Physical Interpretations of the Instabilities Encountered in the Deflection Equations of the Unconstrained Pipeline

1976 ◽  
Vol 98 (3) ◽  
pp. 1099-1102
Author(s):  
G. C. Daley
Keyword(s):  
Differential Equations ◽  
Parametric Study ◽  
Flexural Rigidity ◽  
Unit Length ◽  
Vertical Force ◽  
Continuous Beam ◽  
Pipeline Construction ◽  
Sea Floor ◽  
Maximum Value

For a pipeline modeled as having constant rigidity, horizontal tension, and submerged weight per unit length, there is a maximum value that the maximum sag-bend moment attains as the distance from the pin-supported end of the pipe to the sea floor increases. This paper presents the results of a parametric study analyzing a pipeline displaced from the sea floor to some pipeline construction configuration. The pipeline is modeled as a continuous beam having constant submerged weight per unit length and a constant horizontal tension or force with one end supported vertically by the sea floor. The governing differential equations are solved in terms of dimensionless combinations of the three characteristic variables—the submerged weight per unit length, the flexural rigidity, and the constant horizontal tension. This allows any possible pipeline configuration meeting stated constraints to be analyzed. The analysis performed specifies the maximum sag-bend moment. This maximum sag-bend moment is changed by varying the sea floor vertical force until a further change in sea floor reaction does not give a pipeline configuration. This maximum attainable maximum sag-bend moment is then computed and graphed as a function of the three characteristic pipeline values, the horizontal tension, the flexural rigidity, and the submerged weight per unit length.

scholarly journals The Existence and Uniqueness of Solutions and Lyapunov-Type Inequality for CFR Fractional Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Xia Wang ◽  
Run Xu
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Type Inequality ◽  
Uniqueness Theorems ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Maximum Value ◽  
Fractional Differential ◽  
Lyapunov Type Inequality

In this paper, we research CFR fractional differential equations with the derivative of order 3<α<4. We prove existence and uniqueness theorems for CFR-type initial value problem. By Green’s function and its corresponding maximum value, we obtain the Lyapunov-type inequality of corresponding equations. As for application, we study the eigenvalue problem in the sense of CFR.

Member distortional buckling behaviour of hybrid double-I-box beams

2018 ◽  
Vol 45 (8) ◽  
pp. 605-622 ◽  
Author(s):  
M.S. Deepak ◽  
V.M. Shanthi
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Parametric Study ◽  
Flexural Rigidity ◽  
Numerical Study ◽  
Plate Thickness ◽  
Distortional Buckling ◽  
Study Results ◽  
Box Beams ◽  
The Moment

This paper compiles the experimental and finite-element parametric study on member distortional buckling behaviour of new built-up metal hybrid double-I-box beams (HDIBBs). The cross-section of this built-up beam is unique and looks similar to the shape of a double-I-box fabricated using four channel sections. The flange plates were provided with an intermediate stiffener. In these built-up beams there is more material in the flange portions far away from the horizontal centroidal axis of their cross-section. Hence, there is an increase in the flexural rigidity that enhances the moment capacity of the beam, under major axis bending. The geometry consists of torsionally rigid closed-box web portion that provides high resistance to minor axis lateral-buckling. The varying parameters considered were the ratio of yield stresses of the flange to the web steel plates, the ratio of breadth to the depth of the section, and the flange plate thickness. In the experimental programme, all the HDIBB members failed due to kinds of distortional buckling which was identified by web buckling and flange twist along edges. The results revealed that when flange plate slenderness increases there is a drop in the moment resistance capacity of the beams. The numerical study was performed using ABAQUS software. In comparison, there was good agreement between experimental and numerical results. The validated finite element models were further extended to perform parametric studies on ideal HDIBB models. Both the experimental and parametric study results were compared with the predicted strengths using effective width method equations specified in the Euro code standards EN 3-1-3. It was found that the current Euro code design rules slightly over-estimate the distortional buckling resistance capacity of closed form built-up cold-formed steel members. A new design equation was formulated and recommended for estimating the reduction in distortional buckling moment resistance capacity for HDIBBs.

