Free damped vibration analysis of a truncated sandwich conical shell with a magnetorheological elastomer core

Abstract

In this paper, free vibration analysis of truncated sandwich conical shells with the magnetorheological (MR) core is investigated. The mathematical modeling of the shell is performed based on the first-order shear deformation theory (FSDT) and the set of the governing equations and associated boundary conditions are derived utilizing Hamilton’s principle. A semi-analytical solution is provided for various boundary conditions through an exact solution in the circumferential direction and a numerical solution in the meridional direction via the differential quadrature method (DQM). After validation of the presented model, the influences of various variables on the natural frequencies and loss factors of the shell are investigated including circumferential wave number, magnetic field density, and geometrical parameters of the shell such as semi-vertex angle, length, total thickness and thickness of the MR core.