Analytical solution for vibration and buckling of cylindrical sandwich panels with improved FG metal foam core

Abstract

In this research paper, a novel higher-order porosity distribution is proposed, and free vibration and buckling behavior of cylindrical sandwich panels with functionally graded metal foam core are investigated. It is assumed that the sandwich panel is made of two thin face metal sheets and a moderately thick functionally graded metal foam core. The dynamic governing equations are obtained based on the third-order shear deformation theory and utilizing the Hamilton principle. It is assumed that the voids are distributed non-uniformly along the thickness of the functionally graded metal foam core. The elastic modulus of the core depends on the square of the relative density, thus is changing nonlinearly through the thickness of the core. The Navier technique is implemented to derive closed form solutions for the natural frequencies and the buckling load of the simply supported cylindrical sandwich panels. The accuracy and effectiveness of the proposed model are verified by comparison with previous researches. Results revealed that the presented higher-order porosity distribution can increase the buckling load and fundamental natural frequency by 10% and 5% in comparison to the conventional porosity distributions, respectively. In addition, it is shown that if the flexural vibration is of interest, ignoring the in-plane and rotary inertias, which can significantly reduce the computational complexity, does not have any considerable effect on the natural frequencies.