Analytical Model for Self-Excited Vibration of an Overflow Flexible Plate Weir

1999 ◽  
Vol 121 (3) ◽  
pp. 296-303 ◽  
Author(s):  
S. Kaneko ◽  
H. Nagakura ◽  
R. Nakano
Keyword(s):  
Analytical Model ◽  
Stability Boundary ◽  
Pressure Rise ◽  
Flexible Plate ◽  
Instability Condition ◽  
Simply Supported ◽  
Plate Vibrations ◽  
Excited Vibration ◽  
The Stability ◽  
Tank Sloshing

An analytical model for the self-excited vibration of an overflow flexible weir as observed in the French demonstration fast breeder reactor, Super Phenix-1, is proposed. The instability condition was derived for the case in which the plate vibrates at the frequency of the downstream tank sloshing. In this analysis, the flexible plate weir is modeled as a simply supported-free-simply supported-clamped rectangular plate. Eigenfunction expansions were applied for analyzing both plate vibrations and the downstream tank sloshing. The effect of an overflow liquid is formulated based on the assumption that the momentum change due to the collision of an overflow liquid partly transmitted to the pressure rise on the free surface. As a result, the characteristic equation of the system yielding the theoretical stability boundary was obtained. The stability boundary thus derived agreed well with experimental results.

A New Curve Tracking Algorithm for Efficient Computation of Stability Boundaries of Cutting Processes

2007 ◽  
Vol 2 (4) ◽  
pp. 360-365 ◽  
Author(s):  
Christoph Henninger ◽  
Peter Eberhard
Keyword(s):  
Stability Boundary ◽  
Computational Cost ◽  
Boundary Curve ◽  
Efficient Computation ◽  
Technological Parameters ◽  
Excited Vibration ◽  
The Stability ◽  
Cutting Processes ◽  
Delay Differential ◽  
Curve Tracking

Dynamic stability of cutting processes such as milling and turning is mainly restricted by the phenomenon of the regenerative effect, causing self-excited vibration, which is well known as machine-tool chatter. With the semidiscretization method for periodic delay-differential equations, there exists an appropriate method for determining the stability boundary curve in the domain of technological parameters. The stability boundary is implicitly defined as a level set of a function on the parameter domain, which makes the evaluation computationally expensive when using complete enumeration. In order to reduce computational cost, we first investigate two types of curve tracking algorithms finding them not appropriate for computing stability charts as they may get stuck at cusp points or near-branch zones. We then present a new curve tracking method, which overcomes these difficulties and makes it possible to compute stability boundary curves very efficiently.

On the Unsteady Supersonic Cascade With a Subsonic Leading Edge—An Exact First Order Theory—Part 2

1974 ◽  
Vol 96 (1) ◽  
pp. 23-31 ◽  
Author(s):  
M. Kurosaka
Keyword(s):  
Closed Form ◽  
Stability Boundary ◽  
Pressure Rise ◽  
Leading Edge ◽  
Order Theory ◽  
Back Pressure ◽  
First Order ◽  
First Order Theory ◽  
The Stability ◽  
Stagger Angle

Pursuant to Part 1, the analysis of the aerodynamic forces acting on slowly oscillating airfoils in a supersonic cascade with a subsonic leading edge is presented. First the flow field between adjacent airfoils is determined. In the limit of sonic leading edge, the present results for the velocity potential agree with the sonic limit of Lane’s supersonic leading edge analysis. The requirement of the continuity of pressure in the “train” leads to functional equations for the train velocity; their solutions, obtained in closed form, are found to involve arbitrary constants which are related to the back pressure. The effect of the back pressure on the “train” is discussed in detail. For a cascade with zero pressure rise across it, the train velocity is determined completely and the formulas for lift and moment, accurate to the first order of a frequency parameter, are obtained in closed form. Stability criteria for a single-degree-of-freedom motion are examined. A pure bending motion is found to be stable, but a pure torsional motion becomes unstable under certain circumstances. These results are consistent with analogous oscillations of an isolated airfoil. However, the stability boundary for a typical cascade differs significantly from the case of the isolated airfoil, being strongly influenced by such cascade parameters as solidity, blade-to-blade phase difference, and stagger angle.

