Free Vibration Analysis Of A Nose Cone Using A Pseudospectral Method

A free vibration analysis method for a nose cone based on the first-order shear deformation theory is developed. In the nose cone, a conical shell is attached to one end by a spherical shell and to the other by a cylindrical shell. Chebyshev polynomials of the first kind are employed as the admissible functions, and the equations of motion are collocated at the Gauss collocation points to yield the system of algebraic equations. The spherical, conical and cylindrical shell segments are modeled separately. The number of expansions of each shell segment is larger than that of the intended degrees-of-freedom so that the surplus expansions can accommodate the compatibility and the boundary conditions. Numerical examples are provided to demonstrate the robustness of the proposed method.