Inclusion of a Support Friction Into a Computerized Solution of a Self-Compensating Pipeline

1972 ◽  
Vol 94 (3) ◽  
pp. 797-802 ◽  
Author(s):  
J. Sobieszczanski
Keyword(s):  
Differential Equation ◽  
Computer Program ◽  
Fourth Order ◽  
Order Differential Equation ◽  
Bending Moment ◽  
Variable Coefficients ◽  
Point Boundary ◽  
Friction Forces ◽  
The One ◽  
Fourth Order Differential Equation

Thermal elongations of a pipeline are compensated in many cases by bending of pipeline branches. If the pipeline lies on a horizontal rough and flat foundation that bending is influenced by friction forces. Analysis of that influence is given in the paper. A nonlinear, fourth order differential equation with variable coefficients governing the phenomenon is derived and solved numerically as a two-point boundary problem. A version of the solution suitable for a pipeline on discrete supports has been developed. It may be used in conjunction with any existing computer program for pipeline stress analysis. The results demonstrate existence of a very significant additional bending moment due to friction. It may exceed several times the one computed for a pipeline on frictionless foundation.

COMMENTS ON THE STRUCTURAL FEATURES OF THE PAIS–UHLENBECK OSCILLATOR

2013 ◽  
Vol 28 (14) ◽  
pp. 1375001 ◽  
Author(s):  
B. BAGCHI ◽  
A. GHOSE CHOUDHURY ◽  
PARTHA GUHA
Keyword(s):  
Differential Equation ◽  
Fourth Order ◽  
Order Differential Equation ◽  
Structural Features ◽  
The Other ◽  
Alternative Derivation ◽  
The One ◽  
Fourth Order Differential Equation

We explore the Jacobi last multiplier (JLM) as a means for deriving the Lagrangian of a fourth-order differential equation. In particular, we consider the classical Pais–Uhlenbeck problem and write down the accompanying Hamiltonian. We then compare such an expression with our alternative derivation of the Hamiltonian that makes use of the Ostrogradski's method and show how a mapping from the one to the other is achievable by variable transformations.

scholarly journals Asymptotic theory for a critical case for a general fourth-order differential equation

1998 ◽  
Vol 21 (3) ◽  
pp. 479-488
Author(s):  
A. S. A. Al-Hammadi
Keyword(s):  
Differential Equation ◽  
Fourth Order ◽  
Critical Case ◽  
Asymptotic Theory ◽  
Order Differential Equation ◽  
Fourth Order Equations ◽  
Fourth Order Differential Equation

In this paper we identify a relation between the coefficients that represents a critical case for general fourth-order equations. We obtained the forms of solutions under this critical case.

25.—On the Eigenfunction Expansion associated with a Singular Complex-valued Fourth-order Differential Equation

1976 ◽  
Vol 75 (4) ◽  
pp. 325-332
Author(s):  
Jyoti Chaudhuri ◽  
V. Krishna Kumar
Keyword(s):  
Differential Equation ◽  
Fourth Order ◽  
Representation Theorem ◽  
Eigenfunction Expansion ◽  
Order Differential Equation ◽  
Convergence Theory ◽  
Infinite Intervals ◽  
Complex Valued ◽  
Class Of Functions ◽  
Fourth Order Differential Equation

SynopsisThe direct convergence theory of eigenfunction expansions associated with boundry value problems, not necessarily self-adjoint, generated from complex-valued fourth-order symmetric ordinary differential expressions on semi-infinite intervals, is discussed. An admissible class of functions for the expansion is characterised. Also a generalisation of Stieltjes representation theorem for analytic functions discussed in [13, §§ 22.23 and 24] is obtained.

XXIII.—On an Extension to an Integro-differential Inequality of Hardy, Littlewood and Polya

1972 ◽  
Vol 69 (4) ◽  
pp. 295-333 ◽  
Author(s):  
W. N. Everitt
Keyword(s):  
Differential Equation ◽  
Fourth Order ◽  
Differential Inequality ◽  
Order Differential Equation ◽  
Order Equation ◽  
Second Order ◽  
Image Position ◽  
Fourth Order Differential Equation

SynopsisThis paper considers an extension of the following inequality given in the book Inequalities by Hardy, Littlewood and Polya; let f be real-valued, twice differentiable on [0, ∞) and such that f and f are both in the space fn, ∞), then f′ is in L,2(0, ∞) andThe extension consists in replacing f′ by M[f] wherechoosing f so that f and M[f] are in L2(0, ∞) and then seeking to determine if there is an inequality of the formwhere K is a positive number independent of f.The analysis involves a fourth-order differential equation and the second-order equation associated with M.A number of examples are discussed to illustrate the theorems obtained and to show that the extended inequality (*) may or may not hold.

scholarly journals The Solution of Nonlinear Fourth-Order Differential Equation with Integral Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yanli Fu ◽  
Huanmin Yao
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Reproducing Kernel ◽  
Order Differential Equation ◽  
Integral Boundary Conditions ◽  
Reproducing Kernel Space ◽  
Integral Boundary ◽  
Derivatives Of ◽  
Fourth Order Differential Equation

An iterative algorithm is proposed for solving the solution of a nonlinear fourth-order differential equation with integral boundary conditions. Its approximate solutionun(x)is represented in the reproducing kernel space. It is proved thatun(x)converges uniformly to the exact solutionu(x). Moreover, the derivatives ofun(x)are also convergent to the derivatives ofu(x). Numerical results show that the method employed in the paper is valid.

Sign in / Sign up

Export Citation Format

Share Document