A Method for Evaluating the Aerodynamic Stability of Multi-Stage Axial-Flow Compressors

2009 ◽  
Author(s):  
Tsuguji Nakano ◽  
Andy Breeze-Stringfellow
Keyword(s):  
Steady State ◽  
Flow Field ◽  
Stability Boundary ◽  
Axial Flow ◽  
Pressure Rise ◽  
State Density ◽  
Constant Density ◽  
Multi Stage ◽  
The Stability ◽  
Axial Flow Compressors

A new simple engineering parameter to evaluate the stability of multi-stage axial compressors has been derived. It is based on the stability analysis for a small circumferential disturbance imposed on the steady state flow field. The analytical model assumes that the flow field is two dimensional and incompressible in the ducts between blade rows although the steady state density is permitted to change across the blade rows. The resulting stall parameter contains terms that relate to the slope of the pressure rise characteristic of the blade rows and the inertia effects of the fluid in the blade rows and ducts. The parameter leads to the classical stability criteria based on the slope of the overall total to static pressure rise coefficient in the limit where constant density and constant blade rotational speed are assumed across the compressor. The proposed stall parameter has been calculated for three different multi-stage axial flow compressors and the results indicate that the parameter has a strong correlation with the measured stability of the compressors. The good correlation with the test data demonstrates that the newly derived stall parameter captures much of the fundamental physics of instability inception in multi-stage compressors, and that it can be a good guideline for designers and engineers needing to evaluate the stability boundary of multi-stage machines.

Roles of vanes in diffuser on stability of centrifugal compressor

2019 ◽  
Vol 233 (14) ◽  
pp. 5380-5392
Author(s):  
Wangzhi Zou ◽  
Xiao He ◽  
Wenchao Zhang ◽  
Zitian Niu ◽  
Xinqian Zheng
Keyword(s):  
High Pressure ◽  
Centrifugal Compressor ◽  
Dynamic Pressure ◽  
Pressure Ratio ◽  
Pressure Rise ◽  
Rotating Stall ◽  
Centrifugal Compressors ◽  
Compression System ◽  
The Stability ◽  
Rotating Instability

The stability considerations of centrifugal compressors become increasingly severe with the high pressure ratios, especially in aero-engines. Diffuser is the major subcomponent of centrifugal compressor, and its performance greatly influences the stability of compressor. This paper experimentally investigates the roles of vanes in diffuser on component instability and compression system instability. High pressure ratio centrifugal compressors with and without vanes in diffuser are tested and analyzed. Rig tests are carried out to obtain the compressor performance map. Dynamic pressure measurements and relevant Fourier analysis are performed to identify complex instability phenomena in the time domain and frequency domain, including rotating instability, stall, and surge. For component instability, vanes in diffuser are capable of suppressing the emergence of rotating stall in the diffuser at full speeds, but barely affect the characteristics of rotating instability in the impeller at low and middle speeds. For compression system instability, it is shown that the use of vanes in diffuser can effectively postpone the occurrence of compression system surge at full speeds. According to the experimental results and the one-dimensional flow theory, vanes in diffuser turn the diffuser pressure rise slope more negative and thus improve the stability of compressor stage, which means lower surge mass flow rate.

Tertiary solutions and their stability in rotating plane Couette flow

1998 ◽  
Vol 358 ◽  
pp. 357-378 ◽  
Author(s):  
M. NAGATA
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Stability Boundary ◽  
Streamwise Vortex ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Plane Couette Flow ◽  
Streamwise Direction ◽  
The Stability ◽  
Oscillatory Instabilities

The stability of nonlinear tertiary solutions in rotating plane Couette flow is examined numerically. It is found that the tertiary flows, which bifurcate from two-dimensional streamwise vortex flows, are stable within a certain range of the rotation rate when the Reynolds number is relatively small. The stability boundary is determined by perturbations which are subharmonic in the streamwise direction. As the Reynolds number is increased, the rotation range for the stable tertiary motions is destroyed gradually by oscillatory instabilities. We expect that the tertiary flow is overtaken by time-dependent motions for large Reynolds numbers. The results are compared with the recent experimental observation by Tillmark & Alfredsson (1996).

Nonstationary Response of a Two-Degrees-of-Freedom Nonlinear Ship Model Under Modulated Excitation

1995 ◽  
Author(s):  
Ruigui Pan ◽  
Huw G. Davies
Keyword(s):  
Degrees Of Freedom ◽  
Stability Boundary ◽  
Period Doubling ◽  
Approximate Solutions ◽  
Loss Of Stability ◽  
Two Degrees Of Freedom ◽  
Ship Model ◽  
Nonstationary Response ◽  
Period 2 ◽  
The Stability

