The calculations of natural frequencies and forced vibration responses of conical shell using the Rayleigh–Ritz method

An effective method for analyzing the forced vibration of conical shell is presented. Hamilton’s principle with the Rayleigh–Ritz method is employed to derive the equation of motion of the conical shell. A set of simpler principal vibration modes of the conical shell with two simply supported boundaries are presented. The natural frequencies of conical shell can be obtained by solving eigenvalue problem of the equation of motion and the steady responses of forced vibration can also be obtained by solving the equation of motion. Numerical comparisons with the results in the open literature are made to validate the present methodology. Moreover, the forced vibration responses of a conical shell are also calculated.