Buy article PDF
The purchased file will be sent to you
via email after the payment is completed.
US$ 35
|
Steel and Composite Structures Volume 30, Number 6, March25 2019 , pages 603-615 DOI: https://doi.org/10.12989/scs.2019.30.6.603 |
|
|
|
Free vibration of imperfect sigmoid and power law functionally graded beams |
||
Mehmet Avcar
|
||
| Abstract | ||
| In the present work, free vibration of beams made of imperfect functionally graded materials (FGMs) including porosities is investigated. Because of faults during process of manufacture, micro voids or porosities may arise in the FGMs, and this situation causes imperfection in the structure. Therefore, material properties of the beams are assumed to vary continuously through the thickness direction according to the volume fraction of constituents described with the modified rule of mixture including porosity volume fraction which covers two types of porosity distribution over the cross section, i.e., even and uneven distributions. The governing equations of power law FGM (P-FGM) and sigmoid law FGM (S-FGM) beams are derived within the frame works of classical beam theory (CBT) and first order shear deformation beam theory (FSDBT). The resulting equations are solved using separation of variables technique and assuming FG beams are simply supported at both ends. To validate the results numerous comparisons are carried out with available results of open literature. The effects of types of volume fraction function, beam theory and porosity volume fraction, as well as the variations of volume fraction index, span to depth ratio and porosity volume fraction, on the first three non-dimensional frequencies are examined in detail. | ||
| Key Words | ||
| vibration; power-law FGM; sigmoid FGM; porosity volume fraction; classical beam theory; first order shear deformation beam theory | ||
| Address | ||
| Department of Civil Engineering, Faculty of Engineering, Suleyman Demirel University, Cunur, Isparta, Turkey. | ||