Band-Gap Resonances in a Linear Diatomic Chain With General Boundary Conditions: Closed-Form Existence Conditions

2021 ◽  
Author(s):  
Mary Bastawrous ◽  
Mahmoud Hussein
Keyword(s):  
Boundary Conditions ◽  
Closed Form ◽  
Band Gap ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Diatomic Chain ◽  
Existence Conditions

scholarly journals Closed-Form Solutions of Linear Ordinary Differential Equations with General Boundary Conditions

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 226
Author(s):  
Efthimios Providas ◽  
Stefanos Zaoutsos ◽  
Ioannis Faraslis
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Closed Form ◽  
Linear Operators ◽  
General Boundary ◽  
Order Differential Operator ◽  
General Boundary Conditions ◽  
Symbolic Form ◽  
Closed Form Solutions

This paper deals with the solution of boundary value problems for ordinary differential equations with general boundary conditions. We obtain closed-form solutions in a symbolic form of problems with the general n-th order differential operator, as well as the composition of linear operators. The method is based on the theory of the extensions of linear operators in Banach spaces.

Closed Form Buckling Solutions of Euler-Bernoulli Columns With Multiple Singularities

2009 ◽  
Author(s):  
Salvatore Caddemi ◽  
Ivo Calio`
Keyword(s):  
Boundary Conditions ◽  
Closed Form ◽  
Parametric Study ◽  
Generalized Functions ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Buckling Mode ◽  
Different Boundary Conditions ◽  
Integration Procedure ◽  
Mode Solution

In this paper the Euler-Bernoulli column in presence of multiple concentrated open cracks and for general boundary conditions is studied. The request of an integration procedure able to lead to exact closed form buckling solutions for any number, position and intensity of the cracks is satisfied. A model of concentrated crack based on the adoption of the distributions (generalized functions) is presented. In particular, the exact buckling mode solution and the corresponding exact buckling load equation is obtained. A parametric study for different boundary conditions is presented.

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