a railway vehicle based on multibody dynamics analysis is presented. The equations for the contact points and contact forces between the wheel and the rail are derived using a wheelset model. The dynamics equations of the wheelset are combined with the dynamics equations of the other parts of the railway vehicle, which are obtained by general multibody dynamics analysis. The equations of motion of the railway vehicle are linearized by using the perturbation method. The eigenvalues of these linear dynamics equations are calculated and the critical speed is found.

Basic Study on the Seismic Response of the High-Speed-Moving Vehicle Considering Passengers' Dynamics

2012 ◽  
Vol 452-453 ◽  
pp. 1200-1204
Author(s):  
Atsuhiko Shintani ◽  
Tomohiro Ito ◽  
Yudai Iwasaki
Keyword(s):  
High Speed ◽  
Equations Of Motion ◽  
Seismic Excitations ◽  
Lagrangian Equation ◽  
Basic Study ◽  
Moving Vehicle ◽  
Seismic Input ◽  
The Stability ◽  
Risk Rate ◽  
Two Degree Of Freedom

The stability of the high-speed running vehicle subjected to seismic excitations considering passengers' dynamics are considered. A vehicle consists of one body, two trucks and four wheel sets. A passenger is modeled by simple two degree of freedom vibration system. The equations of motion of the vehicle and passengers are calculated by Lagrangian equation of motion. Combining two models, the behavior of the vehicle subjected to actual seismic input considering passengers' dynamics are calculated by numerical simulation. The stability of the vehicle is evaluated by using the risk rate of rollover. We investigate the possibility of the rollover of the vehicle. We focus on the effect of the dynamic characteristics of the human and the number of the passengers when the vehicle is subjected to the seismic excitation.

Free Vibration and Stability Analysis of Internally Damped Rotating Shafts With General Boundary Conditions

1998 ◽  
Vol 120 (3) ◽  
pp. 776-783 ◽  
Author(s):  
J. Melanson ◽  
J. W. Zu
Keyword(s):  
Boundary Conditions ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Beam Theory ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Rotating Shaft ◽  
Classical Boundary ◽  
Rotating Shafts ◽  
The Stability

Vibration analysis of an internally damped rotating shaft, modeled using Timoshenko beam theory, with general boundary conditions is performed analytically. The equations of motion including the effects of internal viscous and hysteretic damping are derived. Exact solutions for the complex natural frequencies and complex normal modes are provided for each of the six classical boundary conditions. Numerical simulations show the effect of the internal damping on the stability of the rotor system.

Experimental Study of the Stability of a High-Speed Gas Jet Under the Influence of Liquid Cross-Flow

2007 ◽  
Author(s):  
Chris Weiland ◽  
Jon Yagla ◽  
Pavlos Vlachos
Keyword(s):  
Mach Number ◽  
Free Boundary ◽  
Boundary Conditions ◽  
High Speed ◽  
Cross Flow ◽  
Upper And Lower Bounds ◽  
Gas Jet ◽  
Mode Shapes ◽  
Free Boundary Conditions ◽  
The Stability

This paper reports on the interfacial character and deflection of a high-speed gas jet transverse to an aqueous cross-flow as a function of cross-flow speed and gas jet Mach number. Several gas exit velocities were tested including subsonic cases up to supersonic cases at cross-flow velocities from 0.3 m/s to 0.7 m/s. For the subsonic cases, it was found that the stability and resistance of the gas jet to deflect in the presence of cross-flow were increased with the jet Mach number. However, the Mach 1.6 jet was more stable than the Mach 1.9 jet, suggesting that there exists upper and lower bounds for jet stability which are Mach number dependent. Unstable gas jets were shown to pinch-off, meaning the interface of the gas jet in a plane parallel to the ejector exit collapsed to almost a point and an independent bubble rose to the free surface. The stagnation side gas/liquid interfaces were analyzed using the Proper Orthogonal Decomposition (POD) method to better understand the fundamental mode shapes contained in the interface waveforms. It was found that the subsonic jets shared many of the same characteristics in their first, second, and third mode shapes. The supersonic jets differed from the subsonic mode shapes. Interestingly, the mode shapes for the subsonic cases compared well to those of a beam in transverse vibration with sliding-free boundary conditions. The supersonic cases compared relatively well to pinned-free boundary conditions, owing to the more columnar nature of the gas jet as it exited the ejector.

On The Steady State and Dynamic Performance Characteristics of Floating Ring Bearings

1981 ◽  
Vol 103 (3) ◽  
pp. 389-397 ◽  
Author(s):  
Chin-Hsiu Li ◽  
S. M. Rohde
Keyword(s):  
Steady State ◽  
Linear Theory ◽  
High Speed ◽  
Dynamic Performance ◽  
Equations Of Motion ◽  
Nonlinear Behavior ◽  
Journal Bearings ◽  
Transient Problem ◽  
The Stability ◽  
Bearing System

An analysis of the steady state and dynamic characteristics of floating ring journal bearings has been performed. The stability characteristics of the bearing, based on linear theory, are given. The transient problem, in which the equations of motion for the bearing system are integrated in real time was studied. The effect of using finite bearing theory rather than the short bearing assumption was examined. Among the significant findings of this study is the existence of limit cycles in the regions of instability predicted by linear theory. Such results explain the superior stability characteristics of the floating ring bearing in high speed applications. An understanding of this nonlinear behavior, serves as the basis for new and rational criteria for the design of floating ring bearings.

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