Approximation of Surge and Pitch Loads on Truncated Vertical Cylinders

2003 ◽  
Author(s):  
Keyvan Sadeghi ◽  
Atilla Incecik ◽  
Martin Downie ◽  
Hoi-Sang Chan
Keyword(s):  
Computer Program ◽  
Deep Water ◽  
Parametric Study ◽  
Unit Length ◽  
Diffraction Theory ◽  
Circular Cylinders ◽  
Offshore Platforms ◽  
Vertical Cylinders

Truncated vertical circular cylinders are used to make deep water floating offshore platforms like Truss Spars. When the draft of the cylindrical hull is not deep enough, prediction of the surge and pitch diffraction loads by integration of McCamy and Fuchs expression of the force per unit length over the cylinder draft causes an error which is not negligible. Using hydrodynamic arguments the approximated surge and pitch loads by McCamy and Fuchs diffraction theory are modified. The modified results are compared with the results of a parametric study using the computer program WaMIT 4.01 based on the linear diffraction theory, reported by Weggel [1].

Free vibration analysis of two parallel beams connected together through variable stiffness elastic layer with elastically restrained ends

2016 ◽  
Vol 20 (3) ◽  
pp. 275-287 ◽  
Author(s):  
Alborz Mirzabeigy ◽  
Reza Madoliat ◽  
Mehdi Vahabi
Keyword(s):  
Differential Equations ◽  
Elastic Layer ◽  
Flexural Rigidity ◽  
Free Vibration Analysis ◽  
Variable Stiffness ◽  
Differential Transform Method ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Transform Method ◽  
Differential Transform

In this study, free transverse vibration of two parallel beams connected together through variable stiffness Winkler-type elastic layer is investigated. Euler–Bernoulli beam hypothesis has been applied and the support is considered to be translational and rotational elastic springs in each ends. Linear and parabolic variation has been considered for connecting layer. The equations of motion have been derived in the form of coupled differential equations with variable coefficients. The differential transform method has been applied to obtain natural frequencies and normalized mode shapes of system. Differential transform method is a semi-analytical approach based on Taylor expansion series which converts differential equations to recursive algebraic equations and does not need domain discretization. The results obtained from differential transform method have been validated with the results reported by well-known references in the case of two parallel beams connected through uniform elastic layer. The effects of variation type and total stiffness of connecting layer, flexural rigidity ratio of beams, and boundary conditions on behavior of system are investigated and discussed in detail.

scholarly journals Navigation by light polarization in clear and turbid waters

2011 ◽  
Vol 366 (1565) ◽  
pp. 671-679 ◽  
Author(s):  
Amit Lerner ◽  
Shai Sabbah ◽  
Carynelisa Erlick ◽  
Nadav Shashar
Keyword(s):  
Orientation Angle ◽  
Single Scattering ◽  
Light Polarization ◽  
Aquatic Species ◽  
Sea Floor ◽  
Turbid Waters ◽  
Maximum Value ◽  
Air Water Interface ◽  
Coastal Sea ◽  
Vector Orientation

Certain terrestrial animals use sky polarization for navigation. Certain aquatic species have also been shown to orient according to a polarization stimulus, but the correlation between underwater polarization and Sun position and hence the ability to use underwater polarization as a compass for navigation is still under debate. To examine this issue, we use theoretical equations for per cent polarization and electric vector (e-vector) orientation that account for the position of the Sun, refraction at the air–water interface and Rayleigh single scattering. The polarization patterns predicted by these theoretical equations are compared with measurements conducted in clear and semi-turbid coastal sea waters at 2 m and 5 m depth over sea floors of 6 m and 28 m depth. We find that the per cent polarization is correlated with the Sun's elevation only in clear waters. We furthermore find that the maximum value of the e-vector orientation angle equals the angle of refraction only in clear waters, in the horizontal viewing direction, over the deeper sea floor. We conclude that navigation by use of underwater polarization is possible under restricted conditions, i.e. in clear waters, primarily near the horizontal viewing direction, and in locations where the sea floor has limited effects on the light's polarization.

