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Investigation of Vibration and Thermal Buckling of Nanobeams Embedded in An Elastic Medium Under Various Boundary Conditions

Published online by Cambridge University Press:  18 November 2015

D. S. Mashat ,
A. M. Zenkour  and
M. Sobhy
D. S. Mashat
Affiliation:
Department of MathematicsFaculty of ScienceKing Abdulaziz UniversityJeddah, Saudi Arabia
A. M. Zenkour
Affiliation:
Department of MathematicsFaculty of ScienceKing Abdulaziz UniversityJeddah, Saudi Arabia Department of MathematicsFaculty of ScienceKafrelsheikh UniversityKafrelsheikh, Egypt
M. Sobhy*
Affiliation:
Department of MathematicsFaculty of ScienceKafrelsheikh UniversityKafrelsheikh, Egypt Department of Mathematics and StatisticsFaculty of ScienceKing Faisal UniversityHofuf, Saudi Arabia
*
*Corresponding author (msobhy2011@gmail.com, msobhy@kfu.edu.sa)
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Abstract

Analyses of free vibration and thermal buckling of nanobeams using nonlocal shear deformation beam theories under various boundary conditions are precisely illustrated. The present beam is restricted by vertically distributed identical springs at the top and bottom surfaces of the beam. The equations of motion are derived using the dynamic version of Hamilton's principle. The governing equations are solved analytically when the edges of the beam are simply supported, clamped or free. Thermal buckling solution is formulated for two types of temperature change through the thickness of the beam: Uniform and linear temperature rise. To validate the accuracy of the results of the present analysis, the results are compared, as possible, with solutions found in the literature. Furthermore, the influences of nonlocal coefficient, stiffness of Winkler springs and span-to-thickness ratio on the frequencies and thermal buckling of the embedded nanobeams are examined.

Keywords

Free vibrationThermal bucklingNanobeamNonlocal elasticity theory

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Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 3 , June 2016 , pp. 277 - 287
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2016 

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