Invariant boundary value problems for a fourth-order dynamic Euler-Bernoulli beam equation

2012 ◽  
Vol 53 (4) ◽  
pp. 043703 ◽  
Author(s):  
Ashfaque H. Bokhari ◽  
F. M. Mahomed ◽  
F. D. Zaman
Keyword(s):  
Boundary Value Problems ◽  
Fourth Order ◽  
Boundary Value ◽  
Beam Equation ◽  
Bernoulli Beam ◽  
Euler Bernoulli Beam

scholarly journals Numerical Solution of Fourth-Order Boundary Value Problems for Euler-Bernoulli Beam Equation using FDM

2021 ◽  
Vol 2070 (1) ◽  
pp. 012052
Author(s):  
M. Adak ◽  
A. Mandal
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Difference Method ◽  
Boundary Value ◽  
Stability And Convergence ◽  
Beam Equation ◽  
Bernoulli Beam ◽  
Euler Bernoulli Beam

Abstract Euler-Bernoulli beam equation is widely used in engineering, especially civil and mechanical engineering to determine the deflection or strength of bending beam. In physical science and engineering, to predict the deflection for beam problem, bending moment, soil settlement and modeling of viscoelastic flows, fourth-order ordinary differential equation (ODE) is widely used. The analytical solution of most of the higher order ordinary differential equations with complicated boundary condition that occur in any engineering problems is not easy way. Therefore, numerical technique based on finite difference method (FDM) is comparatively easy and important for solving the boundary value problems (BVP). In this study four boundary conditions (Neumann condition) are considered for solving BVP. Absolute error calculation, numerical stability and convergence are discussed. Two examples are considered to illustrate the finite difference method for solving fourth order BVP. The numerical results are rapidly converged with exact results. The results shows that the FDM is appropriate and reliable for such type of problems. Thus present study will enhance the mathematical understanding of engineering students along with an application in different field.

Symmetries and integrability of a fourth-order Euler–Bernoulli beam equation

2010 ◽  
Vol 51 (5) ◽  
pp. 053517 ◽  
Author(s):  
Ashfaque H. Bokhari ◽  
F. M. Mahomed ◽  
F. D. Zaman
Keyword(s):  
Fourth Order ◽  
Beam Equation ◽  
Bernoulli Beam ◽  
Euler Bernoulli Beam

On Solvability and Well-Posedness of Boundary Value Problems for Nonlinear Hyperbolic Equations of the Fourth Order

2008 ◽  
Vol 15 (3) ◽  
pp. 555-569
Author(s):  
Tariel Kiguradze
Keyword(s):  
Hyperbolic Equation ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Hyperbolic Equations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Nonlinear Hyperbolic Equation ◽  
Well Posedness ◽  
Nonlinear Hyperbolic Equations ◽  
Right Hand

Abstract In the rectangle Ω = [0, a] × [0, b] the nonlinear hyperbolic equation 𝑢(2,2) = 𝑓(𝑥, 𝑦, 𝑢) with the continuous right-hand side 𝑓 : Ω × ℝ → ℝ is considered. Unimprovable in a sense sufficient conditions of solvability of Dirichlet, Dirichlet–Nicoletti and Nicoletti boundary value problems are established.

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