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Abstract
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In this paper, the FG thin truncated conical shell formulation is developed using the
modified couple stress theory. The material distributions in FG conical shell are
assumed to vary continuously along shell thickness according to volume fraction of
constituents based on power law distribution. The governing equations and boundary
conditions are derived using Hamilton’s principle, and, in the special case, the free
vibration of the simply supported FG conical nanoshell is investigated using Galerkin
method. Finally, the effects of parameters such as dimensionless length scale
parameter, apex angle, gradient index and length on the natural frequency are
examined. According to the studies conducted, the modified couple stress theory
predicts the stiffness of conical nanoshell with higher accuracy than the
classical continuum theory. Besides, the increasing effect of the length scale
parameter on increase in natural frequency caused by decrease in length
and increase in circumferential and axial wave numbers is investigated as
well.
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Keywords
free vibration, modified couple stress theory, thin shell
model, functionally graded material, truncated conical
shell, length scale parameter
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Milestones
Received: 6 January 2015
Revised: 2 October 2015
Accepted: 16 December 2015
Published: 23 February 2016
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