Investigation of Vibration and Thermal Buckling of Nanobeams Embedded in An Elastic Medium Under Various Boundary Conditions
Author(s) -
Daoud S. Mashat,
Ashraf M. Zenkour,
Mohammed Sobhy
Publication year - 2015
Publication title -
journal of mechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.27
H-Index - 23
eISSN - 1811-8216
pISSN - 1727-7191
DOI - 10.1017/jmech.2015.83
Subject(s) - buckling , beam (structure) , vibration , boundary value problem , stiffness , thermal , materials science , mechanics , equations of motion , timoshenko beam theory , classical mechanics , physics , mathematical analysis , composite material , mathematics , thermodynamics , optics , acoustics
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.
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