A unified Jacobi-Ritz formulation for vibration analysis of the stepped coupled structures of doubly-curved shell. (15th July 2019) - Qin, Bin; Choe, Kwangnam; Wang, Tiantian; Wang, Qingshan
Abstract: The free vibration of different kinds of stepped coupled doubly-curved shell structures with elastically constrained edges are investigated by adopting the Jacobi-Ritz method for the first time. Coupled structures are comprised of substructures, where paraboloidal, hyperbolical, elliptical, and cylindrical stepped shells are typical ones. The Flügge's thin shell theory is utilized to construct the analytical model, together with the multi-segment partitioning strategy. For each shell segment, despite of various boundary conditions, the displacement components along the meridional directions are expressed by Jacobi polynomials and those along the circumferential directions are represented by Fourier series. Then the unknown coefficients of the displacements are obtained by introducing the Rayleigh-Ritz method. The solutions proposed here for coupled structures have two main advantages: first, there is no need to vary the displacement or the motion equations; and secondly, the efficiency of modeling can be notably enhanced. By comparison with (Finite Element method) FEM and others' results, the reliability of current method can be validated. At last, the free vibrations of different kinds of coupled structures containing stepped shell are analyzed by presenting several numerical examples, the results of which may be served as reference data.