Abstract
This article aims to investigate free vibration and buckling of functionally graded (FG) nanoporous metal foam (NPMF) nanoshells. The first-order shear deformation (FSD) shell theory is adopted and the theoretical model is formulated by using Mindlin’s most general strain gradient theory, which can derive several well-known simplified models. The symmetric and unsymmetric nanoporosity distributions are considered for the structural composition. Hamilton’s principle is employed to deduce the governing equations as well as the boundary conditions. Then, via the Navier solution technique, an analytical solution for the free vibration and buckling of FG NPMF nanoshells is presented. Afterwards, a detailed parametric analysis is conducted to highlight the effects of the nanoporosity coefficient, nanoporosity distribution, length scale parameter, and geometrical parameters on the mechanical behaviors of FG NPMF nanoshells.
Highlights
Graded materials (FGMs) have a continuous and smooth graded distribution of material properties in the spatial field
One of the size-dependent continuum theories is Mindlin’s strain gradient theory (SGT) [40], which is known as the general form of the SGT containing five additional material length scale parameters compared to the classical continuum theory
Size-dependent free vibration and axial buckling of an functionally graded (FG) nanoporous metal foam (NPMF) nanoshell supported at both ends are studied
Summary
Graded materials (FGMs) have a continuous and smooth graded distribution of material properties in the spatial field. Due to the lack of intrinsic material length scale parameters, the classical continuum theory has no ability to predict the mechanical characteristics of micro/nanostructures. One of the most popular forms is the modified strain gradient theory (MSGT) [37] This theory is a more useful form of Mindlin’s SGT including three material length scale parameters related to symmetric rotation gradients, deviatoric stretch gradients, and dilatation gradients. We aim to make an attempt to investigate the vibration and buckling of circular cylindrical nanoshells made from FG NPMFs. In order to accommodate the size dependency of the nanostructure, the general SGT is used to develop the size-dependent first-order shear deformable nanoporous nanoshell model. The influence of some key parameters on the vibration and buckling properties of the system is shown
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