Steel and Composite Structures

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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

  • Arefi, Mohammad (Faculty of Mechanical Engineering, Department of Solid Mechanics, University of Kashan) ;
  • Zenkour, Ashraf M. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
  • Received : 2017.08.19
  • Accepted : 2017.11.24
  • Published : 2018.02.25
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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.

Keywords

Acknowledgement

Supported by : University of Kashan

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