A Spectro-geometric solution of dynamic characteristics of submarine-like structures

In this paper, the Spectro-geometric method is used to study the vibration behaviors of the submarine-like structure. The substructures of the geometric model include: cylindrical shell, conical shell, spherical shell, annular plate and rectangular plate. The energy formula of the sub-structure is deduced by the principle of first-order shear deformation. In order to satisfy the continuity conditions between the sub-structures and the related boundary conditions, the artificial spring technology is introduced in this paper. The Lagrange energy functional for the entire model is established. For efficient modeling, the displacement functions used here is the two-dimensional spectral geometric functions. Substitute the displacement function into the energy functional and solve it by the Ritz method to obtain the displacement coefficient and natural frequency of the structure. Through the convergence analysis and the comparative studies for the substructures and the whole structure under different boundary conditions, it is verified that the method in this paper is feasible. The effects of coupling parameters, material parameters, and molecular structure dimensions on the free and forced vibrations of the submarine-like structure are also investigated.