A two-dimensional closed-form solution for the free-vibrations analysis of piezoelectric sandwich plates

2002 ◽  
Vol 39 (6) ◽  
pp. 1463-1486 ◽  
Author(s):  
Ayech Benjeddou ◽  
Jean-François Deü
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Free Vibrations ◽  
Form Solution ◽  
Sandwich Plates ◽  
Two Dimensional

Extension of the Circle Theorems by Surface Source Distribution

1989 ◽  
Vol 111 (3) ◽  
pp. 243-247 ◽  
Author(s):  
O. Rand
Keyword(s):  
Circular Cylinder ◽  
Closed Form ◽  
Closed Form Solution ◽  
Strength Distribution ◽  
Form Solution ◽  
Source Distribution ◽  
Arbitrary Distribution ◽  
Normal Velocity ◽  
Two Dimensional ◽  
Surface Source

The paper presents a closed-form analytical solution for the source strength distribution along the circumference of a two-dimensional circular cylinder that is required for producing an arbitrary distribution of normal velocity. Being suitable to be used with flows having arbitrary vorticity distribution, the present formulation can be considered as an alternative and extensive form of the circle theorems. Using the conformal transformation technique, the formulation also serves as a closed-form solution of Laplace’s equation in any two-dimensional flow domain that is reducible to the outer or inner region of a circular cylinder having arbitrary prescribed normal velocity over its boundary.

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