Structural similitude in free vibration of orthogonally stiffened cylindrical shells

In this paper, the necessary similarity conditions, or scaling laws, for free vibrations of orthogonally stiffened cylindrical shells are developed using the similitude theory. The Donnell-type nonlinear strain–displacement relations along with the smearing theory are used to model the structure. Then the principle of virtual work is used to analyze the free vibration of the stiffened shell. After non-dimensionalizing the derived formulations, the scaling laws are developed, using the similitude theory. Then, different examples are solved to validate the scaling laws numerically and experimentally. The obtained results show the effectiveness of the derived formulations.