Free vibrations of conical shells via Ritz method

A formulation is presented for the investigation of the free vibrations of open and closed conical shells. Cylindrical ones are derived as a special case. The approach relies upon an efficient implementation of the Ritz method and allows any set of boundary conditions to be accounted for. In addition, the shells can be stiffened via stringers and/or rings, which are modeled by smearing the properties or by accounting for their discreteness. The resulting models are characterized by relatively few degrees of freedom and reduced computational effort. No meshing is required, so even the modeling phase is conducted quickly. A number of test cases is presented, revealing the accuracy of the proposed strategy and suggesting its use a mean for performing preliminary calculations and assisting the analysis and design process of composite shell structures.