scholarly journals Posudzovanie kvality odrazu pri salte vpred na základe časových charakteristík okamžitých síl na krivkách odrazu vo vertikálnych a horizontálnych rovinách v realizačnej fáze

2010 ◽  
Vol 4 (1) ◽  
pp. 53-58
Author(s):  
Rastislav Feč ◽  
Tibor Klaček
Keyword(s):  
Horizontal Plane ◽  
Test Group ◽  
Time Frame ◽  
Vertical Force ◽  
Spearman Correlation ◽  
Maximum Value ◽  
Potential Indicator ◽  
Coeffi Cients ◽  
Correct Technique ◽  
Correlation Coeffi

The paper deals with looking for potential indicators of correct technique of bounce concerning a tucked forward somersault on the base of relations between time characteristics of instantaneous forces in a vertical and horizontal plane in a realization phase of the bounce. Our test-group was created by 13 students of Faculty of Sport. We used statistical signifi cance of Spearman correlation coeffi cients p ≤ 0,05 as a method for judging whether or not a particular ratio of the impulses of forces in the vertical and horizontal plane represents a suitable indicator of correct technique of bounce. We assumed that some of the observed ratios will represent the potential indicator of correct technique of bounce. Th e hypothesis was confi rmed. Th e potential indicators of bounce are the following: variable 4 (time frame since vertical force reached its maximum value to the end of jump to total time of bounce), variable 6 (time frame since vertical force reached its maximum value to the end of bounce to the time frame from when horizontal force reached its maximum value to the end of bounce), variable 2 (time frame since vertical force reached its maximum value to the end of bounce).

scholarly journals Analisa Gaya Penekanan pada Proses ECAP Batang Kuningan CuZn 70/30

2019 ◽  
Vol 8 (1) ◽  
pp. 39-46
Author(s):  
Suryadi ◽  
Amin Suhadi ◽  
Dedi Priadi ◽  
E. S. Siradj
Keyword(s):  
Plastic Deformation ◽  
Severe Plastic Deformation ◽  
Unit Length ◽  
Area Under The Curve ◽  
Pressing Force ◽  
The Third ◽  
Angular Pressing ◽  
Maximum Value ◽  
First Pass ◽  
Fourth Pass

Telah dilakukan percobaan severe plastic deformation (SPD) dengan metodeequal channel angular pressing (ECAP) pada batang kuningan CuZn 70/30 diameter 10 mm sampai 5 pas. Gaya penekanan meningkat secara signifikan pada awal langkah penekanan dan mencapai nilai maksimum lalu melandai. Pada pas pertama gaya penekanan mencapai 115 kN, pas kedua 130 kN, pas ketiga mecapai 150 kN dan pada pas keempat 165 kN. Dari pengukuran luas area di bawah kurva gaya penekanan diperoleh energi total pembentukan pada proses ECAP batang kuningan persatuan panjang adalah 95 Joule/mm pada pas pertama, sampai 130 Joule/mm pada pas ketiga, dan turun 125 Juole/mm pada pas keempat. Secara kumulatif total energi persatuan panjang meningkat secara linier sesuai dengan peningkatan jumpah pas, dimana pada pas keempat mencapai 597 MPa. Peningkatan gaya penekanan dan energi penekanan sebanding dengan terjadinya peningkatan kekerasan pada batang kuningan dan terjadinya penghalusan butir.Kata kunci: ECAP, gaya penekanan, energi pembentukan, kekerasan, penghalusan butir, kuningan.AbstractExperiments of severe plastic deformation (SPD) have been carried out by the method of equal channel angular pressing (ECAP) on brass rods CuZn 70/30 diameter 10 mm to 5 pas. Pressing force significantly is increased emphasis on early steps and reaches a maximum value and then ramp. At the first pas the pressing force reached 115 kN, the second pass 130 kN, the third pass 150 kN and fouth pass is 165. From measurements of the area under the curve of pressing force, the total forming energy per unit length generated to form the brass rod in ECAP is 95 Joule / mm at the first pass, 130 Joules / mm at third pass and down to 125 Joule/mm at fouth pass. Cumulatively, the total forming energy per unit length increases linearly according to the increase in number of ECAP pass, where the fourth pass reach 597 Joule/mm. Increased emphasis pressing load and forming energy is proportional to the increase in hardness of the brass rod and the grain refinement.Keywords: ECAP, pressing load, forming energy, hardness, grain refinement, Brass

