Saeed Amir - Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Ehsan Arshid - Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
Davood Mazaheri - Faculty of Engineering, Mahallat Institute of Higher Education, Mahallat, Iran

The present study analyzed free vibration of three layered annular plate which its core and face sheets are made of functionally graded porous materials and functionally graded carbon nanotubes reinforced composites, respectively. The structure is located onviscoelastic substrate and also is subjected to electric field and electro-mechanical pre loads. Mechanical properties of porous core and also FG-CNTRC face sheets are varied through the thickness direction. Using dynamic Hamilton’s principle, the motion equationsbased on the first order shear deformation theory are derived and solved via GDQ as an efficient numerical method. Effect of different parameters such as porosity coefficient, CNTs distribution and amount, viscoelastic substrate, electro-mechanical pre loads and aspect ratio of the plate are investigated. It is seen by increasing the porosity coefficient, the natural frequency of the plate decreases. Also by comparing two different types of CNTs distribution through the thickness of the face sheets, it is found that FG-VA leads to more values of the frequencies rather than FG-AV. The findings of this study can be useful for designing smart structures such as sensor and actuator.

Free vibration, Porous material, Carbon nanotubes reinforced composites, Annular plate, Viscoelastic substrate