Narrow Results

It is challenging to establish analytical solutions for conventional inverse and semi-inverse approaches because of the intricacy of standard mathematical calculations. In this study, the symplectic superposition approach is used to provide the analytical solution for the free vibration of a thin plate with a polyline shape. The polyline plate is separated into four sub-plates based on the superposition principle, and then the problem is solved by using the symplectic eigen-expansion method. Multiple sets of constants dependent on boundary conditions can be found by applying a specific mechanical quantity to the edge of each sub-plate. The four sub-plate solutions can be combined to provide the final analytical solution. By contrasting the numerical results obtained under various boundary restrictions, the correctness and effectiveness of the method are confirmed. The frequency values decrease with increasing a₂/a₁ due to the decrease of structure’s stiffness. The method proposed in this work can be extended to solve the vibration of anisotropic thin plate with other boundary conditions and irregular plates.

A method is proposed for finding the normal mode eigenvalues in shallow water waveguide. We transform the problem determining eigenvalues in complex wave number plane into solving a "true" one dimensional Hamilton system. Simulations are performed, the result agrees very well with that calculated by the normal mode program KrakanC.

Based on Hamilton's principle, a new accurate solution methodology is developed to study the torsional bifurcation buckling of functionally graded cylindrical shells in a thermal environment. The effective properties of functionally graded materials (FGMs) are assumed to be functions of the ambient temperature as well as the thickness coordinate of the shell. By applying Donnell's shell theory, the lower-order Hamiltonian canonical equations are established, from which the eigenvalues and eigenvectors are solved as the critical loads and buckling modes of the shell of concern, respectively. The effects of various aspects, including the combined in-plane and transverse boundary conditions, dimensionless geometric parameters, FGM parameters and changing thermal surroundings, are discussed in detail. The results reveal that the in-plane axial edge supports do have a certain influence on the buckling loads. On the other hand, the transverse boundary conditions only affect extremely short shells. With increasing thermal loads, the material volume fraction has a different influence on the critical stresses. It is concluded that the optimized FGM mixtures to withstand thermal torsional buckling are Si₃N₄/SUS304 and Al₂O₃/SUS304 among the materials studied in this paper.