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Steel and Composite Structures Volume 26, Number 4, February25 2018 , pages 421-437 DOI: https://doi.org/10.12989/scs.2018.26.4.421 |
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Free vibration analysis of a three-layered microbeam based on strain gradient theory and three-unknown shear and normal deformation theory |
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Mohammad Arefi and Ashraf M. Zenkour
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| Abstract | ||
| Free vibration analysis of a three-layered microbeam including an elastic micro-core and two piezo-magnetic face-sheets resting on Pasternak's foundation are studied in this paper. Strain gradient theory is used for size-dependent modeling of microbeam. In addition, three-unknown shear and normal deformations theory is employed for description of displacement field. Hamilton's principle is used for derivation of the governing equations of motion in electro-magneto-mechanical loads. Three micro-length-scale parameters based on strain gradient theory are employed for prediction of vibrational characteristics of structure in micro-scale. The results show that increase of three micro-length-scale parameters leads to significant increase of three natural frequencies especially for increase of second micro-length-scale parameter. This result is according to this fact that stiffness of a micro-scale structure is increased with increase of micro-length-scale parameters. | ||
| Key Words | ||
| free vibration analysis; strain gradient theory; micro-length-scale parameters; three unknown shear and normal deformation theory; natural frequencies | ||
| Address | ||
| (1) Mohammad Arefi: Faculty of Mechanical Engineering, Department of Solid Mechanics, University of Kashan, Kashan 87317-51167, Iran; (2) Ashraf M. Zenkour: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia; (3) Ashraf M. Zenkour: Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt. | ||