Free vibration analysis of truncated conical fiber metal laminate (FML) shells

Abstract

In this paper, an analytical solution is developed for free vibration analysis of conical fiber metal shells. In order to find constitutive relations, the assumptions of thins hells are used and the governing equations are based on Love's theory. The Galerkin method is employed to solve the governing equations in which beam functions are used to approximate the mode shapes. Using beam functions enables us to assess the effects of different boundary conditions on the frequency response of the shells. Numerical comparisons of the present and previously published results confirm the accuracy of the current approach. Additionally, the influences of geometrical parameters and embedding aluminum plies in different layers of the structure on natural frequency of the conical shells with various boundary conditions are investigated. It can be observed that the more the aluminum plies are used, the greater natural frequency of the structure will be reached. Except the clamped-free boundary conditions, the results also indicate that if the aluminum plies are embedded in the top and bottom layers of the laminate, natural frequency reaches its maximum value.

A review of the dynamic analysis and free vibration analysis on fiber metal laminates (FMLs)

“…It was stated that the natural frequency increased by raising the height-to-width ratio. For instance, Ghasemi et al [38] investigated 7 plies θ = 0 • , 90 • Hinged-hinged FML beam [35] geometrical parameters and embedded aluminum plies with different layers on the natural frequency of the truncated conical FML shell with various boundary conditions. It was found that increasing the number of embedding aluminum increased the frequency parameter.…”

Free vibration analysis of fiber-metal laminated composite plates using differential, generalized and harmonic quadrature methods: experimental and numerical studies

“…The vibration equation for the cylindrical or shell-shaped element can be obtained using Kirchoff's theory or shear deformation theories. These equations can be solved numerically by the Galerkin method, and dynamic analysis can be performed (Ghasemi et al, 2013a;Khalili et al, 2010;Malekzadeh et al, 2010). It has been determined that the natural frequencies have the maximum values when the aluminum layer is located at the bottom and top of the structure in the clamped-free boundary condition.…”

“…The vibration equation for the cylindrical or shell-shaped element can be obtained using Kirchoff's theory or shear deformation theories. These equations can be solved numerically by the Galerkin method, and dynamic analysis can be performed (Ghasemi et al. , 2013a; Khalili et al.…”