Investigation of Free Vibration of Laminated Composite Conical Shell With Local Attached Mass

In this paper, for the first time, the free vibrations of the conical shell with the locally attached mass are investigated. the equilibrium equations of the conical shell are written based on classical shell theory using the energy method and hamilton’s principle. boundary conditions are considered to be fully simply supported. according to the boundary conditions, the displacement components are written as double fourier series expansions. relationships of the strain-displacement and curvature-displacement are considered based on first love’s approximation theory. the governing equations of the conical shell are solved using the galerkin method and the natural frequencies are obtained. also, for the first time, the effect of the attached mass using the cone differential operator and heaviside function on equilibrium equations has been considered and its effect on the free vibration of the conical shell has been investigated. the results have been verified with the literature and abaqus finite element software. finally, the effect of different parameters of attached mass including width, height, subtended angle, position, density, and elastic modulus on the free vibrations of the composite conical shell are investigated.