Vibration and buckling of first-order shear deformable circular cylindrical micro-/nano-shells based on Mindlin's strain gradient elasticity theory

Abstract

Abstract In this research, a size-dependent first-order shear deformable model is developed based on the Mindlin's strain gradient elasticity theory to analyze the free vibration and axial buckling of circular cylindrical micro-/nano-shells. The size-dependent governing equations and corresponding boundary conditions are established through Hamilton's principle. For some specific values of the gradient-based material parameters, the most general form of shell formulation can be reduced to those based on simple forms of the strain gradient elasticity theory such as the modified strain gradient theory (MSGT), modified couple stress theory (MCST) and strain gradient theory (SGT). To illustrate the characteristics of a micro-/nano-shell obtained by the size-dependent shell formulation, the axial buckling and free vibration problems of a simply-supported (SS) microshell are analyzed by employing a Navier-type solution. Selected numerical results are presented to get an insight into the effects of dimensionless material length scale parameters, length-to-radius ratio and circumferential mode number on the non-dimensionless natural frequencies and buckling loads. For comparison purpose, the non-dimensional natural frequencies and buckling loads predicted by MSGT, MCST, SGT and classical theory (CT) are also presented. It is shown that the effect of small scale is more prominent for lower values of dimensionless length scale parameter.