Effects of Shearing Loads and In-Plane Boundary Conditions on the Stability of Thin Tubes Conveying Fluid

1979 ◽  
Vol 46 (4) ◽  
pp. 779-783 ◽  
Author(s):  
J. Tani ◽  
H. Doki
Keyword(s):  
Boundary Conditions ◽  
Fourier Integral ◽  
Integral Theory ◽  
Plane Boundary ◽  
Simply Supported ◽  
Thin Walled ◽  
Shell Equation ◽  
Divergence Velocity ◽  
The Stability ◽  
Conveying Fluid

The hydroelastic stability of short, simply supported, thin-walled tubes conveying fluid is examined with an emphasis on the effects of shearing loads and in-plane boundary conditions. The Donnell shell equation is used in conjunction with linearized, potential flow theory. The solution is obtained by using Fourier integral theory and Galerkin’s method. It is found that an increase of the shearing load reduces the critical divergence velocity and raises the corresponding number of circumferential waves. A change in the in-plane boundary conditions exerts the significant effect on the critical divergence velocity of short tubes.

Low Buckling Loads of Axially Compressed Conical Shells

1970 ◽  
Vol 37 (2) ◽  
pp. 384-392 ◽  
Author(s):  
M. Baruch ◽  
O. Harari ◽  
J. Singer
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Plane Boundary ◽  
Essential Difference ◽  
Physical Reason ◽  
Buckling Loads ◽  
Conical Shells ◽  
Simple Supports ◽  
Interaction Curves ◽  
The Stability

The stability of simply supported conical shells under axial compression is investigated for 4 different sets of in-plane boundary conditions with a linear Donnell-type theory. The first two stability equations are solved by the assumed displacement, while the third is solved by a Galerkin procedure. The boundary conditions are satisfied with 4 unknown coefficients in the expression for u and v. Both circumferential and axial restraints are found to be of primary importance. Buckling loads about half the “classical” ones are obtained for all but the stiffest simple supports SS4 (v = u = 0). Except for short shells, the effects do not depend on the length of the shell. The physical reason for the low buckling loads in the SS3 case is explained and the essential difference between cylinder and cone in this case is discussed. Buckling under combined axial compression and external or internal pressure is studied and interaction curves have been calculated for the 4 sets of in-plane 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.

EXACT EIGEN-RELATIONS OF CLAMPED-CLAMPED AND SIMPLY SUPPORTED PIPES CONVEYING FLUIDS

2012 ◽  
Vol 04 (03) ◽  
pp. 1250035 ◽  
Author(s):  
PIN LU ◽  
HONGYU SHENG
Keyword(s):  
Boundary Conditions ◽  
Dynamic Stability ◽  
Dynamic Properties ◽  
Pipe Conveying Fluid ◽  
Simply Supported ◽  
Pipeline Systems ◽  
Benchmark Solutions ◽  
Conveying Fluid ◽  
Flow Velocities

The exact eigen-equations of pipe conveying fluid with clamped-clamped and simply supported boundary conditions are derived. The simplified forms of the general eigen-equations for some specific cases are determined, and the corresponding dynamic properties are calculated and discussed. These properties provide a better understanding on the relationships between the dynamic stability and the flow velocities of the fluid-conveying components and help to design stable pipeline systems. In addition, the dynamic properties obtained by the exact eigen-equations can also serve as benchmark solutions for verifying results obtained by other approximate approaches.

The Stability of Fluid Filled, Circular Cylindrical Pipes Part I - Theoretical Solutions

1986 ◽  
Vol 10 (1) ◽  
pp. 34-46
Author(s):  
A.N. Sherbourne ◽  
J.L. Urrutia-Galicia
Keyword(s):  
Fourier Series ◽  
Stress Field ◽  
Fluid Density ◽  
Natural Boundary ◽  
Simply Supported ◽  
Thin Walled Pipe ◽  
Thin Walled ◽  
Natural Boundary Conditions ◽  
The Stability ◽  
Arbitrary Level

It was shown previously that the usual engineering approach to the problem of shell stability conforms with the more general variational method. Whereas the former entails the equilibrium of all forces acting on an infinitesimal element at incipient buckling, the latter simply replaces the load terms in the general differential equations of equilibrium by equivalent “parametric” or “reduced” loads. The theory is applied to the applied to the problem of the circular, thin walled pipe acting as a simply supported beam containing fluid to any arbitrary level. By expressing the displacements and compatible internal loads in doubly infinite Fourier series which satisfy geometric and natural boundary conditions and using a Bubnov-Galerkin technique, it is possible to obtain estimates of he critical fluid density required to buckle the shell. Two cases of buckling are examined involving full and partially loaded pipes and the solution is seen to be sensitive to the number and location of harmonics included in the numerical calculations. Some logarithmic relationships are proposed between the buckling load and the shell parameters defining length and sectional slenderness. It is shown that the results can be conveniently interpreted using the parameter K which defines the nature of the stress field.

scholarly journals Assessment of Model Uncertainty in the Prediction of the Vibroacoustic Behavior of a Rectangular Plate by Means of Bayesian Inference

