Dynamics And Stability Of Structures With Initial Stresses In Local Areas

Initial stresses often exist in many working structures in modern military and civil engineering. So studying the mechanical characteristics, especially that of dynamics is exactly worthy in practice. In this paper, the dynamics and stability of beams, plates and cylindrical shells with initial stresses in local areas are studied with the distributed transfer function method (DTFM). The main original work includes:1. Based on Euler-Bernoulli beam theory, the dynamics and stability of a multiple-step slender beam under stepped axial pressures are analyzed with DTFM. And then beased on Timoshenko beam theory, free vibration and stability of the short or anisotropic beam with multiple-step changes in geometry of section and in axial pressure are analyzed. Many types of classical and degenerated boundary conditions are taken into consideration in each theory analyzing.2. Based on Mindlin's first-order shear deformation theory, the equations of motion for analyzing dynamics and stability of moderate thick plate are estabilished with the strip transfer function method. The method of solving in patch then composing is adopted to get their semi-analytic solution. The dynamics and stability of moderate thick plate with belt-shape or patch-shape initial stresses area are analyzed.3. The DTFM for analyzing the dynamics and stability of composite cylindrical shells under axial and external pressure are obtained. The analytic solutions of natural frequencies and buckling loads and their mode shapes are obtained for the cylindrical shells under differenct boundaries.The experimental study is made for composite cylindrical shells and the results are compared with the analytic solutions.4. Using series expansion and state space technique, The DTFM for free vibration of a stepped cylindrical shell with stepped initial stresses sections is presented. Analytic solutions of vibration characteristic value problem are gained for the very shell under various types of boundary contions.