Abstract
In this paper, a novel size-dependent functionally graded (FG) cylindrical shell model is developed based on the nonlocal strain gradient theory in conjunction with the Gurtin-Murdoch surface elasticity theory. The new model containing a nonlocal parameter, a material length scale parameter, and several surface elastic constants can capture three typical types of size effects simultaneously, which are the nonlocal stress effect, the strain gradient effect, and the surface energy effects. With the help of Hamilton’s principle and first-order shear deformation theory, the non-classical governing equations and related boundary conditions are derived. By using the proposed model, the free vibration problem of FG cylindrical nanoshells with material properties varying continuously through the thickness according to a power-law distribution is analytically solved, and the closed-form solutions for natural frequencies under various boundary conditions are obtained. After verifying the reliability of the proposed model and analytical method by comparing the degenerated results with those available in the literature, the influences of nonlocal parameter, material length scale parameter, power-law index, radius-to-thickness ratio, length-to-radius ratio, and surface effects on the vibration characteristic of functionally graded cylindrical nanoshells are examined in detail.
Highlights
Graded (FG) materials are an advanced class of composite structures with material properties changing continuously in one or more directions
Since the experimental study in nanoscale may be technically difficult and financially expensive, and molecular dynamics simulation is timeconsuming for analyzing large size system, the continuum mechanics approach, as an alternative way to model the mechanical response of nano-/micro-structures, has been widely used
The thickness of the Functionally graded (FG) cylindrical nanoshell is considered as h = 1 nm, axial wave number is fixed at m = 1, and the shear correction factor is taken as κ = 5/6
Summary
Graded (FG) materials are an advanced class of composite structures with material properties changing continuously in one or more directions. Since the experimental study in nanoscale may be technically difficult and financially expensive, and molecular dynamics simulation is timeconsuming for analyzing large size system, the continuum mechanics approach, as an alternative way to model the mechanical response of nano-/micro-structures, has been widely used. It is well-known that classical continuum mechanics is size-independent and cannot capture the size effects in small scale. Several non-classical continuum theories have been developed to assess the remarkable size effects on the mechanical characteristics of nano/micro-structures, such as nonlocal elasticity theory[1,2], strain gradient elasticity theory[3,4,5,6], and surface elasticity theory[7,8]
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