Abstract Nonstationary response of a two-degrees-of-freedom system with quadratic coupling under a time varying modulated amplitude sinusoidal excitation is studied. The nonlinearly coupled pitch and roll ship model is based on Nayfeh, Mook and Marshall’s work for the case of stationary excitation. The ship model has a 2:1 internal resonance and is excited near the resonance of the pitch mode. The modulated excitation (F0 + F1 cos ωt) cosQt is used to model a narrow band sea-wave excitation. The response demonstrates a variety of bifurcations, loss of stability, and chaos phenomena that are not present in the stationary case. We consider here the periodically modulated response. Chaotic response of the system is discussed in a separate paper. Several approximate solutions, under both small and large modulating amplitudes F1, are obtained and compared with the exact one. The stability of an exact solution with one mode having zero amplitude is studied. Loss of stability in this case involves either a rapid transition from one of two stable (in the stationary sense) branches to another, or a period doubling bifurcation. From Floquet theory, various stability boundary diagrams are obtained in F1 and F0 parameter space which can be used to predict the various transition phenomena and the period-2 bifurcations. The study shows that both the modulation parameters F1 and ω (the modulating frequency) have great effect on the stability boundaries. Because of the modulation, the stable area is greatly expanded, and the stationary bifurcation point can be exceeded without loss of stability. Decreasing ω can make the stability boundary very complicated. For very small ω the response can make periodic transitions between the two (pseudo) stable solutions.

Study on Self-Excited Vibration Mechanism of Wheel-Rail Lateral Contact System

2013 ◽  
Vol 427-429 ◽  
pp. 257-261
Author(s):  
Li Xia Sun ◽  
Jian Wei Yao ◽  
Fu Guo Hou ◽  
Xin Zhao
Keyword(s):  
Feedback Mechanism ◽  
Point Of View ◽  
Contact System ◽  
Vibration System ◽  
Lateral Contact ◽  
System A ◽  
Vibration Model ◽  
Excited Vibration ◽  
Vibration Mechanism ◽  
The Stability

In order to investigate self-excited vibration mechanism of wheel-rail lateral contact system, a two DOF elasticity position wheelset lateral vibration model is established which considers the dry friction; the mechanism of the wheelset lateral self-excited vibration is investigated from the energy point of view. It shows that: the bifurcation diagram of this wheel-rail lateral contact system has a supercritical Hopf bifurcation. The energy of self-excited vibration derives from a part of traction energy; the creep rate in the wheel-rail system act as a feedback mechanism in the wheelset lateral self-excited vibration system. The stability of the wheelset self-excited vibration system depends mainly on the total energy removed from and imported into the system.

scholarly journals Flexural-Torsional Vibration of Thin-Walled Beams Subjected to Combined Initial Axial Load and End Bending Moment: Application to the Design of Saw Tooth Blades

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Van Binh Phung ◽  
Anh Tuan Nguyen ◽  
Hoang Minh Dang ◽  
Thanh-Phong Dao ◽  
V. N. Duc
Keyword(s):  
Boundary Conditions ◽  
Axial Load ◽  
Stability Boundary ◽  
Bending Moment ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Rayleigh Method ◽  
Thin Walled ◽  
The Stability ◽  
Fixed End

The present paper analyzes the vibration issue of thin-walled beams under combined initial axial load and end moment in two cases with different boundary conditions, specifically the simply supported-end and the laterally fixed-end boundary conditions. The analytical expressions for the first natural frequencies of thin-walled beams were derived by two methods that are a method based on the existence of the roots theorem of differential equation systems and the Rayleigh method. In particular, the stability boundary of a beam can be determined directly from its first natural frequency expression. The analytical results are in good agreement with those from the finite element analysis software ANSYS Mechanical APDL. The research results obtained here are useful for those creating tooth blade designs of innovative frame saw machines.

Double-diffusive instabilities in a vertical slot

1999 ◽  
Vol 392 ◽  
pp. 213-232 ◽  
Author(s):  
OLIVER S. KERR ◽  
KIT YEE TANG
Keyword(s):  
Temperature Difference ◽  
Salinity Gradient ◽  
Stability Boundary ◽  
Large Temperature ◽  
Vertical Slot ◽  
Stability And Instability ◽  
Heat Diffusivity ◽  
Prandtl Numbers ◽  
The Stability ◽  
Double Diffusive

A fluid stably stratified by a salinity gradient and enclosed between two vertical boundaries can become unstable when it is subjected to a temperature difference between the walls. The linear stability of such a fluid in a vertical slot is investigated. Errors in earlier results are found, confirming recent results of Young & Rosner (1998). Four different asymptotic regimes on the stability boundary are identified. One of these, the limit of a strong salinity gradient, has previously been analysed. The analyses of the separate asymptotic limits of weak salinity gradient, large temperature difference and small wavenumber are also given. These four cases make up much of the total boundary between stability and instability for double-diffusive instabilities in a vertical slot, and so most of this boundary can be mapped out for general Prandtl numbers and salt/heat diffusivity ratios using these results.

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