In this paper, an analytical solution for the free vibration of rotating composite conical shells with axial stiffeners (stringers) and circumferential stiffener (rings), is presented using an energy-based approach. Ritz method is applied while stiffeners are treated as discrete elements. The conical shells are stiffened with uniform interval and it is assumed that the stiffeners have the same material and geometric properties. The study includes the effects of the coriolis and centrifugal accelerations, and the initial hoop tension. The results obtained include the relationship between frequency parameter and circumferential wave number as well as rotating speed at various angles. Influences of geometric properties on the frequency parameter are also discussed. In order to validate the present analysis, it is compared with other published works for a non-stiffened conical shell; other comparison is made in the special case where the angle of the stiffened conical shell goes to zero, i.e., stiffened cylindrical shell. Good agreement is observed and a new range of results is presented for rotating stiffened conical shells which can be used as a benchmark to approximate solutions.

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This paper presents effects of boundary conditions and axial loading on frequency characteristics of rotating laminated conical shells with meridional and circumferential stiffeners, i.e., stringers and rings, using Generalized Differential Quadrature Method (GDQM). Hamilton's principle is applied when the stiffeners are treated as discrete elements. The conical shells are stiffened at uniform intervals and it is assumed that the stiffeners have similar material and geometric properties. Equations of motion as well as equations of the boundary condition are transformed into a set of algebraic equations by applying the GDQM. Obtained results discuss the effects of parameters such as rotating velocities, depth to width ratios of the stiffeners, number of stiffeners, cone angles, and boundary conditions on natural frequency of the shell. The results will then be compared with those of other published works particularly with a non-stiffened conical shell and a special case where angle of the stiffened conical shell approaches zero, i.e. a stiffened cylindrical shell. In addition, another comparison is made with present FE method for a non-rotating stiffened conical shell. These comparisons confirm reliability of the present work as a measure to approximate solutions to the problem of rotating stiffened conical shells.

Vibration suppression of a carbon nanotube–reinforced sandwich beam with magnetorheological fluid core is numerically investigated by employing the differential quadrature method. The beam has functionally graded carbon nanotube–reinforced composite base and constraining layers while its core layer is made of magnetorheological fluid. Four different types of distribution of carbon nanotubes along the thickness direction are considered. The extended rule of mixture is used to explain the effective material properties of the base and constraining layers of the beam. The equations of motion and corresponding boundary conditions are derived by applying Hamilton’s principle, and then these coupled differential equations are transformed into a set of algebraic equation applying the differential quadrature method. Natural frequencies and loss factors are extracted and compared with those available in literature. Convergence study has been performed to verify stability of the method. Effects of various parameters such as magnetic field intensity, mode number, and thickness of the magnetorheological fluid core layer on the natural frequencies and loss factors are studied.

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