2021 ◽  
pp. 264-277
Author(s):  
Nikolai Kleinfeller ◽  
Christopher M. Gehb ◽  
Maximilian Schaeffner ◽  
Christian Adams ◽  
Tobias Melz
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Bayesian Inference ◽  
Boundary Conditions ◽  
Model Uncertainty ◽  
Prediction Error ◽  
Finite Element Models ◽  
Simply Supported ◽  
Thin Walled Structures ◽  
Thin Walled

AbstractDesigning the vibroacoustic properties of thin-walled structures is of particularly high practical relevance in the design of vehicle structures. The vibroacoustic properties of thin-walled structures, e.g., vehicle bodies, are usually designed using finite element models. Additional development effort, e.g., experimental tests, arises if the quality of the model predictions are limited due to inherent model uncertainty. Model uncertainty of finite element models usually occurs in the modeling process due to simplifications of the geometry or boundary conditions. The latter highly affect the vibroacoustic properties of a thin-walled structure. The stiffness of the boundary condition is often assumed to be infinite or zero in the finite element model, which can lead to a discrepancy between the measured and the calculated vibroacoustic behavior. This paper compares two different boundary condition assumptions for the finite element (FE) model of a simply supported rectangular plate in their capability to predict the vibroacoustic behavior. The two different boundary conditions are of increasing complexity in assuming the stiffness. In a first step, a probabilistic model parameter calibration via Bayesian inference for the boundary conditions related parameters for the two FE models is performed. For this purpose, a test stand for simply supported rectangular plates is set up and the experimental data is obtained by measuring the vibrations of the test specimen by means of scanning laser Doppler vibrometry. In a second step, the model uncertainty of the two finite element models is identified. For this purpose, the prediction error of the vibroacoustic behavior is calculated. The prediction error describes the discrepancy between the experimental and the numerical data. Based on the distribution of the prediction error, which is determined from the results of the probabilistic model calibration, the model uncertainty is assessed and the model, which most adequately predicts the vibroacoustic behavior, is identified.

Stability Analysis of the Stiffened Plate with Rids under the Longitudinal Loads

2011 ◽  
Vol 243-249 ◽  
pp. 279-283
Author(s):  
Yu Zhang
Keyword(s):  
Potential Energy ◽  
Boundary Conditions ◽  
Critical Loads ◽  
Minimum Condition ◽  
Stiffened Plates ◽  
Stiffened Plate ◽  
Simply Supported ◽  
Total Potential ◽  
The Stability ◽  
Work Done

The stiffened plate with rids was considered as a whole structure. Using energy method the stability of stiffened plates with rids under the longitudinal forces was analyzed. Calculating the potential energy of deformation of plate and that of rids and the work done by the neutral plane forces of plate when the plates were buckled, the formulas of critical loads of the stiffened plate with rids under longitudinal forces were derived from the minimum condition of total potential energy. Using the formulas in this paper engineers can easily calculate the critical loads of the stiffened plate with rids under the boundary conditions: the opposite sides are fixed and the other opposite sides are simply supported, four sides are simply supported. The formula of critical loads of the stiffened plate with rids under other boundary conditions can be derived using the method in this paper.

Stability Analysis of Elastic Plate in Axial Subsonic Flow

2014 ◽  
Vol 1065-1069 ◽  
pp. 2104-2107
Author(s):  
Yu Dong ◽  
Yi Ren Yang ◽  
Li Lu
Keyword(s):  
Boundary Conditions ◽  
Governing Equation ◽  
Elastic Plate ◽  
Subsonic Flow ◽  
Axial Flow ◽  
Vibration Displacement ◽  
Simply Supported ◽  
The Matrix ◽  
The Stability ◽  
Analytical Approaches

The stability and dynamics of the two-dimensional elastic plate with simply supported boundary conditions in uniform axial subsonic flow were studied. The governing equations of coupled elastic plate in axial flow were derived based on the potential theory. The finite difference method was employed to discrete the governing equation and the flow potential function. The governing equation can be expressed as the function of structural transverse vibration displacement by the matrix operations. The eigenvalue method was used to analyze the stability of the elastic plate, the results of which show that the models with simply supported boundary conditions undergo divergent instability when flow velocity reaches the critical value, the critical divergence velocity is in close agreement with theoretical result using other analytical approaches.

scholarly journals Buckling of elastically restrained cantilever wall with free edge stiffening

2014 ◽  
Vol 13 (3) ◽  
pp. 291-298
Author(s):  
Andrzej Szychowski
Keyword(s):  
Boundary Conditions ◽  
Cross Section ◽  
Free Edge ◽  
Stability Loss ◽  
Buckling Analysis ◽  
Thin Walled ◽  
The Stability ◽  
Elastically Restrained ◽  
Plate Deflection ◽  
Open Cross Section

The issue of the stability loss in a compressed wall of a thin-walled member with an open cross section was reduced to the buckling analysis of the cantilever wall. The wall was unilaterally elastically restrained against rotation. The stiffening of the free edge of the wall was susceptible to deflection. The plate deflection functions and stiffenings that allow the modelling of boundary conditions on both longitudinal edges were proposed. Graphs of buckling coefficients for different indexes of the elastic restraint of the supported edge and different geometries of the edge stiffening were determined.

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