scholarly journals A SIMPLE METHOD OF SOLVING ILKOVIC'S DIFFERENTIAL EQUATION FOR THE TRANSFER OF DEPOLARIZER TO THE DROPPING MERCURY ELECTRODE

1962 ◽  
Vol 40 (2) ◽  
pp. 296-300 ◽  
Author(s):  
R. S. Subrahmanya
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Laplace Transform ◽  
Mercury Electrode ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Simple Method ◽  
Dropping Mercury Electrode ◽  
The Laplace Transform ◽  
New Variables

The method developed by Ilkovic for solving the differential equation[Formula: see text]which governs the diffusion of the depolarizer to the surface of the dropping mercury electrode is very difficult. In the present work a simple method is presented. The above equation is transformed into ∂C/∂T = ∂2C/∂s2 by introducing the two new variables s = xt2/3/2. √((3/7)D) and T = (1/4)t/7/3. The boundary conditions for the transformed differential equation are formulated and the equation is solved by the Laplace transform method.

Static Deflections and Stresses in Sandwich Beams under Various Boundary Conditions

1982 ◽  
Vol 24 (1) ◽  
pp. 11-20 ◽  
Author(s):  
S. R. Sharma ◽  
D. K. Rao
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Laplace Transform ◽  
Energy Method ◽  
Sandwich Beams ◽  
Laplace Transform Method ◽  
Transform Method ◽  
System Parameters ◽  
Various Boundary Conditions ◽  
The Laplace Transform

Expressions for deflections and stresses of sandwich beams are derived for all practically important boundary conditions for both uniform as well as concentrated loads. The energy method is used in deriving the differential equations governing deflection which are then solved by using the Laplace transform method. The influence of system parameters on deflections and stresses is illustrated for important boundary conditions by means of graphs and formulae. These investigations reveal that riveting an edge can reduce the deflections and stresses by as much as 40 per cent.

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