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In order to ensure the safety of the missile-canister system in silo during the earthquake, a modified transfer matrix method is provided to study the dynamic characteristics of the system. Firstly, a discrete viscoelastic connected double-beam model is developed taking account of the structural nonuniformity and the discrete distribution of the adapters. Secondly, the transfer matrix method of a single beam is modified to solve the problem of discrete connection between the two beams of the double-beam model. Then the natural circular frequencies and mode shapes are calculated by the proposed method, comparing with the finite element method (FEM). Finally, the influence of the stiffness of radial vibration isolators and adapters on the dynamic characteristics of the system is analysed. The comparison shows that the results of the proposed method are well consistent with the FEM calculations and the proposed method is validated. The variations of the first six natural circular frequencies with radial vibration isolator stiffness and adapter stiffness are obtained, which provides a basis for the seismic-relieving design.

The optimized design of composite adaptive structures puts forward higher requirements and challenges to the actual configuration of the structural section. In this paper, a trapezoidal laminate model of composite materials is established. Based on the classical laminates theory, the bending problem of trapezoidal laminates is solved by using the Kantorovich method and the principle of minimum potential energy. The analytic form of the solution is found to satisfy the Euler equation and displacement boundary conditions. Taking the wing of a jet transport aircraft as an example, the accuracy of the analytical solution is verified by the finite element method. The Differential Evolution algorithm is used to realize the multi-objective optimal design of the bending–twisting coupled trapezoidal laminates, and the hygrothermal stability of laminates is verified by the finite element method. Finally, based on the Monte Carlo method, the robustness analysis of the bending–twisting coupling effect of laminate is realized; meanwhile the feasibility and reliability of the design scheme are verified. The stress and strain functions at each point of the trapezoidal laminate can be further obtained by the analytical solution, making it more convenient to analyze the stresses and calculate the static forces of the trapezoidal laminate and its composite structures, which is of great significance to effectively improve the comprehensive mechanical properties of the cross-section structure of composite materials. [ABSTRACT FROM AUTHOR]