Global Static Instability of Risers

1984 ◽  
Vol 28 (04) ◽  
pp. 261-271
Author(s):  
Michael M. Bernitsas ◽  
Theodore Kokkinis
Keyword(s):  
Boundary Conditions ◽  
Internal Pressure ◽  
Stability Boundary ◽  
Critical Length ◽  
Bending Rigidity ◽  
Buckling Mode ◽  
Stability Boundaries ◽  
Various Boundary Conditions ◽  
Static Instability ◽  
The Stability

Global instability of risers depends on riser weight, internal and external fluid static pressure forces, tension exerted at the top of the riser, and boundary conditions. The purpose of this work is to study the effects of these factors on the stability boundaries of risers and specifically.(i) compare buckling loads for various boundary conditions; (ii) find the long-riser instability behavior from the asymptotics of the stability boundaries; (iii) find the short-riser instability behavior; (iv) analyze the relative effects of boundary conditions, weight, internal pressure, and bending rigidity on stability; (v) show the variation of the stability boundary shape with the order of the buckling mode; and (vi) compare the critical length at which risers in tension over their entire length may buckle due to internal pressure, for various boundary conditions.

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.

Buckling of Risers in Tension due to Internal Pressure: Nonmovable Boundaries

1983 ◽  
Vol 105 (3) ◽  
pp. 277-281 ◽  
Author(s):  
M. M. Bernitsas ◽  
T. Kokkinis
Keyword(s):  
Internal Pressure ◽  
Fluid Pressure ◽  
Critical Length ◽  
Entire Length ◽  
Tubular Columns ◽  
Internal Fluid ◽  
Static Instability

Open-ended tubular columns may buckle globally as Euler columns due to the action of internal fluid pressure even while they are in tension along their entire length. Hydraulic columns, marine drilling and production risers are, therefore, prone to such static instability. This paper explains this phenomenon, defines the critical riser length for which this instability may occur and provides graphs with values of the critical length which can readily be used for design purposes. Risers with nonmovable boundaries are considered; namely, hinged-hinged, clamped-hinged, hinged-clamped and clamped-clamped risers.

The Stability of Self-Acting Gas Journal Bearings With Noncircular Members and Additional Elements of Flexibility

1969 ◽  
Vol 91 (1) ◽  
pp. 113-119 ◽  
Author(s):  
H. Marsh
Keyword(s):  
Stability Boundary ◽  
Journal Bearings ◽  
Satisfactory Explanation ◽  
Unusual Behavior ◽  
Stability Boundaries ◽  
Linearized Theory ◽  
New Type ◽  
The Stability ◽  
Theory And Experiments ◽  
Bearing System

The linearized theory for the stability of self-acting gas bearings is extended to include bearing systems with noncircular members or additional elements of flexibility and damping. The theory offers a satisfactory explanation for the unusual behavior of a bearing system with a three-lobed rotor, including the whirl at low speeds and the whirl cessation. A comparison between the theory and experiments for a flexibly mounted bearing system shows that the theory can be applied to predict the stability boundaries of bearing systems with additional elements of flexibility. A new type of bearing apparatus is proposed in which it would be possible to obtain information about bearing stability without operating at the stability boundary.

The Stability of Plane Poiseuille Flow in a Finite-Length Channel

2021 ◽  
Author(s):  
Lei Xu ◽  
Zvi Rusak
Keyword(s):  
Kinetic Energy ◽  
Boundary Conditions ◽  
Linear Stability ◽  
Finite Length ◽  
Poiseuille Flow ◽  
Weak Form ◽  
Plane Poiseuille Flow ◽  
Various Boundary Conditions ◽  
New Perspective ◽  
The Stability

Abstract The linear stability of plane Poiseuille flow through a finite-length channel is studied. A weakly-divergence-free basis finite element method with SUPG stabilization is used to formulate the weak form of the problem. The linear stability characteristics are studied under three possible inlet-outlet boundary conditions and the corresponding perturbation kinetic energy transfer mechanisms are investigated. Active transfer of perturbation kinetic energy at the channel inlet and outlet, energy production due to convection and dissipation at the flow bulk provide a new perspective in understanding the distinct stability characteristics of plane Poiseuille flow under various boundary conditions.

Vibration and Frequency Analysis of Non-Uniform Timoshenko Beams Subjected to Axial Forces

2003 ◽  
Author(s):  
A. R. Ohadi ◽  
H. Mehdigholi ◽  
E. Esmailzadeh
Keyword(s):  
Stability Analysis ◽  
Boundary Conditions ◽  
Axial Force ◽  
Frequency Equation ◽  
Axial Loads ◽  
Various Boundary Conditions ◽  
Axial Forces ◽  
First Case ◽  
The Stability ◽  
Elastically Supported

