This paper proposes theoretical and numerical approaches to scrutinize the free vibration of orthogonal stiffened cylindrical shells. According to K´arman-Donnell shell theory, the total energy of the stiffened cylindrical shells is derived. Based on the principle of minimum potential energy, the eigenfunction related to the frequency is established and solved by developing a Matlab program. Analytical solutions of the natural frequency for free vibraion of the stiffened cylindrical shells are calculated and are verified against the finite element results from ABAQUS software. On account of the observations from the parametric study, an optimization scheme of the stiffeners is proposed.
Weak formulations of mixed state equations of closed laminated cylindrical shells are presented in the Hamilton System. The Hamilton canonical equation of closed cylindrical shell is established. By means of applying the transfer matrix method and taking the advantage of Hamiltonian matrix in the calculation, a unified approach and three-dimensional thermoelastic solutions are obtained for the buckling analysis of closed trick laminated cylindrical shells. All equations of elasticity can be satisfied and all elastic constants can be taken into account. Numerical results are given to compare with those of FEM calculated using SAP5.The principle and method suggested here have clear physical concepts. The equations and boundary conditions proposed in this paper are weakened. The solutions and results given here may serve as a benchmark for other numerical procedures.
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