scholarly journals Eigenfrequency correction of Bloch–Floquet waves in a thin periodic bi-material strip with cracks lying on perfect and imperfect interfaces

Wave Motion ◽  
2012 ◽  
Vol 49 (2) ◽  
pp. 258-270 ◽  
Author(s):  
A. Vellender ◽  
G.S. Mishuris
Keyword(s):  
Imperfect Interfaces ◽  
Floquet Waves

The Influence of Torsional-Rigidity Bounds for Composite Shafts with Specific Cross-Sections

2011 ◽  
Vol 462-463 ◽  
pp. 674-679
Author(s):  
I Tung Chan ◽  
Tung Yang Chen ◽  
Min Sen Chiu
Keyword(s):  
Shear Modulus ◽  
Cross Sections ◽  
Variational Principles ◽  
Torsional Rigidity ◽  
Lower And Upper Bounds ◽  
Imperfect Interfaces ◽  
Section Shape ◽  
The Matrix ◽  
Rigorous Bounds ◽  
Low Shear

We consider the Saint-Venant torsion problem of composite shafts. Two different kinds of imperfect interfaces are considered. One models a thin interphase of low shear modulus and the other models a thin interphase of high shear modulus. The imperfect interfaces are characterized by parameters given in terms of the thickness and shear modulus of the interphases. Using variational principles, we derive rigorous bounds for the torsional rigidity of composite shafts with cross-sections of arbitrary shapes. The analysis is based on the construction of admissible fields in the inclusions and in the matrix. We obtain the general expression for the bounds and demonstrate the results with some particular examples. Specifically, circular, elliptical and trianglar shafts are considered to exemplify the derived bounds. We incorporate the cross-section shape factor into the bounds and show how the position and size of the inclusion influence the bounds. Under specific conditions, the lower and upper bounds will coincide and agree with the exact torsional rigidity.

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