Free Vibration Response of FG Porous Joined Hemispherical–Cylindrical–Hemispherical Shell Vessels Reinforced by Graphene Platelet

Abstract

In this research, the natural frequency behavior of functionally graded (FG) porous joined hemispherical–cylindrical–hemispherical shell vessels reinforced by graphene platelet (GPLs) has been studied for the first time. Three various types of porosity distribution are assumed through the thickness direction of shell vessel. In the two types of porosity patterns, a pattern of porosities in metal matrix is symmetric and the other one is uniform. Besides, five GPL patterns are assumed for dispersing of GPLs in metal matrix. Extended role of mixture and Tsai-Halpin is used to determine the mass density and Young’s modulus of elasticity of the structure, respectively. By employing 3D elasticity theory, Hamilton’s Principal and FEM in conjunction with Rayleigh–Ritz method, the governing equations of motion of the joined shell vessel are obtained and natural frequencies are extracted. The impact of various factors such as coefficient of porosity, several porosity patterns along with different GPLs distributions and weight fraction of graphene nanofillers on natural frequency behavior of FG porous joined hemispherical–cylindrical–hemispherical shell vessels reinforced by GPLs nanofillers has been reported for the first time.