Natural vibration analysis of pressurised and rotating toroidal shell segment by Rayleigh-Ritz method

A semi-analytical procedure for natural vibration analysis of a simply supported toroidal shell segment is presented. The segment is closed in the circumferential direction and open in the meridional direction. The open edges are assumed to be simply supported. The segment therefore roughly resembles the geometry of a rotating tyre. The energy approach is used assuming shell displacements in the form of Fourier series in both circumferential and meridional directions. In the circumferential direction only one term of the Fourier series is necessary to describe exactly each vibration mode. In the meridional direction a relatively small number of Fourier series terms is necessary to achieve convergence. Tensional forces induced by the pressure and centrifugal loads are also determined by the energy approach. The application of the proposed procedure is illustrated by a numerical example. The increase in the internal pressure increases values of natural frequencies, whereas the shell rotation causes their bifurcation and the occurrence of travelling modes. In order to validate the method, the obtained results are compared with those determined by the finite strip method and by the finite element method