Dynamical Modeling and Analysis of the Human Jumping Process

2002 ◽  
Author(s):  
A. Meghdari ◽  
M. Aryanpour
Keyword(s):  
Great Influence ◽  
Linear Velocity ◽  
The Body ◽  
Vertical Force ◽  
Dynamical Equations ◽  
Modeling And Analysis ◽  
Hand Motion ◽  
Maximum Value ◽  
Time Histories ◽  
Off Time

A dynamical model was developed in order to study the jumping process in human, and the effect of factors like joint speeds and hand motion. An experiment was designed and setup to compare the theoretical model with the experimental observations. Time histories of vertical force, mass center velocity and driving torques were obtained too. Using dynamical equations, the effect of joint speeds on the maximum values of these quantities is discussed. It is shown that reducing the joint speeds of a body can lead to an unsuccessful jump in which the body does not enter the flight phase. An increase in speed reduces the take-off time (the time necessary for the body to leave the ground) and increases the body’s linear velocity at take-off, as well as, the maximum value of driving torques. Effect of hand motion is also investigated through suppressing motion of the Shoulder and Elbow. It is observed that hand motion has an improving effect on the body’s linear velocity. Although speed of joints did not show to have a great influence on most torques, those at the Shoulder and Elbow were observed to be more sensitive to it.

THE COSMIC STRINGS GENERATED FROM THE TORSION

1993 ◽  
Vol 08 (06) ◽  
pp. 491-501 ◽  
Author(s):  
TAKEHIKO T. FUJISHIRO ◽  
MITSUO J. HAYASHI ◽  
SHOJI TAKESHITA
Keyword(s):  
Cosmic Strings ◽  
Unit Length ◽  
Three Dimensional ◽  
Fine Tuning ◽  
Crystalline Solid ◽  
Dimensional Model ◽  
Einstein Theory ◽  
Maximum Value ◽  
Deficit Angle ◽  
Space Time Structure

The cosmic strings can be described naturally by torsion formalism which has a direct analogy with dislocations in three-dimensional crystalline solid. We have obtained an exact solution in a four-dimensional model on M2×T2 and may be expected to describe a space-time structure of our universe. The relation between the mass per unit length and the deficit angle are different from that of the Einstein theory, but can be made consistent since our model could reproduce its prediction. We could also obtain the maximum value of the mass per unit length µ~10−6(~1022 g/cm ) by fine tuning of a parameter, which is consistent with the recent observations.

scholarly journals A Spectral Solenoidal-Galerkin Method for Rotating Thermal Convection between Rigid Plates

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Cihan Yıldırım ◽  
Durmuş Yarımpabuç ◽  
Hakan I. Tarman
Keyword(s):  
Differential Equations ◽  
Thermal Convection ◽  
Parametric Study ◽  
Numerical Experiments ◽  
Spectral Representation ◽  
Basis Functions ◽  
Galerkin Procedure ◽  
Governing System ◽  
Dependent Variables ◽  
Nonlinear Simulations

The problem of thermal convection between rotating rigid plates under the influence of gravity is treated numerically. The approach uses solenoidal basis functions and their duals which are divergence free. The representation in terms of the solenoidal bases provides ease in the implementation by a reduction in the number of dependent variables and equations. A Galerkin procedure onto the dual solenoidal bases is utilized in order to reduce the governing system of partial differential equations to a system of ordinary differential equations for subsequent parametric study. The Galerkin procedure results in the elimination of the pressure and is facilitated by the use of Fourier-Legendre spectral representation. Numerical experiments on the linear stability of rotating thermal convection and nonlinear simulations are performed and satisfactorily compared with the literature.

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