Dynamic and stability analysis of non-uniform Timoshenko beam under axial loads is carried out. In the first case of study, the axial force is assumed to be perpendicular to the shear force, while for the second case the axial force is tangent to the axis of the beam column. For each case, a pair of differential equations coupled in terms of the flexural displacement and the angle of rotation due to bending was obtained. The parameters of the frequency equation were determined for various boundary conditions. Several illustrative examples of uniform and non-uniform beams with different boundary conditions such as clamped supported, elastically supported, and free end mass have been presented. The stability analysis, for the variation of the natural frequencies of the uniform and non-uniform beams with the axial force, has also been investigated.

scholarly journals ENSURING STABILITY OF HYDRO-MECHANICAL CONTROL SYSTEMS WITH CONSTANT PRESSURE VALVES

2020 ◽  
Vol 6 (2) ◽  
pp. 26-33
Author(s):  
Evgeniy V. Shakhmatov ◽  
V. P. Shorin ◽  
T. A. Chubenko
Keyword(s):  
Boundary Conditions ◽  
Control Systems ◽  
Constant Pressure ◽  
Stability Boundary ◽  
Experimental Studies ◽  
Mechanical Control ◽  
The Stability

In this article, theoretical dependencies for constructing the stability boundary of the system were determined. The influence of the characteristics of the connected circuits on the stability of the constant pressure valve is analyzed. To confirm the established theoretical dependences, experimental studies of the valve with the corresponding boundary conditions were carried out. As a result, oscillograms of valve tests were obtained for various connected lines.

Phase-Locked Mode Stability for Coupled van der Pol Oscillators

1999 ◽  
Vol 122 (3) ◽  
pp. 318-323 ◽  
Author(s):  
Duane W. Storti ◽  
Per G. Reinhall
Keyword(s):  
Variational Equation ◽  
Stability Boundary ◽  
Series Expansions ◽  
Van Der Pol ◽  
Stability Boundaries ◽  
Power Series Expansions ◽  
Mode Stability ◽  
Van Der Pol Oscillators ◽  
The Stability ◽  
The Hill

The critical variational equation governing the stability of phase-locked modes for a pair of diffusively coupled van der Pol oscillators is presented in the form of a linear oscillator with a periodic damping coefficient that involves the van der Pol limit cycle. The variational equation is transformed into a Hill’s equation, and stability boundaries are obtained by analytical and numerical methods. We identify a countable set of resonances and obtain expressions for the associated stability boundaries as power series expansions of the associated Hill determinants. We establish an additional “zero mean damping” condition and express it as a Pade´ approximant describing a surface that combines with the Hill determinant surfaces to complete the stability boundary. The expansions obtained are evaluated to visualize the first three resonant surfaces which are compared with numerically determined slices through the stability boundaries computed over the range 0.4<ε<5. [S0739-3717(00)00502-X]

On the Elastic Stability of a Rectangular Plate, when Subjected to a Variable Edge Thrust

1935 ◽  
Vol 31 (3) ◽  
pp. 368-381 ◽  
Author(s):  
D. M. A. Leggett
Keyword(s):  
Boundary Conditions ◽  
Approximate Method ◽  
Rectangular Plate ◽  
General Problem ◽  
Elastic Stability ◽  
Detailed Consideration ◽  
Various Boundary Conditions ◽  
The Stability

The stability of a rectangular plate, subjected to constant thrust over opposite pairs of edges, has been treated with some degree of completeness for various boundary conditions. The more general problem, in which the thrusts are no longer constant, has not yet received any treatment apart from the approximate method developed by E. Schwerin†, which would appear to be capable of only limited extension. The object of this paper is accordingly the detailed consideration of a simple case when the thrust is no longer constant.

Numerical study of nonlinear stability boundaries for orifice-compensated hole-entry hybrid journal bearings

2019 ◽  
Vol 234 (12) ◽  
pp. 1867-1880 ◽  
Author(s):  
Jian Li ◽  
Runchang Chen ◽  
Haiyin Cao ◽  
Zhuxin Tian
Keyword(s):  
Finite Length ◽  
Nonlinear Stability ◽  
Critical Speed ◽  
Stability Boundary ◽  
Initial Point ◽  
Journal Bearings ◽  
Stability Boundaries ◽  
Rotating Speed ◽  
The Stability ◽  
Bearing System

A high-performance and finite-length bearing system requires that the shaft can be stabilized even under a strong perturbation. The linear stability theory neglects the effects of nonlinear forces and the initial point of the shaft. Therefore, the stability of the bearing system is largely determined by the rotating speed of the shaft. In the present numerical investigation, the nonlinear forces and initial point of the shaft are accounted for to obtain the nonlinear stability boundary. The objective of this study is extended to orifice-compensated and hole-entry hybrid journal bearings with finite length. The critical rotating speed and the shaft center trajectory are acquired by solving Reynolds equation using the finite element method. By identifying the states of the orbits (stable or unstable), the nonlinear stability boundaries can be obtained. Results show that for the hybrid bearing system under the nonlinear conditions, the critical speed is a determinant factor while the initial location is another key factor. The shaft can be unstable if the initial point is outside of the stability boundary, although the speed is lower than the critical speed. There exists an obvious transitional region between the stable and unstable condition when the speed approaches the critical speed.

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